Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) WW Part 15 pps

Advantages and Disadvantages of Various Sensor and Actuator TechnologiesType of Sensor or Actuator Advantages Disadvantages rUsed as sensors and actuators rRelatively low strain and low

Table 1 Advantages and Disadvantages of Various Sensor and Actuator Technologies

Type of Sensor or Actuator Advantages Disadvantages

rUsed as sensors and actuators rRelatively low strain and low displacement

rVery large frequency range capability (typically, less than 0.1% strain,

rQuick response time and 1–100 microns displacement for

rVery high resolution and dynamic range stack actuators)

rPossibility of integration in the structure rActuators require relatively costlyfor thin PZT actuators and PVDF voltage amplifiers

sensors rLow recoverable strain (0.1%)

rPossibility of shaping PVDF sensors rPiezoelectric ceramics are brittle(spatial filtering) rCannot measure direct current

rSusceptible to high hysteresisand creep when strained in direction

of poling (e.g., stack actuators)

Electrostrictive materials

Example:

Lead-magnesium

niobate (PMN)

rUsed as sensor and actuators rMore sensitive to temperature

rLower hysteresis and creep variations than piezoelectricscompared to piezoelectric

rPotentially larger recoverable strainthan piezoelectric

Magnetostrictive materials

Example:

Terfenol-D

rHigher force and strain capability than rLow recoverable strain (0.15%)piezoceramics (typically, 1000 rOnly for compression componentsmicrostrain deformation) rNonlinear behavior

rSuited for high-precision applications

rSuited for compressive load carryingcomponents

rVery durable

Shape-memory alloys (SMA)

Example:

NITINOL

rLarge recoverable strain (8%) rSuited for low-frequency (0–10 Hz)used largely for actuation due to large and low-precision application force generation rSlow response time

rLow voltage requirements rComplex constitutive behavior

with large hysteresis

Optical fibers

Examples:

Bragg grating,

Fabry-Perot

rSuited for remote sensing of structures rUsed for sensing alone

rCorrosion resistant rBehavior is complicated by thermal strains

rImmune to electric interference

rSmall, light, and compatible withadvanced composite

Electrorheological fluids (ER)

Example:

Alumino-silicate

in paraffin oil

rSimple and quiet devices rLow-frequency applications

rSuitable for vibration control rNonlinear behavior

rOffers significant capability and rCannot tolerate impuritiesflexibility for altering structural response rFluid and solid phases tend to separate

rLow density rNot suitable for low temperature applications

rHigh-voltage requirements (2–10 kV)

rHigherη p /τ2

y ratio than MR*

Magnetorheological rSimple and quiet devices rNonlinear behavior

fluids (MR) rQuick response time rHigher density than ER

rSuitable for vibration control

rOffers significant capability andflexibility for altering structural response

rLow voltage requirements

rBehavior not affected by impurities

rSuitable for wide range of temperatures

rLowerη p/τ2

yratio than ER*

rLarge dynamic range rNeed to achieve directionality in

rExcellent linearity some active control systems (e.g., ducts)

rNeed protection to dust,moisture, high temperature

(cont.)

rGood low-frequency sensitivity (0–10 Hz) rLow-frequency range (typically, below 100 Hz)

rNoncontacting measurement (proximity probe) rLow dynamic range (typically, 100 : 1)

rWell suited to measurement of relative rLow resolutiondisplacement in active mounts

Velocity sensors rNoncontacting measurement rLow dynamic range (typically 100 : 1)(magnetic) rWell suited to measurement of relative rLow resolution

velocity in active mounts rHeavy

Accelerometers rLarge dynamic range rLow sensitivity in low frequency (0–10 Hz)

rExcellent linearity rRequire relatively expensive charge

amplifiers (piezoelectric accelerometers)

Loudspeakers rLow cost rNonlinear behavior if driven close to maximum power

rSpace requirement (backing enclosure)

rNeed protection to dust, moisture, hightemperature, corrosive environment

Electrodynamic and rRelatively large force/large rMay need a large reaction mass to

electromagnetic displacement capability transmit large forces

actuators rExcellent linearity rSpace requirement

rExtended frequency range

Hydraulic and rLarge force/large rLow-frequency range (0–10 Hz for

pneumatic actuators displacement capability pneumatic; 0–150 Hz for hydraulic)

rNeed for hydraulic or compressed air power supply

rNonlinear behavior

rSpace requirement

in an annular armature When the coil is activated, the

TERFENOL rod expands and produces a displacement

The TERFENOL-D bar, coil, and armature are

assem-bled between two steel washers and put inside a

protec-tive wrapping to form the basic magnetoacprotec-tive induced

strain actuator unit (7) The main advantage of terfenol is

its high-force capability at relatively low cost (21) It also

has the advantage of small size and light weight, which

makes it suitable for situations where no reactive mass is

required such as in stiffened structures of aircraft and

sub-marine hulls The disadvantages of TERFENOL include

its brittleness and low tensile strength (100 MPa)

com-pared to compressive strength (780 MPa) Its low

displace-ment capability is also a major disadvantage especially in

the low-frequency range (less than 100 Hz) In addition, it

also exhibits large hysteresis resulting in a highly

nonlin-ear behavior that is difficult to model in practical

applica-tions (20,21) Tani et al (20) have reviewed of studies on

modeling the nonlinear behavior of TERFENOL-D as well

as its application in smart structures Ackermann et al

(22) developed a transduction model for magnetostrictive

actuators through an impedance analysis of the

electro-magneto-mechanical coupling of the actuator device This

model provided a tool for in-depth investigation of the

frequency-dependent behavior of the magnetostrictive

ac-tuator, such as energy conversion, output stroke, and force

The feasibility of using embedded magnetostrictive mini

actuators (MMA) for vibration suppression has been

in-vestigated by (20)

Shape-Memory Alloys (SMAs)

Shape-memory alloys (SMAs) are materials that undergoshape changes due to phase transformations associatedwith the application of a thermal field When a SMAmaterial is plastically deformed in its martensitic (low-temperature) condition, and the stress is removed, it re-gains (memory) its original shape by phase transforma-tion to its austenite (high-temperature) condition, whenheated SMAs are considered as functional materials be-cause of their ability to sense temperature and stressloading to produce large recovery deformations with forcegeneration TiNi (nitinol), which is an alloy comprisingapproximately 50% nickel and 50% titanium, is the mostcommonly used SMA material Other SMA material in-cluding FeMnSi, CuZnAl, and CuAlNi alloys have also beeninvestigated (20,23)

Typically, plastic strains of 6% to 8% can be completelyrecovered by heating nitinol beyond its transition temper-ature (of 45–55◦C) According to Liang and Rogers (24) re-straining the material from regaining its memory shapecan yield stresses of up to 500 MPa for 8% plastic strainand a temperature of 180◦C By transformation from themartensite to austenite phase, the elastic modulus of niti-nol increases threefold from 25 to 75 GPa, and its yieldstress increases eightfold from 80 to 600 MPa (25).SMAs can be used for sensing or actuation, althoughthey are largely used for actuation due to their largeforce generation capabilities They have very low voltage

requirements for operation and are very suited for

low-frequency applications However, their use is limited by

their slow response time, which makes them suitable for

low-precision applications only Also, they exhibit complex

constitutive behavior with large hysterises, which makes it

difficult to understand their behavior in active structural

systems To provide a better understanding of the behavior

of SMAs, several researchers have focused on the

develop-ment of constitutive models for SMAs Some of the most

prominent and commonly used ones are those by Tanaka

(26), Liang and Rogers (24), and Boyd and Lagoudas (27)

These models are derived from phenomenological

consid-erations of the thermomechanical behavior of the SMAs

Because of the numerous advantages they offer, several

investigations on the application of SMAs have been

car-ried out within the present decade Reviews of these

ap-plications, focusing on fabrication of SMA hybrid

com-posites, analytical and computational modeling, active

shape control, and vibration control, are presented in

(20,23)

Optical Fibers

For many applications, ideal sensors would have such

at-tributes as low weight, small size, low power,

environmen-tal ruggedness, immunity to electromagnetic interference,

good performance specifications, and low cost The

emer-gence of fiber-optic technology, which was largely driven by

the telecommunication industry in the 1970s and 1980s, in

combination with low-cost optoelectronic components, has

enabled fiber-optic sensor technology to realize its potential

for many applications (28–30) A wide variety of fiber-optic

sensors are now being developed to measure strain,

tem-perature, electric/magnetic fields, pressure, and other

mea-surable quantities Many physical principles are involved

in these measurements, ranging from the Pockel, Kerr, and

Raman effects to the photoelastic effect (31) These sensors

use intensity, phase, frequency, or polarization modulation

(32) In addition, multiplexing is largely used for

many-sensor systems Fiber-optic many-sensors can also be divided in

discrete sensors and distributed sensors to perform

spa-tial integration or differentiation (33) Three types of

fiber-optic strain sensors are reviewed in the following: extrinsic

interferometric sensors, Bragg gratings, and sensors based

on the photoelastic effect

The most widely used phase modulating fiber-optic

sen-sors are the extrinsic interferometric sensen-sors Two fibers

and directional couplers are generally used for these

sen-sors One of the fibers acts as a reference arm, not affected

by the strain, while the other fiber acts as the sensing arm

measuring the strain field By combining the signals from

both arms, an interference pattern is obtained from the

optical path length difference This interference pattern

is used to evaluate the strain affecting the sensing arm

(e.g., by fringe counting) These sensors have a high

sen-sitivity and can simultaneously measure strain and

tem-perature One interferometer now being used in industrial

applications is the Fabry-Perot interferometer, where a

sensing cavity is used to measure the strain (34) This

sen-sor uses a white-light source and a single multiple mode

Multimodefiber

Cavitylength

Weldedspot

250 µm

DielectricmirrorsMicrocapillary

Gauge length(∼3, 5 mm)

Figure 3 Fabry-Perot sensors used for ice impact monitoring and

encapsulated version.

fiber, and provides absolute measurements This extrinsicinterferometer sensor is shown in Fig 3

Bragg grating reflectors can be written on an optical

fiber using a holographic system or a phase mask to ate a periodic intensity profile (35) These sensors can beused as point or quasi-distributed sensors The reflectedsignal from these sensors consist of frequency componentsdirectly related to the number of lines per millimeter ofeach grating reflector and, thus, to the strain experienced

gener-by the sensor Fiber-optic sensors based on Bragg gratingsare used to measure strain and temperature, either si-multaneously or individually (36) The Bragg gratings aretraditionally interrogated using a tunable Fabry-Perot or

a Mach-Zender interferometer Recently, long-period ings have been used to interrogate Bragg sensing gratings(37) Bragg gratings have been used to measure vibrationseither directly or through the development of novel ac-celerometers A typical fiber Bragg grating (FBG) system

grat-is illustrated in Fig 4

The principle of operation of the sensors based on the

photoelastic effect is a phase variation of the light passing

through a material (fiber) that is undergoing a strainvariation This phase variation can be produced by twoeffects on the fiber: (1) the variation of the length produced

by the strain; (2) the photo-elastic effect and the modaldispersion caused by the variation of the diameter of thefiber These sensors are classified in modal interferometricsensors and polarimetric sensors As it integrates thestrain effect over its length, the modal interferometricsensor can act as a spatial filter if the propagation constant

is given a spatial weighting (38)

Reflectedwave

Bragggrating

Transmittedwave

Incidentwave

Figure 4 Bragg grating on an optical fiber.

Electrorheological Fluids (ER)

Electrorheological fluids (ER) are a class of controllable

fluids that respond to an applied electric field with a

dra-matic change in rheological behavior The essential

cha-racteristic of ER fluids is their ability to reversibly change

from free-flowing linear viscous liquids to semisolids

hav-ing controllable yield strength in milliseconds when

ex-posed to an electric field (23) The ER fluids provide very

simple, quiet and rapid response interfaces between

elec-tronic controls and mechanical systems They are very

suit-able for vibration control because of the ease with which

their damping and stiffness properties can be varied with

the application of an electric field

ER materials consist of a base fluid (usually a low

vis-cosity liquid) mixed with nonconductive particles, typically

in the range of 1 to 10 m diameter These particles become

polarized on the application of an electric field, leading to

solidification of the material mixture Typical yield stresses

in shear for ER materials are about 5 to10 kPa The most

common type of ER material is the class of dielectric oils

doped with semiconductor particle suspensions, such as

aluminosilicate in paraffin oil The material exhibits

non-linear behavior, which is still not completely understood by

the research community This lack of understanding has

hindered efforts in developing optimal applications of ER

materials However, electrorheological fluids may be

suit-able for many devices, such as shock absobers and engine

mounts (23,25)

Magnetorheological Fluids (MR)

Magnetorheological fluids (MR) are similar to ER

materi-als in that they are materi-also controllable fluids These materimateri-als

respond to an applied magnetic field with a change in the

rheological behavior MR fluids, which are less known than

ER materials, are typically noncolloidal suspensions of

micron-sized paramagnetic particles The key differences

between MR and ER fluids are highlighted in Table 1 In

general, MR fluids have maximum yield stresses that are

20 to 50 times higher than those of ER fluids, and they

may be operated directly from low-voltage power supplies

compared to ER fluids which require high-voltage (2–5 kV)

power supplies Furthermore, MR fluids are less sensitive

to contaminants and temperature variations than are ER

fluids MR fluids also have lower ratios ofη p /τ2

y than ERmaterials, whereη pis the plastic viscosity andτ ythe max-

imum yield stress This ratio is an important parameter in

the design of controllable fluid device design, in which

min-imization of the ratio is always a desired objective These

factors make MR fluids the controllable choice for recent

practical applications Several MR fluid devices developed

by Lord Corporation in North Carolina under the

Rheo-netic trade name (23)

Microphones

Microphones are usually the preferred acoustic sensors in

active noise control applications Relatively inexpensive

microphones (electret or piezoelectric microphones) can be

used in most active noise control systems because the

fre-quency response flatness of the microphones is not critical

Microphonesupport section

Detection pipesection

Figure 5 Sound pressure and particle velocity sensing.

in digital active control systems, as it is compensated in theidentification of the control path The most common types

of microphones are omni-directional, directional, and probemicrophones

Whenever turbulent flow is present in the acousticmedium (e.g., a turbulent flow in a duct conveying a gas or

a fluid), turbulent random pressure fluctuations are ated in the flow, adding to the disturbance pressure field.The most common way of reducing the influence of turbu-lent noise is to use a probe tube microphone consisting of

gener-a long, ngener-arrow tube with gener-a stgener-andgener-ard microphone mounted

at the end The walls of the tube are porous or containholes or an axial slit The probe tube microphone must beoriented with the microphone facing the flow Probe tubemicrophones are convenient as reference sensors in activecontrol systems in ducts because they act as both direc-tional sensors and turbulence filtering sensors Details onthe principle of operation can be found in (39) Low-costmicrophone probes for hot corrosive industrial environ-ments are also available from Soft dB Inc Figure 5 shows amicrophone adapted for such environments

Displacement and Velocity Transducers

Although their dynamic range is usually much less thanthat for accelerometers, displacement and velocity trans-ducers are often more practical for very low frequencies(0–10 Hz) where vibration amplitudes can be of the order

of a millimeter or more for heavy structures whose sponding accelerations are small Also, in low-frequencyactive control systems, displacement or velocity ratherthan acceleration can be the preferred quantities to min-imize The displacement and velocity transducers are de-scribed below

corre-Proximity probes are the most common type of

displace-ment transducers There are two main types of proximityprobes, the capacitance probe and the Eddy current probe.Proximity probes allow noncontact measurement of vibra-tion displacements They are well suited to vibration dis-placement measurements on rotating structures The dy-namic range of proximity probe is very small—typically

100 : 1 for low-frequency applications (<200 Hz) The

res-olution varies from 0.02 to 0.4 mm

The linear variable differential transformer (LVDT) is a

displacement transducer that consists of a single primaryand two secondary coils wound around a cylindrical bobbin

A movable nickel iron core is positioned inside the

wind-ings, and it is the movement of this core that is measured

The dynamic range of an LVDT is typically 100 : 1, with

a resolution ranging from 0.01 to 1 mm The frequency

range is typically dc to 100 Hz The total length of the

sen-sor varies from 30 to 50 mm for short stroke transducers

to about 300 mm for long stroke transducers

The linear variable inductance transformer (LVIT) is a

displacement transducer based on the measurement of

in-ductance changes in a cylindrical coil The coil is excited

at about 100 kHz, and the inductance change is caused by

the introduction of a highly conductive, nonferrous coaxial

rod sliding along the coil axis It is the movement of this

coaxial rod that is measured This type of transducer is

particularly suited for measuring relative displacements

in suspension systems Transducer sizes vary from

dia-meters of a few millidia-meters to tens of millidia-meters

Often used among the velocity transducers is the

non-contacting magnetic type consisting of a cylindrical

perma-nent magnet on which is wound with an insulated coil A

voltage is produced by the varying reluctance between the

transducer and the vibrating surface This type of

trans-ducer is generally unsuitable for absolute measurements,

but it is very useful for relative velocity measurement such

as needed for active suspension systems The frequency

range of operation is 10 Hz to 1 kHz; the low-resonance

frequency of the transducer makes it relatively heavy

Velocity transducers cover a dynamic range between 1 and

100 mms−1 Low-impedance, inexpensive voltage

ampli-fiers are suitable

Accelerometers

Accelerometers are the most employed technology for

vi-bration measurements They provide a direct

measure-ment of the acceleration, usually in the transverse

direc-tion of a vibrating object The acceleradirec-tion is a quantity

well correlated to the sound field radiated by the

vibrat-ing object Therefore, accelerometers can be a convenient

alternative to microphones as error sensors for active

structural acoustic control Accelerometers usually have a

much larger dynamic range than displacement or velocity

sensors A potential drawback of accelerometers, in

low-frequency active noise control systems, is their low

sensi-tivity at low frequency (typically 0–10 Hz)

Small accelerometers can measure higher frequencies,

and they are less likely to affect the dynamics of the

struc-ture by mass loading it However, small accelerometers

have a lower sensitivity than bigger ones

Accelerome-ters range in weight from miniature 0.65 g for high-level

vibration amplitudes up to 18 kHz on lightweight

struc-tures, to 500 g for low-level vibration amplitudes on

heavy structures up to 1 kHz Because of the

three-dimensional sensitivity of piezoelectric crystals,

piezoelec-tric accelerometers are sensitive to vibrations at right

an-gle to their main axis The transverse sensitivity should be

less than 5% of the axial sensitivity There are two main

types of accelerometers: piezoelectric and piezoresistive

A piezoelectric accelerometer consists of a small

seis-mic mass attached to a piezoelectric crystal When the

ac-celerometer is attached to a vibrating body, the inertia force

due to the acceleration of the mass produces a mechanicalstress in the piezoelectric crystal that is converted into anelectric charge on the electrodes of the crystal Providedthat the piezoelectric crystal works in its linear regime,the electric charge is proportional to the acceleration of theseismic mass The mass may be mounted to produce eithercompressive or tensile stress, or alternatively, shear stress

in the crystal A piezoelectric accelerometer should be usedbelow the resonance of the seismic mass–piezoelectric crys-tal system Since piezoelectric accelerometers essentiallybehave as electric charge generators, they must generally

be used with high-impedance charge amplifiers The cost ofsuch amplifiers can represent a significant amount of thetotal cost of an active control system when a large number

of accelerometers are used

Piezoresistive accelerometers rely on the measurement

of resistance change in a piezoresistive element usuallymounted on a small beam and subjected to stress Piezore-sistive accelerometers are less sensitive than piezoelectric.They require a stable, external dc power supply to excitethe piezoresistive elements However, piezoresistive ac-celerometers have a better sensitivity at low frequency, andthey require less expensive, low-impedance voltage ampli-fiers The piezoresistive element is sometimes replaced by apiezoelectric polymer film (PVDF), and the electric chargeacross the electrodes of the PVDF is collected as the sen-sor output Such a PVDF accelerometer has a sensitivityand frequency response similar to the piezoresistive ac-celerometer, and it is less expensive than the piezoelectricaccelerometer

Loudspeakers

The electrodynamic loudspeaker is the most commonly ployed actuator technology for active noise control applica-tions When selecting a loudspeaker for an active noise con-trol system, the important parameter is the cone volumevelocity required to cancel the primary sound field (21).For small systems, (small-duct, low-noise, domesticventilation system), active acoustic noise control can beachieved with small commercial medium-quality speakers(radio-type speaker) However, for bigger systems, precau-tions have to be taken

em-Electrodynamic loudspeakers exhibit a nonlinear havior when they are driven close to maximum power ormaximum membrane deflection It can significantly de-grade the performance of active control systems based onlinear filtering techniques It is thus important that loud-speakers should be driven at a fraction of the maximumpower or maximum deflection specifications, especially insituations where single-frequency or harmonic noise has

be-to be attenuated For random noise, the peak cone velocityrequirements for active control are likely to be four or fivetimes the estimated rms velocity requirements (39)

In active control of single-frequency noise, it is desirable

to design the loudspeaker so that its mechanical resonancelies close to the frequency of interest This resonance fre-quency can be adjusted to suit a particular application ei-ther by adding mass to the cone (to reduce the frequency) or

by adding a backing enclosure to the speaker (to increasethe frequency)

Standard speaker

Perforated metal sheets

Teflon 0,005′′

Figure 6 Protective system for loudspeaker membrane.

Operation in industrial environments requires

consid-erable precautions In high-humidity, high-temperature

and corrosive environments, the loudspeaker cone must be

protected with a heat shield Soft dB used a Teflon

brane and a perforated metal sheet to protect the

mem-brane of the speaker from corrosive gas (see Fig 6)

Electromagnetic Actuators

For vibration control purposes, electromagnetic actuators

can be classified into electrodynamic shakers and

elec-trical motors The latter can be used for low-frequency

vibration control Electrodynamic shakers are generally

defined as devices having a central inertial core (usually

a permanent magnet) surrounded by a winding This type

of inertial actuator applies a point force to a structure by

reacting against the inertial mass As in a loudspeaker, a

time-varying voltage is applied to the coil in order to move

the inertial mass and to force the movement of the

struc-ture onto which the shaker is attached

Electricmotors

SynchronousASynchronous

Induction Brushless DC Sine wave Hysteresis Step Reluctance

Figure 7 Classification of electric motors (42).

Other inertial type actuators are available which use,for example, the piezoelectric effect, instead of a coil, tomove the inertial mass Proof-mass actuators (also calledinertial actuators) are very similar in their operation toelectrodynamic shakers They usually consist of a massthat is moved by an alternating electromagnetic field.These devices can generate relatively large forces anddisplacements and can be good alternatives to costlyelectrodynamic shakers The devices can excite very stiffstructures such as electrical power transformers Anotheradvantage of proof-mass actuators is that their resonantfrequency can be easily tuned for optimal efficiency at agiven frequency

Electrical Motors

The advent of new control strategies and digital controllershas revolutionized the way electrical motors can be usedand now allows for the use of motor technologies that werepreviously difficult to implement in practical applications.Simple motor drives were traditionally designed withrelatively inexpensive analog components that suffer fromsusceptibility to temperature variations and componentaging New digital control strategies now allow for the use

of electrical motors in active vibration control applications.These efficient controls make it possible to reduce torqueripples and harmonics and to improve dynamic behavior

in all speed ranges The motor design is optimized due tolower vibrations and lower power losses such as harmoniclosses in the rotor Smooth waveforms allow an optimiza-tion of power elements and input filters Overall, these im-provements result in a reduction of system cost and betterreliability

Electrical motors can be divided into motors with a manent magnet rotor (ac and dc motors) and motors with acoiled rotor Figure 7 illustrates a detailed classification ofthe electrical motors With the advent of new controllers,the tendency is to classify electrical motors under ac or dcaccording to the control strategy

per-Due to its high reliability and high efficiency in a

re-duced volume, the brushless motor is actually the most

interesting motor for application to active vibration control

(40) Although the brushless characteristic can be applied

to several kinds of motors, the brushless dc motor is

con-ventionally defined as a permanent magnet synchronous

motor with a trapezoidal back EMF waveform shape, while

the brushless ac motor is conventionally defined as a

per-manent magnet synchronous motor with a sinusoidal back

EMF waveform shape New brushless and coreless motors

are now available which are very linear over a wide speed

range (41) The brushless motor control consists of

generat-ing variable currents in the motor phases The regulation

of the current to a fixed 60◦reference can be realized in two

modes: pulse width modulation (PWM) or hysteresis mode.

Shaft position sensors (incremental, Hall effect, resolvers)

and current sensors are used for the control Linear

per-manent magnet motors are also available that, in addition

to the linear action, allow better magnetic dissipation in

the core as it is distributed in space

If volume is not a major concern, a second type of motor

to be used in active vibration control is the induction or

ac motor (41) As for the brushless motor, the performance

of an ac motor is strongly dependent on its control DSP

controllers enable enhanced real time algorithms There

are several ways to control an induction motor in torque,

speed, or position; they can be categorized in two groups:

the scalar and the vector control Scalar control means that

variables are controlled only in magnitude, and the

feed-back and command signals are proportional to dc

quanti-ties The vector control is referring to both the magnitude

and phase of these variables Pulse width modulation

tech-niques are also used for the control of induction motors, and

indirect current measurement (using a shunt or Hall effect

sensor) is used as a feedback information for the controller

The third electrical motor used for active vibration

con-trol is the switched reluctance motor (40) This motor is

widely used mainly because of its simple mechanical

con-struction and associated low cost and secondarily because

of its efficiency, its torque/speed characteristic and its very

low requirement for maintenance This type of motor,

how-ever, requires a more complicated control strategy The

switched reluctance motor is a motor with salient poles on

both the stator and the rotor Only the stator carries

wind-ings One stator phase consists of two series-connected

windings on diametrically opposite poles Torque is

pro-duced by the tendency of its movable part to move to a

position where the inductance of the excited winding is

maximized There are two ways to control the switched

re-luctance motor in torque, speed and position Torque can

be controlled by the current control method or the torque

control method The pulse width modulation (PWM)

strat-egy is used in both current and torque control approaches

to drive each phase of the switched reluctance motor

ac-cording to the controller signal

Hydraulic and Pneumatic Actuators

Hydraulic and pneumatic actuators are good candidate

technologies when low frequency, large force, and

displace-ments are required Hydraulic actuators consist of a

hy-draulic cylinder in which a piston is moved by the action

of a high-pressure fluid The main advantage of hydraulic

actuators is their large force and large displacement bility for a relatively small size The disadvantages includethe need for a hydraulic power supply (which can requirespace and generate noise), the high cost of servo-valves,the nonlinear relation between the servo-valve input volt-age and the output force or displacement produced by theactuator, and the limited bandwidth of the actuator (0–

capa-150 Hz) Hydraulic actuators have been used in the design

of active dynamic absorbers for ship structures (42,43).The principle of operation of pneumatic actuators is verysimilar to hydraulic actuators, except that the hydraulicfluid is replaced by compressed air Due to the higher com-pressibility of air, the bandwidth of pneumatic actuators

is reduced (typically 0–10 Hz), which restricts the tion to nonacoustic problems Pneumatic actuators may be

applica-an attractive option when applica-an existing air supply is alreadyavailable

APPLICATIONS OF NOISE CONTROL

IN SHIP STRUCTURES

A typical marine diesel engine mounted on a ship hull

is schematically depicted in Fig 1 The figure shows thevarious vibroacoustic paths through which the engine vi-bration is transmitted to the ship structure, and eventu-ally radiated into seawater In the figure the coupling be-tween structural and acoustic energy is classified using thefollowing symbols: AA: acoustic to acoustic coupling, SS:structural to structural coupling, AS: acoustic to structuralcoupling, SA: structural to acoustic coupling The relativeimportance of energy coupling for radiation into seawater

is illustrated by a number As shown, there are five ble energy transmission paths, including (1) the mountingsystem, consisting of the engine cradle, isolation mounts,raft, and foundation; (2) the exhaust stack; (3) the fuel in-take and cooling system; (4) the drive shaft; and (5) theairborne radiation of the engine In this study, these fivepaths are grouped into four categories, corresponding togeneric active control problems:

possi-rPath 1: Active vibration isolation (mounting system).

rPath 2: Active control of noise in ducts and pipes haust stack; fuel intake and cooling system)

(ex-rPath 3: Active control of vibration propagation inbeam-type structures (drive shaft)

rPath 4: Active control of enclosed sound fields borne radiation of the engine)

(air-Path 1: Active Vibration Isolation

Active vibration isolation involves the use of an active tem to reduce the transmission of vibration from one body

sys-or structure to another (e.g., transmission of periodic bration from a ship’s engine to the ship’s hull) Such anactive isolation system will be used in practice to comple-ment passive, elastomeric isolation mounts between theengine and supporting structure An active isolation sys-tem is usually much more complex and expensive thanits passive counterpart, but has the advantage of offer-ing better low-frequency isolation performances, and can

vi-be designed for a vi-better static stability of the supported

equipment

The first class of system involves the control of

sys-tem damping, and is often referred as a semiactive

isola-tion system, Fig 8(a) The damping modificaisola-tion is usually

achieved by a hydraulic damper with varying orifice sizes

This system is often used for active suspensions in cars

Such a system involves control time constants significantly

longer than the disturbance time constants, with the

ad-vantage of a simpler and less expensive implementation

However, low-frequency performance is much less than for

fully active systems described in the following

A second class of system involves an active control

ac-tuator in parallel with a passive system, with the acac-tuator

Vibrating body

Spring

(a)

Variabledamper

Figure 8 Active vibration isolation systems: (a) semiactive

sys-tem with variable damper; (b) active syssys-tem with control force

ap-plied to both vibrating body and base structure; (c) active system

with control force in series with passive mount.

exerting a force on either the base structure or the rigidmass, Fig 8(b) In this parallel configuration, the actua-tor is not required to withstand the weight of the machine;

as compared to the configuration of Fig 8(c), the requiredcontrol force is smaller above the natural frequency of thesystem (44) The main disadvantage of this configuration

is that at higher frequency (outside the frequency rangewhere the actuator is effective), the actuator itself can be-come a transmission path At low frequency, the large dis-placement/large force requirements for heavy structurespreclude the use of piezoelectric, magnetostrictive actua-tors Instead, hydraulic, pneumatic, or electromagnetic ac-tuators (with their associated weight, space, and possiblyfluid supplies problems) must be used As far as practicalapplication of active control is concerned, the use of an ac-tuator in parallel with a passive isolation stage could havedistinct advantages In a given application, if an actuatorcan be found that provides a control force of the order of theprimary force exciting the machine, then it may be possible

to use of much higher mounted natural frequency ated with the passive isolation stage than would be other-wise possible This in turn has advantages for the stability

associ-of the mounted machine

A third configuration with the active system in serieswith the passive mount is shown on Fig 8(c) Such a sys-tem has several advantages over the parallel configuration.The active system is now isolated from the dynamics of thereceiving structure, which simplifies the control in the case

of a flexible base structure, and the use of an intermediatemass creates a two-stage isolation system that offers betterisolation performance in higher frequency

Path 2: Active Control of Noise in Ducts and Pipes

The reduction of duct noise is the first-known application

of active noise control Active control systems for duct noiseare now a mature technology, with several commercial sys-tems available for ventilation systems, chimney stacks, orexhausts All existing commercial systems are based onfeedforward adaptive control systems In the case of ductscontaining air or a gas, loudspeakers are generally used ascontrol sources, and microphones as error sensors.Two important classes of systems must be distin-guished, depending on the frequency and the cross-sectional dimension of the duct:

1 Systems for which only plane wave propagation ists in the duct Such systems will necessitate asingle-channel control system (one control source andone error sensor)

ex-2 Systems for which higher-order acoustic modes agate in the duct Such systems will require a multi-channel control system

prop-The occurrence of higher-order modes in a duct depends

on the value of the cut-on frequency For a rectangular

duct, the cut-on frequency is given by f c = c0/2d, where d

is the largest cross-sectional dimension and c0is the speed

of sound in free space For a circular duct, f c = 0.586 c0/d,

where d is the duct diameter Higher-order modes will agate at frequencies larger than f c

prop-For active noise control (ANC) in the large duct,

mul-tichannel acoustical ANC systems are necessary, and M

error sensors have to be used to control M modes for

high-order propagation cases The error sensors should not be

located at the nodal lines (observability condition) (45) For

a rectangular duct, the location of the error sensors is

rel-atively simple because the nodal lines are fixed along the

duct axis However, in circular ducts, the location of the

nodal lines changes along the duct axis, since the modes

usually spin as a function of the frequency, temperature,

and speed (46,47) Those variations of the nodal lines may

explain why ANC of high-order modes in circular or

ir-regular ducts appears to be difficult (48) Instead of using

the modal approach (i.e., the shape of the modes to be

con-trolled) to determine the error sensors location, an

alterna-tive strategy has recently been proposed by A L’Esp´erance

(49)—the error sensor plane concept This concept calls

for a quiet cross section to be created in the duct so that,

based on the Huygen’s principle, the noise from the

pri-mary source cannot propagate over this cross section A

multichannel ANC in a circular duct accords with this

strategy (50)

The principles of active control of noise propagating in

liquid-filled ducts are much the same as in air ducts (51)

The higher speeds of sound in liquids means that plane

wave propagation occurs in a larger frequency range than

in air ducts However, considerable care must be exercised

to the possible transmission of energy via the flexible duct

walls in this case, as a result of the strong coupling between

the duct walls and the interior fluid

Path 3: Active Control of Vibration Propagation

in Beam-Type Structures

The active control of vibration in one-dimensional systems

such as beams, rods, struts, and shafts can be approached

from two different perspectives, depending on the

descrip-tion of the structural response The response can be

de-scribed in terms of vibration modes or in terms of waves

propagating in the structure The modal perspective is

more appropriate to finite, or short, beams and to global

reduction of the vibration The description of the response

in terms of structural waves is more appropriate to

infi-nite, or long, beams and to reducing energy flow from one

part of the beam to another (control of vibration

trans-mission) The wave description is then more appropriate

to the case of the transmission of vibration from a ship’s

engine via the drive shaft, since in this case the source

of vibration is known and the objective is to block the

vi-bration transmission along the shaft The active control

of vibration in beams is widely covered in the literature

(21,44) The following presentation is mostly limited to

feedforward control systems, since it is assumed that for

the problem of vibration transmission along a marine drive

shaft, an advanced signal correlated to the disturbance,

or a measurement of the incoming disturbance, wave is

possible

Simultaneous Control of All Wave Types (Flexural,

Longitudinal, Torsional) In a general adaptive feedforward

controller used for the active control of multiple wave types

in a beam, sensor arrays (e.g., accelerometer arrays) areused to measure the different types of waves propagatingupstream (detection array) or downstream (error array) ofthe control actuators, and an array of actuators is used toinject and control the various wave types in the beam (44).Wave analyzers are necessary to extract the indepen-dent wave types (assumed uncoupled) from the sensor ar-rays, and wave synthesisers are necessary to generate theappropriate commands to the individual actuators Thisapproach has the advantage that independent control fil-ters can be used to control the flexural, longitudinal, andtorsional waves However, it necessitates excellent phasematching of the sensors and a detailed knowledge of thestructure in which the waves propagate An experimen-tal laboratory implementation of this approach has beenconducted by (52), on a thin beam, for the control of twoflexural wave components and one longitudinal wave usingPZT actuators Another, easier option avoids implementingwave analyzers and synthesisers by simply minimizing thesum of squared output of the error sensors to control thedifferent wave types This approach, however, requires afully coupled multichannel control system This approachhas been tested for the control of two flexural waves andone longitudinal wave in a strut using three magnetostric-tive actuators (53,54)

Control of Flexural Waves The dispersive nature of

flex-ural waves implies that a control force applied transversely

to the beam generates propagative waves as well as cent waves localized close to the point of application of theforce If one transverse control force is applied at somelocation on the beam, it generates downstream and up-stream propagating waves plus downstream and upstreamevanescent waves This actuator can minimize the total,transmitted downstream wave, but it generates a reflectedwave toward the source and two evanescent componentsthat may be undesirable A total of four actuators will benecessary to control downstream and upstream, propagat-ing, and evanescent components Therefore, the control of

evanes-flexural waves in beams will in general require actuator

arrays (55) Combinations of force and moment actuators

can also be used in the actuator array The simplest ward control system uses only one control force and one er-ror accelerometer, together with one reference accelerom-eter to measure the incoming wave This system has beenstudied theoretically (56), and tested experimentally (57).Physical limits of this system have been identified Thefirst limit is associated with the detection of the controlactuator evanescent wave by the error sensor that puts alimit on the actuator-error sensor separation: in practice,the sensor should be at least 0.7 from the control actua-tor (λ being the flexural wavelength) The second limit is

feedfor-related to the delay between detection and actuation thatshould be sufficient to allow the active control system toreact at the control actuator location before the primarywave has propagated from the detection sensor to the con-trol actuator This puts a limit on the reference sensor–actuator separation, which depends on the characteristics

of the control system

Similarly to control actuator arrays, error sensor arraysneed to be implemented for the control of flexural waves

x

Accelerometer probeerror sensor

Laservibrometer

Piezoelectricpatch controlactuator

Figure 9 Typical experimental setup for the control of active

structural intensity.

to distinguish between the various propagating waves and

evanescent waves at the error sensor locations This is

par-ticularly needed if the error sensors must be located at

a short distance from the control actuators In this case,

an array of four accelerometers can discriminate between

the two propagating waves and the two evanescent waves

at the location of the error sensor array, and extract the

components that need to be reduced (e.g., the downstream

propagating wave)

Other sensing strategies have also been suggested, such

as measuring and minimizing the structural intensity due

to flexural waves (58,59) Structural intensity can be

mea-sured in practice using an array of four or more closely

spaced accelerometers, as presented in Fig 9

Practical Implementations There are a limited number

of practical implementations of these principles to large,

machinery structures Semiactive or active devices have

been used to attenuate the transmission of longitudinal

vibration on a large tie-rod structure (60) The tie-rod is

similar to that found in marine machinery to maintain the

alignment of a machinery raft A tunable pneumatic

vi-bration absorber was used as the semiactive device, and

an electrodynamic shaker or a magnetostrictive actuator

was used as the active device A load cell was used as the

error sensor, such that the force applied by the tie-rod to a

receiving bulkhead was minimized

The suppression of vibration that is generated on

ro-tating machinery with an overhung rotor has been

pre-sented (61) In this case, the vibration of the rotor-shaft

system is controlled by active bearings The active

bear-ings consist of a bearing housing supported elastically by

rubber springs and controlled actively by electromagnetic

actuators These actuators are controlled by displacement

sensors at the pedestal and/or the roller and can apply an

electromagnetic force that suppresses any vibration of the

roller The active vibration control (AVC) of rotating

ma-chinery utilizing piezoelectric actuators was also

investi-gated (62) The AVC is shown to significantly suppress

vi-bration through two critical speeds of the shaft line

Path 4: Active Control of Enclosed Sound Fields

There exists a vast body of literature on the subject of active

control of enclosed sound fields Only the previous work

re-levant to the problem of canceling the sound field radiated

by a ship engine in its enclosed space will be reviewed here.More comprehensive presentations of the generic problemcan be found in (3,21) Active control of enclosed soundfields has found applications essentially for automobile in-terior noise (63,64) and for aircraft interior noise (65–67),leading in some cases to commercial products

There are two main categories of active control systemsrelated to enclosed sound field minimization:

rActive control of sound transmission through elasticstructures into an enclosure

rActive control of sound field into rigid enclosures.Only the second category will be reviewed here The activecontrol of sound transmission has been investigated usingessentially modal approaches (68,69) The same type of an-alytical approach based on modes of the acoustic enclosurecan be used to investigate the active control of sound fieldinto rigid enclosures It should be mentioned, however, thatfinite element approaches have also been used to studythe active control of sound field into enclosures of com-plex geometries (70,71) Additionally, the objective of the

active control in an enclosure can be to minimize the sound

field globally, or locally Only the approaches directed

to-ward global attenuation of the sound field are reviewedhere In this respect, some important physical aspects ofthis problem are discussed in the following These physi-cal aspects depend primarily on the modal density of theenclosure

Enclosures with a Low Modal Density For enclosures with

a low modal density (i.e., a small enclosure, or at low quency), the active control will usually consist of placing

fre-a series of control loudspefre-akers in the enclosure; the speakers are driven to minimize the sound pressure mea-sured by discrete error microphones In the case of anenclosed acoustic space, the performance metrics for thecontrol should be the acoustic potential energy integratedover the volume of the enclosure,

where p(r) is the local sound pressure, ρ0 is the density

of the acoustic medium, and c0is the speed of sound Theactive control scheme should aim at reducing the acousticpotential energy as much as possible

It has been shown that active control of sound fields

in lightly damped enclosures is most effective at the onance of the acoustic modes (72) In these instances, theproblem is essentially the control of a single mode Sig-nificant attenuation of the acoustic potential energy isobtained using a single control source and a single er-ror microphone (provided that neither the control sourcenor the error microphone is located on a nodal surface ofthe acoustic mode) For a multiple-mode (off-resonance)response of the cavity, the number of control sourcesand error microphones should be increased However, thepotential for attenuation is never as large as at a resonancefrequency

res-The number and placement of control sources and error

sensors are critical for multiple-mode control The

corre-sponding optimization problem is nonlinear and usually

involves many local minima Optimization processes, such

as multiple regression (21) or genetic algorithms (73), are

used As a general rule is that the number and locations

of the control sources should be such that the secondary

sound field matches as closely as possible the primary

sound field in the enclosure

Enclosures with a High Modal Density As the frequency

increases or the enclosure becomes larger, global

attenua-tion of the sound field becomes more difficult to achieve

us-ing an active control system To quantify these limitations,

there are some approximate formulas, which are

summa-rized here These formulas are approximate, but they give

useful expected performance of an active control system in

a high modal density enclosure

First, assuming a single primary point source and a

sin-gle secondary point source in the enclosure, it is possible

to derive the ratio of the minimized potential energy (after

control) to the original potential energy (before control),

(74):

E p ,min

E p ,0 = 1 −1+ π

2M(ω)−2,

where M( ω) is the modal overlap of the cavity, which

quantifies the likely number of resonance frequencies of

other modes lying within the 3 dB bandwidth of a given

modal resonance For a rigid rectangular enclosure and for

oblique acoustic modes, namely three-dimensional modes,

such as the (1,1,1) mode,

M(ω) = ζ ω3V

πc0

,

whereζ is the damping ratio in the enclosure (assumed

identical for all acoustic modes),ω is the angular frequency

of the sound field, and V is volume of the enclosure.

If the modal density is low (at low frequency),

E p ,min

E p ,0 ≈ π M(ω),

which means that the achievable attenuation is dictated

by the modal overlap (and hence the modal density and

damping of the enclosure)

If the modal density is large (at high frequency),

E p ,min

E p ,0 ≈ 1,

which means that no attenuation can be obtained

after control Another expression can be derived from

the asymptotic expression of modal overlap in high

frequency (75),

E p ,min

E p ,0 = 1 − sin c2kd,

where k is the acoustic wave number and d is the

separa-tion between the primary and control sources Thus, as thecontrol source becomes remote from the primary source,

such that kd ≥ π, any global attenuation of the sound field

becomes impossible This provides an explicit analyticaldemonstration that the global control of enclosed soundfields of high modal density is only possible with closelyspaced compact noise sources In other words, assuming anextended primary source such as a ship engine, the only vi-able solution in this case is to distribute control loudspeak-ers around the engine and in the close vicinity of it (within

a fraction of the acoustic wavelength)

Advanced Sensing Strategies Recently, alternatives to

sensing and minimizing squared sound pressure have beensuggested in active control of enclosed spaces Sensingstrategies based on total acoustic energy density minimiza-tion instead of sound pressure minimization have been sug-gested (76,77) The advantage of sensing the total energydensity is that the control is less sensitive to the sensor lo-cations, and in general, a superior attenuation is obtained.The energy density can be measured using combinations ofmicrophones (2 to 6); in this case, finite differences betweenindividual microphones are applied to obtain approximatemeasurements of the pressure gradient in several direc-tions Precise measurements of the pressure gradient re-quires an excellent phase matching of the individual micro-phones, which can result in more expensive microphones.Associated adaptation algorithms for the minimization ofenergy-based quantities have been derived (78)

RECOMMENDATIONS ON SENSORS AND ACTUATORS FOR ANVC OF MARINE STRUCTURES

Steps in Design of Active Control Systems

of the vibroacoustic behavior of the system on which activecontrol is to be applied This involves carefully identifyingand ranking the various paths along which vibroacousticenergy flows This may imply addressing questions such

as the transmission of moments or in-plane forces throughthe engine mounting, or the relative contribution of fluid-borne and structure-borne energy along pipes This earlyphase is crucial in determining the active control strategy

to be implemented A number of experimental techniquesand numerical simulation tools can be used to estimatethe relative contribution of the various paths at a givenreceiving point (e.g., in water) Based on some contractors’previous experiences, a major transmission path appears

to be the engine-mounting system

Phase 1–Understanding the vibroacoustics of thesystem

Phase 2–Selecting the control actuators

Identifcation of the transmission pathsRanking of the transmission pathsActive control strategy

•

•

Phase 3–Selecting the error sensors

Phase 4–Testing the active control system

Exact quadratic optimizationError sensor configuration forglobal control

Figure 10 Suggested design steps of an active control system.

The second phase will determine the type, number, and

locations of the control actuators When global control is

desirable (e.g., when attenuation of the sound field is

de-sired at all positions in water), these parameters are

deter-mined by the requirement that the sound field generated

by the control actuators should spatially match the

pri-mary sound field The type of control actuators to be used

will be based primarily on the frequency of the disturbance

and the magnitude of the disturbance at the actuator

loca-tion (for simplicity, the control actuators need to generate a

secondary field with a magnitude equal to the disturbance

at the actuator location) Once the type, number, and

loca-tions of the control actuators are known, extensive transfer

function measurements need to be taken between

individ-ual actuators and field points (vibratory or acoustic), with

the primary source turned off Since this may involve a

con-siderable experimental task, numerical simulations can be

of a great help here

The third phase will address the error sensors Again, if

global control is desirable, the type, number, and locations

of the error sensors are dictated by the requirement that

if the control actuators are driven to minimize the signal

at the error sensors, then the resulting sound field is

glob-ally reduced The measured transfer functions between

in-dividual actuators at field points and the magnitude of

the primary disturbance at these field points are used,

in conjunction with classical exact quadratic optimization

techniques, to calculate the optimal control variables (i.e.,the required inputs of the control actuators) that minimizethe error signals for a given error sensor arrangement Thefinal phase will be to test the active control with a realcontroller

Recommended Sensor and Actuator Technologies for Various Ship Noise Paths

Path 1: Active Vibration Isolation In selecting sensors

and actuators for active vibration isolation of engine noise,due consideration has to be given to the size and weight

of the structure (engine) being isolated Since the engine

is a heavy structure weighing over 6000 kg, it is sary that that the actuators are capable of delivering veryhigh control forces In addition, the nature of the noisethrough this path is nonacoustic, and hence nonacousticsensors and actuators have to be used Based on these con-siderations, the recommended sensors and actuators are(1) accelerometers and force transducers for sensing and(2) hydraulic and electrodynamic actuators for actuation.The recommendations are summarized in Table 3 For in-creased efficiency, the control systems must be designed

neces-to provide control forces in translational and rotational rections, since engine vibrations could take place in all di-rections Furthermore, the active control systems should

di-be used in conjunction with passive control systems, to duce cost as well to provide fail-safe designs

re-Path 2: Active Control of Noise in Ducts and Pipes The

feedforward algorithm has been recommended for the trol of noise associated with a marine diesel engine where areference signal is accessible (4) For ducts, generally asso-ciated with large cross-sectional dimensions, higher-ordermodes are more likely to exist, requiring a large number

con-of sensors and actuators with an appropriate positioningstrategy For pipes, generally associated with small cross-sectional dimensions, it is expected that only plane wavepropagation will exist, thereby limiting the number of ele-ments needed to one sensor and one actuator The followingsensing configurations are possible: microphones, piezo-electric sensors, or accelerometers For actuation, loud-speakers and inertial actuators are recommended

Path 3: Active Control of Vibration Propagation in Beam-Type Structures Feedforward control was recom-

mended for the vibration control of a propeller shaft (4).The configuration of sensors and actuators to be used willdepend on the excitation source and on the modal behavior

of the shaft For modal control, the sensors and actuatorscan be located either on the shaft itself or connected to

it by a stationary mechanical link, such as by a bearingmounted on the shaft Potential mounted actuators includecurved piezoelectric actuators (PZT) and magnetostric-tive actuators For wave transmission control, sensors andactuators arrays are required to measure the downstreampropagating and evanescent waves and to inject the controlwaves in the structure

Mounted sensors to be used include piezoelectric(PVDF) sensors to measure the strain and accelerometers,

Table 2 Properties of Selected Piezoelectric Materials

Note: γ0= 8.85 × 10−12farad/m, electric permittivity of air.

if the rotation speed permits, for acceleration

measure-ment The mounted actuators include piezoelectric (PZT)

actuators to induce strain in the structure For

robust-ness, it is recommended that the actuators be combined

with passive control elements such as a viscoelastic layer

bonded to the shaft

Table 3 Recommended Sensors and Actuators for Ship Noise Control

Recommended Sensors and Actuators

Path 1: Active vibration isolation rForce transducers rHydraulic actuators

rAccelerometers rElectrodynamic actuatorsPath 2: Active control of noise rMicrophones rLoudspeakers

in ducts and pipes rPiezoelectric sensors rElectric motors

rAccelerometersPath 3: Active control of vibration rPiezoelectric sensors rPiezoelectric actuatorspropagation in beam-type structures rAccelerometers rMagnetostrictive actuators

rElectrodynamic shakers rElectrodynamic shakers

rLVDTPath 4: Active control of airborne

engine noise Sound field into enclosures rCombination microphones rLoudspeakers

rAccelerometersRadiated noise into sea rPiezoelectric sensors rPiezoelectric actuators

rAccelerometers rMagnetostrictive actuators

Path 4: Active Control of Radiated Sound Fields There

are two types of radiated noise to be controlled for shipstructures These are the airborne engine noise into an en-closure, and the noise radiated by the noise into the sea

As stated in (4) both cases require the use of global trol techniques that involve multiple input and multiple

con-output transducers Control of radiated noise can be

achieved either by active noise cancellation (ANC) or by

active structural acoustic control (ASAC) techniques For

active cancellation, the following sensors and actuators

are recommended: (1) combination microphones and

ac-celerators as sensors and (2) loudspeakers as actuators

For active structural acoustic control the following

sors and actuators are recommended: (1) piezoelectric

sen-sors (shaped or not) and accelerometers as sensen-sors, and (2)

piezoelectric and magnetostrictive materials as actuators

SUMMARY AND CONCLUSIONS

Among the wide range of sensor and actuator materials

that could be used for active noise and vibration control in

ship structures are piezoelectric and electrostrictive

ma-terials magnetostrictive mama-terials, shape-memory alloys,

optical fibers, electrorheological and magnetoeheological

fluids, microphones, loudspeakers, electrodynamic

actua-tors, and hydraulic and pneumatic actuators In making

the selection, due consideration must be given to factors

such as cost, frequency of the disturbance, operating

(ma-rine) environment, experience in other applications, ease

of implementation, and the expected performance In

gen-eral, the following recommendations are made:

1 Nonacoustic sensors and actuators (e.g.,

accelero-meters, force transducers, hydraulic actuators, electric materials, and electrodynamic actuators) arebest for nonacoustic paths, namely for the engine-mounting system, the drive shafts, and mechanicalcouplings

piezo-2 Acoustic sensors and actuators (e.g., microphones

and loudspeakers) are best for acoustic paths, namelyfor the exhaust stacks and piping systems, and theair-borne noise

It was also recommended that the active control strategies

be combined with passive treatments whenever possible,

to increase the robustness of the control system and to

pro-vide a fail-safe design

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Vibration is present almost everywhere we travel in

mod-ern society Vibrationally induced failures are very

com-mon in products such as television sets and computers

that are shipped by trains and trucks Vibrational failure

in a television set may be just an inconvenience However,

vibrational failure in a large passenger airplane can lead to

many deaths Methods of vibrational analysis are available

that are accurate and can reveal weak structural areas

Steps can then be taken either to repair or replace critical

items Vibrational analysis is a combination of science and

art The science uses sophisticated computers extensively

to solve large complex problems This method requires

ex-tensive training and often takes a long time to reach a

satisfactory solution The art uses approximations, short

cuts, and test data to reduce the time needed to reach a

satisfactory solution The approximations and short cutscan sharply reduce the time required for a solution, but italso reduces the accuracy of the analysis Vibrational anal-ysis can be used to make some materials work smarter

by making small changes in their physical properties.These changes can often increase the fatigue life of criti-cal structural members without a significant increase inthe size, weight, cost, or impact on production and deliveryschedules

VIBRATIONAL REPRESENTATION

In a broad sense, vibration means an oscillating motion,where something moves back and forth If the motion re-peats itself, it is called periodic If continuous motion neverrepeats itself, it is called random motion Simple harmonicmotion is the simplest form of periodic motion, and it istypically represented by a sine wave, as shown in Fig 1.The reciprocal of the period is known as the frequency, and

it is measured in cycles per second, or hertz (Hz) The mum displacement is called the amplitude of the vibration

maxi-DEGREES OF FREEDOM

A coordinate system is usually used to locate the positions

of various elements in a system When only one element isinvolved, it is restricted to moving along only one axis, andonly one dimension is required to locate the position of theelement at any instant, then it is called a single-degree-of-freedom system The same is true for a torsional system.When one element is restricted to rotating about one axis sothat only one dimension is required to locate the position ofthe element at any instant, it is a single-degree-of-freedomsystem Two degrees of freedom requires two coordinates

to locate the positions of the elements, and so on

A single rigid body is usually considered to have sixdegrees of freedom, translation along each of the three

orthogonal x, y, and z axes and rotation about each of the

same three axes Real structures are usually considered tohave an infinite number of degrees of freedom

VIBRATIONS OF SIMPLE STRUCTURES

The natural frequency (often called the resonant quency) of a simple single-degree-of-freedom system can

C K

Chassis orPCBM

Figure 2 Single-degree-of-freedom spring-mass system.

often be obtained from the strain energy and the kinetic

energy of the system Consider the single spring and mass

system shown in Fig 2 When there is no damping in the

system, then no energy is lost, and the strain energy must

be equal to the kinetic energy This results in the natural

g= 9.80 m/s2(386 in/s2), the acceleration of gravity and

Ystin meters (inch) is the static displacement

Sample Problem: Natural Frequency of a Simple Structure

When the static displacement of a structure Yst= 1.27 ×

10−5m (0.00050 in), its natural frequency is 140 Hz

The natural frequency is important because it is often

considered the heart of a vibrating system It influences

the number of fatigue cycles and the displacement, which

affect the fatigue life of a system It also influences the

damping, which affects the dynamic acceleration Q level,

and the stress level, which also affects the fatigue life

NATURAL FREQUENCIES OF UNIFORM

BEAM STRUCTURES

Natural frequencies of uniform beam structures can be

de-termined by equating the strain energy to the kinetic

en-ergy without damping This method of analysis leads to

simple solutions and very little error because beam types

of structures normally have very little damping The

re-sulting equations for natural frequency apply to uniform

beams that are forced to bend only in the vertical axis

with-out bending in the horizontal axis and withwith-out torsion or

twisting The beam equation is (1)

a = 3.52 for a cantilevered beam,

a = π2= 9.87 for a beam that is supported (hinged) at

each end,

a = 22.4 for a beam that is clamped (fixed) at both ends,

E in newtons (N) m2(lb/s in2) is the modulus of elasticity

for beam material,

I in m4 (in4) is the area moment of inertia for a beam

cross section,

g = 9.80 m/s2(386 in/s2), the acceleration of gravity,

W in Ns (N) (lb) is the total weight of the beam, and

L in m (in.) is the length of the beam between supports.

Section AA

(2.0 in.)0.0508 meters

0.0254 meters (1.0 in.)

Figure 3 Uniform beam simply supported at each end.

Sample Problem: Natural Frequency of a Simply Supported Uniform Beam

For example, consider the simply supported (hinged)

alu-minum beam shown in Fig 3, where E = 6.894 × 1010

N/m2(10× 106lb/in2), L = 0.254 m (10.0 in), I = 6.937 ×

10−8m4(0.1667 in4), and W = 8.896 N (2.0 lb) The

result-ing natural frequency is 890 Hz

NATURAL FREQUENCIES OF UNIFORM PLATES AND CIRCUIT BOARDS

The natural frequencies of different types of flat, uniformplates that have different types of supports can often beobtained by using trigonometric or polynomial series (1).Again, when damping is ignored, the strain energy can

be equated to the kinetic energy of the bending plate

to obtain the natural frequency A printed circuit board(PCB) that supports and electrically interconnects variouselectronic components can be analyzed as a flat rectan-gular plate, often simply supported (hinged) on all foursides, that has a uniformly distributed load across its sur-face The natural frequency for this type of installation

is (2)

fn= π2



D ρ

h in m (in) is the plate thickness,

µ is Poisson’s ratio, dimensionless,

2/m3(lb s2/in3), the mass per unit area, (5)

g = 9.80 m/s2(386 in/s2), the acceleration of gravity,

W in newtons (lb), is the total weight of the PCB,

a in m (in) is the length of the plate,

b in m (in) is the width of the plate, and

m and n are integers: first harmonic m = 1, n = 1; second harmonic m = 2, n = 1;

third harmonic m = 1, n = 2; fourth harmonic m = 2,

n= 2

X

Xb

Figure 4 Uniform flat plate simply supported on four sides.

Sample Problem: Natural Frequency of a Rectangular PCB

(see Fig 4).

Consider a flat rectangular epoxy fiberglass PCB,

sup-ported (hinged) on four sides, where E = 1.379 × 1010N/s

m2, (2.0×106lb/in2), h = 0.00157 m (0.062 in), µ = 0.12

di-mensionless, D = 4.53 N (40.1 lb in), W = 4.448 N (1.0 lb),

a = 0.203 m (8.0 in), b = 0.178 m (7.0 in), ρ = 12.56 Ns2/m3

(0.463×10−4lb s2/in3) The resulting natural frequency for

the first harmonic (m = 1, n = 1) is 52.6 Hz.

METHODS OF VIBRATIONAL ANALYSIS

Hand calculations are still being used extensively for

sim-ple sinusoidal and random vibrational analyses in small

companies due to the high costs of the computers, the

spe-cialized computer software, and the skilled personnel to

operate the computers Many reference books are available

that show how to perform simplified vibrational analyses

on different types of simple structures However, when

large complex structures are involved, hand calculations

are not adequate to ensure reasonable accuracy Small

com-panies often subcontract the work to outside consulting

organizations that specialize in these areas Sometimes it

can be cheaper, faster, and more accurate to build a model

of the structure, so it can be examined in a vibrational test

laboratory

Most large companies rely extensively on various types

of computers and specially formulated finite element

mod-eling (FEM) software programs for vibrational analyses

Their computers are usually networked together, so each

has access to the wide variety of software analytical

pro-grams available on the network The new desktop personal

computers (PC) are very popular for vibrational analyses

using FEM They are more powerful and faster than the

large main frame computers of a few years ago

PROBLEMS OF VIBRATIONAL ANALYSIS

Almost all computers and computer software FEM

pro-grams for vibrational analysis agree within about 2% when

they are used to determine eigenvalues (resonant cies) and eigenvectors (mode shapes) for many types ofcomplex structures However, sample problems solved byusing different FEM software programs have shown sig-nificant variations in their stress values The stress val-ues from four different FEM programs had a total varia-tion of about 60% This was 30% above the average stressvalue of the four programs and 30% below the averagevalue for similar models of the same structure, subjected tothe same type of vibrational excitation Different computerFEM programs typically use different algorithms to definethe building blocks for their various beam, plate, and brickelements These algorithmic variations probably cause thevariations in the stress values Because the fatigue life of

frequen-a structure is closely relfrequen-ated to its stress vfrequen-alue, significfrequen-antvariations in the calculated stress levels can result in dra-matic changes in the calculated fatigue life of a structure.For example, the results of this investigation showed thatthe fatigue life at the critical point in the structure can beexpected to vary across a wide range because of the vari-ations in the calculated stress values The fatigue life inthe lead wires of PCB electronic component parts can be

as much as five times greater than the average calculatedfatigue life, or it can be as little as one-fifth of the averagecalculated fatigue life [See Ref 5, Chap 12, Figs 12.1–12.19 for more detailed information on finite elementmodeling.]

The results shown before may vary substantially Onlyfour different FEM software programs were involved inthis investigation At least several dozen new softwareprograms are available now When the different modelingtechniques of different computer analysts are considered,these factors are expected to have a significant impact onthe computer calculated stress values and the resultingcalculated fatigue life

PROBLEMS OF MATERIAL PROPERTIES

Material properties are often difficult to evaluate for brational environments The life of any structure excited

vi-by vibration depends on the fatigue properties of the mostcritical materials used in fabricating and assembling thestructure When structural elements are forced to bend andtwist back and forth, perhaps millions of times in severevibrational environments, three very important factorshave to be defined:

1 the very basic fatigue properties of the materials used

mate-plotted on log–log curves of stress (S) against the ber of cycles (N ) to failure Only one average straight-line

N cycles to fail

N1Sb

1= N2Sb 2

Figure 5 S–N fatigue curve showing large variations in the life

test data.

usually represents the fatigue life properties of a material

(1,3–5) When all of the failure test data points for all of

the test samples are plotted, a wide variation in the

fa-tigue life is revealed Because these are log–log plots, the

spread in the possible variation in fatigue life of virtually

identical parts can be very great, sometimes reaching

val-ues of 10 to 1 Engineers involved in vibrational and

fa-tigue life analysis do not like to reveal this type of data to

upper management personnel Personal experience with

nontechnical upper management people is that they often

expect mechanical designers and analysts to predict the

fa-tigue life of their structures to within plus and minus 20%

This is an almost impossible task, when all of the possible

variations are considered

To compensate for these large variations in fatigue life

of virtually identical structural elements, safety factors

(sometimes called factors of ignorance) must be used when

these structures are being designed and analyzed

Build-ing models for vibrational life testBuild-ing in a laboratory can

be a great help in estimating the fatigue life of a structure

However, if no tests are run or if the number of samples

tested is low, there is always the danger of erratic bursts

of high failure rates in the production units because of the

large scatter associated with fatigue

Next, consider the effects of manufacturing tolerances

on the physical dimensions of the structural elements in an

assembly Mass-produced products always show some

vari-ations in the physical dimensions of what appear to be

iden-tical parts Even die cast parts that are made from the same

mold have slightly different physical dimensions Some

manufactured devices, like the automatic transmission in

an automobile, can have many precision gears, ground to

very close tolerances Holding very tight manufacturing

tolerances can be very expensive Therefore, looser

toler-ances are used in production parts that do not require tight

tolerances for precision assembly work because they this

reduce costs When manufactured parts that have loose

tol-erances are exposed to severe vibration, the failure rates

often go up and down erratically Changes in the physical

dimensions of load-carrying structural members can alter

the load path through the structure, which can change the

dynamic loads and stresses in it It is too expensive to keep

track of manufactured parts that have extremes in theirdimensional tolerances These parts can be anywhere inlarge production programs This means that failures whichare difficult to predict and to control, may occur randomly

in harsh environments

To reduce costs, for example, the electronics industrytends to use very loose tolerances in the dimensions thatcontrol the external physical sizes of the length, width, andthickness of their printed circuit boards (PCBs) and elec-tronic component parts These large variations in tolerance

of these parts further increase the difficulty in trying topredict the fatigue life accurately of electronic assembliesthat are exposed to different vibrational environments

RELATION OF DISPLACEMENT TO ACCELERATION AND FREQUENCY

Vibrational displacements are often very small, so theyare difficult to observe during vibrational tests Becausethese displacements are small, it does not mean that theresulting stresses are also small Vibrational environmentsusually impose alternating displacements and alternat-ing stresses on various structural load-carrying elementswithin a system If the vibrating system experiences manythousands of stress reversals, fatigue failures can occur

in critical structural members, even at relatively low placements and stress levels This is the nature of fatiguefailures that occur at relatively low stress levels near smallholes, small notches, and sharp bends These geometricshapes are known as stress concentration factors, whichcan increase peak stress levels in these areas by a factor of

dis-3 or 4 or more (4)

When vibrational tests are run in a laboratory, the mal procedure is to use small accelerometers to monitorthe resulting acceleration values in different parts of thestructure When an electrodynamic shaker is used to gen-erate a sinusoidal wave for the vibrational test, the elec-tronic control system will show the frequency of the im-posed wave in cycles per second, or hertz (Hz) With thistype of setup, the test engineer will know the accelerationlevel and the frequency at any instant This information

nor-is often incomplete without the resulting dnor-isplacement atany instant The resulting displacement at any instant can

be obtained by considering a rotating vector that generates

a sinusoidal wave based on the full relationship (1),

where

Y is the displacement at any time,

Y0is the maximum single amplitude displacement fromzero to peak, and

 = 2π( f ) rad/s, the frequency.

The acceleration a can be obtained from the second

derivative of the displacement with respect to time fromthe preceding equation The maximum acceleration occurswhen the sine function is one It is convenient to represent

the acceleration in terms of gravity units G:

g (gravity units, dimensionless), (7)

where

a in m/s2(in/s2) is the acceleration level and

g = 9.80 m/s2(386 in/s2), the acceleration of gravity

The final results show the displacement Y0in terms of

the frequency f in Hz and the number of dimensionless

G is the acceleration, in gravity units, dimensionless

(same in English units), and

f is the frequency in cycles/s (Hz) (same in English

units)

Sample Problem: Finding the Displacement

from the Frequency and the G Level

For example, when the acceleration G level is 3.0

dimen-sionless gravity units and the frequency is 120 Hz, the

sin-gle amplitude displacement is 0.0000517 m (0.00204 in)

This equation is probably the most important

relation-ship in the entire field of dynamics It shows that when

any two of the parameters of Y0, G or f , are known, then

the third parameter is automatically known This equation

can be used for sine vibration, random vibration, shock,

and acoustics (1)

EFFECTS OF VIBRATION ON STRUCTURES

Vibrational environments can dramatically magnify the

dynamic forces and stresses in different types of structures,

when the structural natural frequencies are excited Forces

and stresses can be magnified and amplified by factors of

10, 30, and even 100 in many different types of structures

for different types of vibrational excitation The magnitude

of the magnification, called the transmissibility Q, often

depends on the amount of damping in the vibrating system

Figure 6 shows damping for a single-degree-of-freedom

sys-tem There are very few single-degree-of-freedom systems

in the real world For example, consider a

two-degree-of-freedom system for an electronic assembly where the

chas-sis is mass1 The plug-in PCBs are attached to the chaschas-sis

so they are mass 2 The response of mass 1 will be the input

to mass 2 Testing experience, including different damping

methods, has shown that the transmissibility Q of PCBs as

mass 2 will depend far more on the dynamic coupling phase

relation and frequency ratio between mass 1 and mass 2

than the damping in either mass 1 or mass 2 because the

transmissibility Q’s between masses 1 and 2 do not add,

they multiply

00.10.20.40.60.81.02

46810

0.5 1.0 1.5 2.0

00.100.20

Figure 6 Effects of damping on the transmissibility Q plots.

The Q of a system is defined as the ratio of the

out-put (or response of the system) divided by the inout-put Theoutput and the input are usually defined in terms of thedisplacements, or the acceleration values If the damp-ing in a simple system is zero, the vibration theory states

that the value of the transmissibility Q will be infinite.

If the transmissibility Q is infinite, the resulting dynamic

forces and stresses will also be infinite However, because

all real systems have some damping, Q can never be nite However, in lightly damped systems, Q can be very high A high Q will result in high forces, displacements, and

infi-stresses, which can sharply reduce the fatigue life of thestructure

ESTIMATING THE TRANSMISSIBILITY

Q IN DIFFERENT STRUCTURES

The transmissibility Q is strongly influenced by the

damp-ing in a vibratdamp-ing structure One form of dampdamp-ing is theconversion of kinetic energy into heat This can be shown

by rapidly bending a metal paper clip back and forth about

20 times through a large angle Immediately place your ger on the paper clip in the bending area This area will bequite warm It may even be hot The strain energy of bend-ing has been converted into heat energy, which cannot beconverted back into strain energy It is lost energy Whenheat energy is lost, it means there is also a loss of kinetic en-ergy Therefore,when damping is increased in a vibratingsystem, there is less energy available to convert into kineticenergy Less kinetic energy means that there is less energyavailable to excite the structure at its natural frequency, so

fin-that the transmissibility Q is decreased Conversely, when

there is a decrease in the damping, this makes more kineticenergy available to excite the structure, so the transmissi-

bility Q is increased.

In general, simple systems that have only a few

struc-tural elements have less damping than more complex

tems that have many structural elements, when both

sys-tems are subjected to the same vibrational environment

Bolted joints usually have a lot of friction and damping at

the bolted interfaces in vibrational environments, so

struc-tures that have many bolted joints usually have high

damp-ing Therefore, a simple beam type of structure usually has

less damping than a more complex plate type structure

Then, a beam structure should have a higher

transmis-sibility Q than a plate structure in the same vibrational

environment The same thinking can be applied to a more

complex box type of structure that has removable bolted

covers to provide access to internal subassemblies The box

type of structure should have more damping than the plate

structure for similar vibrational exposure because the box

structure is much more complex than a plate structure

This means that the box structure should have a lower

transmissibility Q than the plate structure for similar

vi-brational exposure Extensive vivi-brational test data shows

that this is the natural trend for damping in different types

of structures

Higher dynamic forces in a structure typically result

in higher dynamic stresses and higher dynamic

displace-ments This results in higher damping, which reduces the

dynamic transmissibility Q for that system Therefore,

higher acceleration G levels can be expected to result in

lower transmissibility Q values.

Higher natural frequencies result in lower dynamic

dis-placements, when the acceleration G level is held

con-stant, as shown in Eq (8) Lower displacements mean

lower stresses Lower stresses reduce damping Lower

damping increases the transmissibility Q value Therefore,

higher frequencies, at the same G level, increase the

value of Q.

Vibrational test data from different types of structures

can be used to estimate the transmissibility Q values

ex-pected for different types of common systems at the start

of a preliminary vibrational analysis The three most

com-mon types of structures in the order of their complexity are

beams, plates, and enclosed boxes that have bolted covers

The approximate transmissibility Q for these three types

J = 1.0 for a beam type of structure (cantilever or

re-strained at each end),

J = 0.50 for a plate type of structure (supported around

the perimeter),

J = 0.25 for a box type of structure,

fnin Hz is the natural frequency of the structure, and

Gin is the input acceleration G level in dimensionless

gravity units

Sample Problem: Finding the Approximate Q for Beams

and Plates

For example, consider a beam structure whose natural

fre-quency is 300 Hz and input acceleration level is 0.25 G in

a sine vibrational test The expected transmissibility Q is

about 144 Now increase the input acceleration level to

5.0 G The expected transmissibility Q will now drop to

about 37 Next, consider the plate structure for the same

conditions For a 0.25 G input, the Q is about 72 For a 5.0 G input, the Q is about 18.3 Now take the square root

of the 300-Hz resonant frequency for the plate structure,which is 17.3 This shows that a good approximation for the

plate Q (frequently used for PCBs) is the square root of the natural frequency, when the input level is about 5 G (1,2);

Good PCB approximation of Q= fn. (9a)

This demonstration should be taken as a warning

Per-forming vibrational tests at very low input acceleration G levels will result in very high transmissibility Q values Very low input G levels are often used to prevent dam-

age to prototype PCBs These types of tests are not valid

for evaluating PCBs that must operate at much higher G

levels Vibrational tests should be run on prototypes

us-ing the correct input G levels to verify the correct dynamic

characteristics of the test specimen and future productionmodels

METHODS FOR EVALUATING VIBRATIONAL FAILURES

Vibration can cause failures in many different types ofstructures ranging from earthquakes and airplanes to elec-tric knives and washing machines Vibrational failures areoften experienced during vibrational tests to evaluate thereliability of a product Sinusoidal vibration is very use-ful in tests to diagnose the cause of specific structural vi-

brational failures, to determine the transmissibility Q of

a structure, and to find the fatigue life of different types

of structures A very effective device that is often used insinusoidal vibrational tests is the strobe light This oftenallows the observer to see just how structures bend andtwist during resonance This information can be critical

in determining why and where a structure will fail Stepscan then be taken to modify the structure to prevent futurefailures

Finite element modeling (FEM) programs are availablefor use with new high speed small PCs that can gener-ate models of very complex structural systems When thecomputer models are generated by skilled engineers, thedynamic results from the model are often very similar tothe actual vibrational test results The problems most of-ten encountered in these areas are the types of models thatare generated by individuals who are familiar with FEMbut do not have any real testing experience The resultingstructural models may look good, but their vibrational re-sponse will often have gross errors due to improper bound-ary conditions and to improper damping values These pa-rameters can be obtained only from extensive vibrationaltesting experience (1)

Vibrational failures are often difficult to trace

Some-times the failures result from poor design, poor

mainte-nance, or poor manufacturing processes Very often the

failures are a combination of all three These failures are

usually difficult to trace because it is often very difficult to

get the information necessary to implement any corrective

action

DETERMINING DYNAMIC FORCES AND STRESSES

IN STRUCTURES DUE TO SINE VIBRATION

Dynamic forces in a structure can be obtained from

New-ton’s equation where force F is equal to mass m times

ac-celeration a When weight W is used with the acac-celeration

of gravity g, and structural accelerations are in terms of

dimensionless gravity units G, the following relationships

When the dynamic transmissibility Q is included in this

equation and the input acceleration level is shown in

di-mensionless gravity units Gin,then the maximum output

(or response Fout) dynamic force due to sine vibration is

obtained:

Sample Problem: Finding the Natural Frequency,

Transmissibility Q, Dynamic Force, Displacement,

and Stress in a Beam Excited by Sine Vibration

Consider the simply supported (hinged) weightless

alu-minum beam, shown in Fig, 7, that has a modulus of

elas-ticity E of 7 238 × 1010Nm2(10.5 × 106 lb/in2), a

concen-trated load W of 8.896 N (2.0 lb) acting at the center of the

beam, a length L of 0.203 m (8.0 in), a cross-sectional width

of 0.0305 m (1.2 in), a thickness of 0.0127 m (0.50 in), and

an area moment of inertia of 5.206 × 10−9m4(0.0125 in4)

Find the natural frequency, the transmissibility Q, the

maximum expected dynamic force, the dynamic

displace-ment, and the maximum expected bending stress in the

beam due to a 5-G sine vibrational input.

W

L

L2

Figure 7 Simply supported beam that has a concentrated load

at its center.

Beam Natural Frequency The beam natural frequency

can be obtained from the static displacement Ystof a beamthat has a concentrated load, using standard beam equa-tions from a handbook (1):

num-Beam Transmissibility Q The transmissibility Q for the

beam in a 5-G input sine vibrational environment can be obtained from Eq (9), where J = 1.0 and the natural fre- quency is 246 Hz This results in a Q value of about 31.5.

Dynamic Output Force on Beam The dynamic force

act-ing on a beam can be obtained from Eq (12); the given

concentrated load is W, the sine input level is 5 G, and the transmissibility Q is 31.5 This results in an output force

of 1401 N (315 lb)

Single Amplitude Dynamic Displacement of Beam The

single amplitude dynamic displacement at the center ofthe beam can be obtained by using Eq (8) and adding the

transmissibility Q for sine vibrational, as shown in Eq.(14) See Eq (8) for values of A.

Y0= AGinQ

For a 5-G sine input, a transmissibility Q of 31.5 and

a natural frequency of 246 Hz, the single amplitude placement is expected to be about 0.000645 m (0.0254 in)

dis-Maximum Dynamic Bending Stress in Beam for Sine Vibration Equation (15) gives the dynamic bending stress

Sb.Stress occurs at the center of the beam, as shown inFig 8 A dimensionless geometric stress concentration fac-

tor (k) should be included when machined parts will be

exposed to tens of thousands of stress reversals in tional environments These types of fabricated parts usu-ally have small defects in the form of cuts, scrapes, andscratches, which are known as stress risers or stress con-centrations These defects increase the magnitude of thelocal stresses which reduces the fatigue life of the struc-

vibra-ture The stress concentration must be used only once It

can be used directly as shown in Eq.(15), or it can be used

L

R

Shear diagram

Bending momentdiagramM

R

Wd

Figure 8 Shear and bending moment diagram for a beam that

has a concentrated load.

to modify the slope of the fatigue curve shown in Eqs (18)

and (19), but not in both places

Sb= kMc

A stress concentration factor of about 2 is a good place to

start preliminary stress investigations The dynamic

bend-ing moment M can be obtained from the geometry of the

beam, using the reaction force R, as follows:

Because of symmetry, the reaction R will be half of the

dynamic load or 700.5 N (157.5 lb) Using a length L of

0.203 m (8.0 in) results in a bending moment of 71.1 N m

(630 lb in) The c distance is half the beam thickness, or

0.00635 m (0.25 in) Using the value of 5.20 × 10−9 m4

(0.0125 in4) for the moment of inertia from Eq (13) and

substituting it in Eq (15) results in a dynamic bending

stress of 1.737 × 108N/m2(25,200 lb/in2)

DETERMINING THE FATIGUE LIFE IN A SINE

VIBRATIONAL ENVIRONMENT

Accurate fatigue properties of materials that have varying

stress concentrations are very difficult to obtain Figure

5 shows there is a great deal of scatter in typical fatigue

data The normal method for calculating the approximate

fatigue life from a known stress value is to use the S–N

(stress versus number of cycles to failure) curve for the

particular material involved in the investigation If the

fa-tigue properties of the materials are unknown, then the

fatigue life cannot be calculated Tests should be run on

prototypes or on structural members to establish their

fa-tigue properties If the fafa-tigue properties of the materials

are not known, then there is a very great risk of many

fa-tigue failures in production units that will be exposed to

vibrational environments

When the fatigue properties of the materials are known,

these properties are often plotted using a sloped line on a

log–log curve The typical fatigue curve for the aluminum

Figure 9 S–N fatigue curve for a smooth specimen of 6061 T6

), as obtained from Eq (15) The followingfatigue damage equations can be used in several different

ways to obtain the fatigue life of the structure; t is time and Z is displacement:

The slope b of the fatigue line can be obtained by

mod-ifying Eq (17) and using the Fig 9 reference break points

in the following equation:

), and S1be 1.034 × 108N/m2(15,000 lb/in2).Substitute in the preceding equation for the slope:

0.477 = 11.95 (slope of fatigue line). (19)

The b exponent was obtained without any stress

con-centration or safety factor in the material stress A stress

concentration or safety factor should always be used in

vi-bration Sometimes, it is more convenient to use a stress

concentration (typically 2) directly in the stress value, as in

Eq (15) Sometimes it is more convenient to use the stress

concentration in the S–N fatigue curve Either method can

be used, as long as the safety factor is not used twice If a

safety factor of 2 is used in the S–N fatigue curve, the value

of the b exponent is typically 6.4 for nonferrous alloys and

8.3 for ferrous alloys

The approximate fatigue life of the vibrating beam can

be obtained from the bending stress level 1.737 × 108N/m2

(25,200 lb/in2) which was obtained from Eq (15) Use

reference points N1 at 5× 108 cycles and S1 at 1.034 ×

108N/m2(15,000 lb/in2) at the right break point in Fig 9

This results in the number of cycles to failure:

246 Hz for a sine resonant dwell condition can be obtained

EFFECTS OF HIGH VIBRATIONAL ACCELERATION LEVELS

High vibrational acceleration levels can result in many

dif-ferent types of failures in difdif-ferent types of systems High

vibrational acceleration levels can be generated by

earth-quakes, explosions, aircraft buffeting, gunfire, unbalanced

rotating devices, rough roads, and rough tracks, to name a

few Vibrational isolators are often used in the foundations

of large buildings to protect them from earthquakes

Vibra-tional isolators are often used on military naval ships and

submarines to protect sensitive equipment such as

elec-tronics from explosions When vibrational isolation

sys-tems cannot be used, then brute force methods must be

used to reinforce structural elements to keep them from

failing The method of reinforcing often results in very

large, heavy, and expensive products

High vibrational acceleration levels can be caused by

high input acceleration levels, by severe coupling between

adjacent structural elements, and by very low damping in

the structure High vibrational acceleration levels are often

caused by careless structural designs, where the natural

frequencies of closely linked structural members are very

close together When this happens, the transmissibilities of

the adjacent structural elements multiply, they do not add.

This can cause very rapid failure in almost any structure

High accelerations in electronic systems can result in

large PCB deflections, which can cause impacting between

PCBs, high stresses, and rapid failures in the electrical

lead wires and solder joints of the components mounted on

the PCBs, when the PCBs are forced to bend back and forth

thousands of times High PCB displacements can break

pins on electrical connectors and cause electrical short

circuits and cracked components High acceleration levelscan cause relays to chatter, crystal oscillators to malfunc-tion, potentiometers slugs to slip, electrical failures, andcracked castings Cables and harnesses can whip aroundcausing wires and connections to fail

MAKING STRUCTURAL ELEMENTS WORK SMARTER

IN VIBRATION

One of the biggest problems in structures exposed to tion is severe coupling between adjacent structural mem-bers PCBs mounted within a chassis or an enclosure are agood example When the enclosure has an input vibrational

vibra-acceleration level of 10 Gs and a Q of 10 and the PCBs have

a Q of 10 and a natural frequency close to the enclosure, the

PCBs experience acceleration levels of 10×10×10 or 1000

Gs Acceleration levels this high cause electronic failures

in just a few seconds

Using the Octave Rule to Improve Vibrational Fatigue Life

One way that structures can be made to work smarter is

to design them to follow the octave rule Octave means todouble When adjacent structural members have naturalfrequencies that are separated by an octave, or by a factor

of 2 to 1, they cannot experience severe coupling

It does not matter if the natural frequency of each PCB

is two (or more) times greater than the natural frequency ofthe outer housing or if the natural frequency of the outerhousing is two (or more) times greater than the naturalfrequency of each PCB As long as the natural frequencies

of these adjacent structural members are separated by aratio of 2 (or more), there will be a large reduction in the

coupling between them, as long as the weight of the PCB

is very small compared to the weight of the housing If high

shock levels are also expected, then it is best to use the

reverse octave rule The reverse octave rule applies when

the natural frequency of the outer housing is two (or more)times greater than the natural frequency of any PCB (1)

The reverse octave rule works only in dynamic systems

where the weight of each PCB is much smaller than theweight of the outer housing (or enclosure) Much smallermeans by a factor of 10 or more In other words, the weight

of the enclosure must be more than ten times greater thanthe weight of any one PCB in that enclosure If this ratio isnot followed, severe dynamic coupling can occur and causeproblems

There are never any problems using the forward octave

rule, where the natural frequency of each PCB is two ormore times greater than the natural frequency of the outerenclosure This works well no matter what the weight ratio

is between the PCB and the enclosure Each PCB can weighfour times more than the enclosure, or the enclosure can

weigh four times more than any PCB Using the forward

octave, there is never a severe coupling problem Whenthe weight of any one PCBs is less than about one-tenth

the weight of the chassis enclosure, the reverse octave rule

works a little better in high shock environments

The octave rule can be very effective in reducing brational and shock dynamic coupling acceleration levels

vi-in plug-vi-in types of PCBs vi-installed vi-in a chassis enclosure.

When properly used, the octave rule is almost always more

effective than damping in reducing the acceleration G

lev-els transferred from the chassis to the internal PCBs The

dynamic acceleration G response of the chassis, which is

usually the first degree of freedom, will be the dynamic

input to the PCBs, which is usually the second degree of

freedom Transmissibility Q values that are transferred

from the chassis to the PCBs do not add, they multiply

Vibrational test data and computer-generated dynamic

analyses have shown that the octave rule can reduce the

acceleration G levels transferred from the chassis to PCBs

by as much as 75% When the natural frequencies of the

chassis and the internal PCBs are close together, a good

constrained layer damping system will reduce the

acceler-ation G levels transferred to the PCBs by only about 15 to

20% (See (1), Figs 7.2–7.5 and Fig 7.8.)

When a constrained layer damping system is added to a

plug-in type PCB, some electronic components have to be

removed to make room for the damper When a stiffening

rib must be added to a plug-in type of PCB to increase its

natural frequency so that it follows the octave rule, some

electronic components may have to be removed to make

room for the stiffening rib A stiffening rib will take up

much less room on a PCB that a good constrained layer

damper Test data and past experience in damping and

stiffening for PCBs to increase their vibrational reliability

and fatigue life has shown that increasing the PCB natural

frequency has almost always been the better choice

Equation (14) shows that dynamic displacements are

inversely related to the square of the natural frequency

This is a general relationship that applies to almost every

type of structure exposed to dynamic vibration, shock, and

acoustic environments Consider the case where the input

acceleration G level is held constant and the

transmissibi-lity Q value is approximated by Eq (9a) as fn When the

PCB natural frequency is doubled, the resulting dynamic

displacement of the PCB will be reduced:

The fatigue life of the structure will increase because

the displacement is reduced, which reduces the stress in

the same proportion for a linear system The fatigue life is

strongly related to the b fatigue exponent slope of the S–N

fatigue curve shown in Fig 5 and in Eq (17)

For a smooth polished structure that has no stress

con-centrations where k= 1, Eq (19) shows that the exponent

b for materials used in electronic assemblies has a value of

about 11.95 However, real structures almost always have

some type of stress riser or stress concentration A

typi-cal stress concentration value k for electronic structures

is about 2 This results in a value for the b fatigue

expo-nent slope of about 6.4 This means that the vibrational

fatigue lives of typical electric components, their electrical

lead wires, solder joints, fasteners, electrical connectors,

and circuit traces on plug-in type of PCBs are increased

when the natural frequency is doubled However, doubling

the PCB natural frequency uses up the fatigue life twice

as fast This must be considered when the fatigue life provement is evaluated;

im-Fatigue life improvement=

2.836.4

2 = 389 times

(21b)Various damping techniques have been applied verysuccessfully in reducing the displacement amplitudes andstresses in tall buildings and long suspension bridges sub-jected to earthquakes and high winds Damping is alsoused extensively to reduce noise levels in air ducts, au-tomobile panels, washing machines, fan-cooled electronicsystems, and aircraft jet engines Damping, however, hasnot been used extensively to increase the dynamic fatiguelife of plug-in types of PCBs because of cooling problems,repair costs, and changes in material damping properties

at high temperatures

A large midwest electronics company won a large tract to supply an electronic system that was required tooperate in a severe vibrational environment A decisionwas made to use viscoelastic damping materials for plug-in

con-PCBs to reduce the vibrational acceleration G levels

act-ing on the PCBs Each plug-in PCB module consisted oftwo circuit boards bonded together, back to back, using theviscoelastic damping material Vibrational tests were run

on prototypes to verify the reliability and fatigue life ofthe proposed design The tests were very successful, so thecompany went into full production using the viscoelasticdamped plug-in PCB modules One of the production elec-tronic assemblies was selected for the vibrational qualifi-cation test required by the contract The qualification testrequired the electronic system to be operating so that anyelectrical failures could be observed immediately The vi-brational qualification test was a disaster Electronic com-ponent parts were breaking loose and flying off the PCBs.The engineers were stunned The vibrational tests on theprototype viscoelastic damped PCBs were very successful.What happened? The engineers went back to their proto-type test modules and repeated their previous vibrationaltests Their tests were successful once again One of theengineers noted that the vibrational tests on their pro-totypes were run at room temperature They decided torepeat the vibrational tests on their prototype models at

an elevated temperature that simulated the temperaturesexperienced by the electrically operating production as-sembly The elevated temperature vibrational tests on theprototype models were a disaster Electronic componentswere breaking loose and flying off the PCBs The elevatedtemperatures had sharply reduced the damping properties

of their viscoelastic material, so that their design failed.The company was still under contract to deliver productionelectronic systems that could pass the vibrational require-ments while they were operating electrically The companyhad to redesign the electronic system and rerun proto-types at elevated temperatures to prove the new designintegrity They had to scrap the old production systems,retool for the new systems, and go into production to fulfilltheir contract requirements without change in the contractprice The company lost a substantial amount of money onthat contract, and several engineers had to look for newjobs

The octave rule can increase the vibrational fatigue life

of a system and reduce the size, weight, and cost of the

equipment at the same time Once this rule is followed,

it becomes possible to make PCB materials work smarter

This can be accomplished by understanding the

relation-ships between the dynamic forces, displacements, stresses,

and fatigue life of the materials used in fabricating and

as-sembling electronic systems A great deal of information

re-lated to eigenvalues (natural frequencies) and eigenvectors

(mode shapes) can be obtained by using one of the many

finite element analysis (FEA) programs available

Accu-rate dynamic stress levels in various structural members

and approximate fatigue life in different environments are

much more difficult to obtain from any FEA program This

cannot be done by analysis alone An extensive amount

of vibrational test data is required, where several similar

electronic assemblies are vibrated until they fail The failed

parts are then examined closely to evaluate the physics of

the failures The test data are then combined with the FEA

dynamic analysis and fatigue theory This method of

eval-uation can result in eqeval-uations that show what minimum

natural frequency a rectangular plug-in PCB should have

to achieve a fatigue life of about 10 million stress cycles in

a sinusoidal vibrational environment The physical

prop-erties of the circuit board materials, electronic component

materials, solder joint materials, and the effects of

surface-mounted and through-hole assembly practices must be

un-derstood to make these materials work smarter

Finding the Maximum Allowable PCB Dynamic

Displacement for Sine Vibration

Test data for sine vibrational environments are used to

es-tablish maximum allowable dynamic displacements Zmax

for PCBs to achieve a 10-million cycle life This is based on

the size of the PCB, the types and sizes of the electronic

components, and the location of these components on the

PCB The following equation includes an added safety

fac-tor of 1.3 to ensure the effective fatigue life of each PCB

U = 8.90 × 10−7 metric (2.20 × 10−4 English)

B in m (in), the length of the PCB parallel to the length

of a component

h in m (in), thickness of the PCB

L in m (in), the length of an electronic component

C is a component type constant, metric and English

1.0 for a standard dual inline package (DIP)1.26 for a DIP using side brazed lead wires1.26 for a pin grid array (PGA) or hybrid that hastwo parallel rows of wires extending from thebottom surface of the component

1.0 for a PGA that has wires around the ter extending from the bottom surface of thecomponent

perime-2.25 for a leadless ceramic chip carrier (LCCC)

1.0 for a leadless chip carrier that has J leads orgull wing leads

0.75 for axial leaded devices such as resistors andcapacitors

1.75 for ball grid array (BGA) components

r is a relative positional factor for components mounted

on a rectangular PCB supported around its ter, metric and English

perime-1.0 when the component is mounted at the center

of the PCB at x = a/2 and y = b/2

0.707 when the component is mounted off the

cen-ter of the PCB at x = a/2 and y = b/4

0.50 when the component is mounted at the quarter mounting points off the center of the

one-PCB at x = a/4 and y = b/4

Extensive vibrational test data on different types ofPCBs have shown that the electronic component lead wiresfail far more often than their related solder joints inthrough-hole mounted devices Surface-mounted compo-nents experience a small increase in the solder joint fail-ures, but again, the greatest number of failures occur inthe lead wires (1,2)

Combining Eq (22) with Eqs (8) and (9a) results in

the following equation for the minimum desired natural frequency fd that a PCB must have to provide a fatiguelife of about 10 million stress cycles for the most criticalcomponents and their lead wires in a sine vibrational en-vironment (1):

Find the minimum desired PCB natural frequency andthe approximate fatigue life for a 0.00157 m (0.062 in) thickPCB that has a hybrid 0.0508 m (2.0 inch) long made of twoparallel rows of pins extending from the bottom surface

(C = 1.26) The hybrid is mounted at the center of a 0.152 m

(6.0 in)× 0.203 m (8.0 in) rectangular plug-in PCB, parallel

to the 0.203 m (8.0 in) edge The PCB must operate in a

5.0-G peak sine vibrational environment Substituting in the

preceding equation for metric or English units results in aminimum desired natural frequency of 210 Hz

The approximate fatigue life for a resonant dwell dition can be obtained from the expected 10 million cycle

con-fatigue life for sine vibration, as follows:

High vibrational and shock accelerations can produce high

dynamic displacements in structural members, which can

cause very rapid failures These high displacements can

of-ten be reduced by using snubbers Snubbers are small

de-vices that can be added to adjacent structural elements to

make them act smarter by limiting their dynamic

displace-ments When these snubbers are properly placed, they

leave only small clearances between the adjacent

snub-bing members, so that the snubbers strike each other

The striking action between the snubbers reduces the

dy-namic displacements, forces, and stresses in these

struc-tures and results in increased fatigue life [See (1), Figs

7.6 and 7.7.] Snubbers can be made from different grades

and shapes of rubber, nylon, aluminum, or epoxy fiberglass

Rubber snubbers work well on PCBs that have low

natu-ral frequencies below about 50 Hz When the PCB

nat-ural frequency is above about 100 Hz, the resulting

dy-namic displacements are so small that soft rubber does not

work well A harder material, similar to epoxy fiberglass,

works much better Good results have been obtained

us-ing 0.0063-m (0.25-in) diameter epoxy fiberglass snubbers

epoxy bonded directly to the surface of the PCB near the

center Snubbers work well even if they cannot be mounted

at the center of each PCB For a new design, it is

usu-ally possible to leave a small amount of room at the center

of each PCB for mounting snubbers For existing PCBs,

there may not be any room near the center, so the

snub-bers may have to be bonded to almost any convenient space

between the components The snubbers should not be

di-rectly bonded to the electronic components themselves The

snubbers should not be allowed to impact any components

or any protruding lead wires or solder joints on adjacent

PCBs because impact during vibration may cause failures

in these areas (6)

Increasing PCB Stiffness to Decrease

Dynamic Displacements

PCBs are often considered the heart of an electronic

sys-tem because they hold most of the important electronic

components that control the system Large dynamic

dis-placements on PCBs must be avoided in vibrational

en-vironments because they can result in high stresses and

rapid fatigue failures PCBs can be made to act smarter by

increasing their natural frequency This rapidly reduces

the dynamic displacements and stresses and substantially

increases the fatigue life For new PCB designs, it is

of-ten very easy simply to increase the basic thickness of the

circuit board A 10% increase in the basic circuit board

thickness can increase the PCBs natural frequency by 15%,

which can increase the fatigue life of the components by a

factor of about 6

When the basic circuit board thickness cannot be creased, the PCBs natural frequency for a new designcan often be increased to make the PCB act smarter byadding more copper planes to the multilayer board assem-bly Many circuit boards already have at least two full one-ounce copper planes, 0.0000356 m (0.00140 in) thick forground and for voltage The natural frequency can be in-creased by simply doubling the thickness of the copper andadding another two copper planes (which can be called heatsinks), totaling four copper planes The high copper modu-lus of elasticity can increase the natural frequency of thePCB by about 12%, which can increase the component fa-tigue life four times

in-Stiffening ribs are often added to new designs of PCBs

to increase the stiffness and the natural frequency (1).Stiffening ribs can significantly increase the natural fre-quency, but ribs take up room on the PCB, so that fewercomponents can be mounted on it The probability ofadding effective stiffening ribs to existing PCBs is verylow When improved vibrational or shock performance isrequired on existing hardware, a better choice is usingsnubbers

Adding Doublers to Increase Local Stiffness

in Critical PCB Areas

When existing PCBs experience component vibrational tigue failures, it is often possible to make these PCBs actsmarter by increasing the stiffness of the PCB in local areas

fa-of the critical components This can fa-often be done by simplybonding shims (sometimes called doublers) to the criticalareas on the PCB The shims should be fabricated from thesame material as the circuit board Strips about half thethickness of the board should be bonded to both sides ofthe PCB, where possible, under the component on the topside of the PCB and on the back side of the PCB just underthe component Metal shims are sometimes used instead ofplastic shims Metals have a higher modulus of elasticitythan plastics, so they should work better than plastics Theproblem is that metal shims often do not work as well asplastic shims Metals are usually very smooth and hard.Epoxy type adhesives do not adhere well to hard smoothsurfaces, so metal shims often fall off Think of a mountainclimber It is very difficult, almost impossible, to climb asteep mountain without punching holes in the mountain-side to get a better grip If there is no grip, the climber willslip and fall The same holds for metal shims If there is

no grip, they will slip A large shim may require at leasteight small, well separated holes to be punched (or drilled)through the shims to allow the adhesive to flow throughthe holes and form adhesive rivets Tests have shown thatthese plastic rivets will hold metal shims very securely

to PCBs in severe vibrational, shock, and thermal cyclingenvironments

Making Component Lead Wires Work Smarter

by Changing Their Form

Stiff component electrical lead wires have been known tocause lead wire and solder joint failures in vibrational,shock, and thermal cycling environments (2) It is often

Camel hump wirestrain relief

wire loopstrain relief

Figure 10 Electrical lead wire camel hump and wire loop strain

relief.

possible to increase the fatigue life of lead wires and solder

joints by reducing the stiffness of the lead wires This is

the theory behind this observation

The spring rate K of a linear elastic system is defined

as the force P divided by the displacement Y Then, the

force in the system is the product of the spring rate and

the displacement:

When a system has a fixed (or constant) displacement Y,

this equation shows that the best way to reduce the force P

is to reduce the spring rate K A constant displacement

sys-tem occurs in vibration for an existing piece of hardware,

when the natural frequency is known and the acceleration

G level is known Equation (8) shows that the displacement

is fixed (or constant) when the natural frequency and the

acceleration G level are defined.

Most lead wire and solder joint failures in vibration can

be related to the bending action of the PCB, when its

nat-ural frequency is excited The bending action of the PCB

forces the component lead wires to bend as well The spring

rate of a wire in bending can be obtained by treating the

wire as a beam, as shown in Eq (13) Again defining the

spring rate as the load divided by the displacement and

ig-noring the parameters that define the beam end restraints,

the spring rate of the bending wire is:

K= EI

An examination of this equation shows that the easiest

parameter to change is the length L of the wire Because

this is a cubic function, a small change in the length of

the wire produces a large reduction in the spring rate of

the wire It is often very easy to increase the length of the

wire by looping it, adding camel humps in it, or simply

by adding a small kink in the wire, as shown in Fig 10

Another popular method for reducing the spring rate of

the wire is to coin the wire In this process, the wire is

squeezed from a round cross section to a flat cross section

This reduces the area moment of inertia I which reduces

the spring rate but not the area

HOW STRUCTURES RESPOND TO RANDOM VIBRATION

Random vibration contains many different frequencies

si-multaneously across a broad frequency range This means

that all of the natural frequencies in a structure that

are within the bandwidth of the random vibration will be

vibra-G2/Hz is plotted on the y axis and frequency in Hz is ted on the x axis, as shown in Fig 11 The square root of

plot-the area under plot-the curve represents plot-the root-mean-square

(rms) of the acceleration level Grms,(1):

√Area=

ability of the value of instantaneous accelerations at any

time The Rayleigh distribution, which is the probability

of the distributions of peak accelerations, is also used The argument here is that peak forces and stresses cause fail-

ures A combination of these two functions, which is known

as the three-band technique (1), is a Gaussian skewed ward a Rayleigh This method is convenient for obtainingquick and relatively accurate solutions to random vibra-tional problems without using a computer In the three-band technique, the rms represents the one-sigma (1σ) ac-

to-celeration G level The two-sigma (2 σ) acceleration G levels

are two times greater than the rms G level The

three-sigma (3σ) acceleration G levels, which are the maximum

levels expected for the Gaussian distribution, are three

times greater than the rms G level The percentage of time

that these levels occur in the three-band technique are asfollows:

1σ values occur 68.3% of the time;

3σ values occur 4.33% of the time.

Response of PCBs in Random Vibrational Environments

PCBs operating in random vibrational environments can

be evaluated accurately as single-degree-of-freedom

sys-tems (1) The G rms response for the PCB can then be obtained from the input psd value in G2/Hz, the natural

Table 1 Fatigue Cycle Ratio n/N

Environment Sine Vibration Random Vibration Thermal Cycles

The maximum allowable dynamic displacement Zmaxfor

the PCB can still be shown by Eq (22) for random vibration

The PCB fatigue life for random vibration is now expected

to be about 20 million stress cycles Because the maximum

random displacement is based upon the 3-σ value, Eq (8)

must be multiplied by 3 Now Eqs (8) and (22) can be

com-bined with Eqs (9a) and (29) to obtain the minimum

de-sired PCB natural frequency for a component fatigue life

of about 20 million stress cycles:

natural frequency), (30)where

V = 0.744 metric (29.4 English)

U = 8.90 × 10−7metric (2.20 × 10−4English)psd= G2/Hz, power spectral density input, metric

(English)

Sample Problem—Finding the Minimum Desired PCB

Natural Frequency

Use the same physical dimensions for the PCB, as shown

in the sine vibrational sample problem following Eq (23),

except use a PCB length of 0.228 m (9.0 in), parallel to the

component length, and a random vibrational psd input of

0.10 G2/Hz in the area of the PCB natural frequency This

results in a minimum desired natural frequency of about

Find the Maximum Expected Displacement for the PCB

The maximum displacement expected for the PCB can beobtained from Eq (8), which results in a dynamic displace-ment of 4.54 × 10−4m (0.0179 in)

MINER’S CUMULATIVE DAMAGE FOR ESTIMATING FATIGUE LIFE

Miner’s cumulative damage theory states that every time

a structure experiences a stress cycle, part of its life is used

up This is shown as a series of ratios where the actual

num-ber of stress cycles (n) is divided by the numnum-ber of cycles required to produce a failure (N ) for many different stress

environments When the total of all of the ratios equalsone, all of the life will be used up, so the structure will fail.Miner’s method can be used to add up all of the damage ac-cumulated in sine vibrational, random vibrational, shock,acoustic noise, and thermal cycling environments Miner’s

significant power change there is a significant temperature

change, which is considered a thermal cycle

Fatigue failures are difficult to predict because of the

typically wide scatter in the fatigue life test data available

To ensure the reliability of the electronic systems in a

mili-tary aircraft, it is good policy to include a scatter factor, or

safety factor, in the design and analysis of these systems

Therefore, a scatter factor of 2.0 will be used to evaluate

the fatigue life for the electronics The normal design life

for a military aircraft is about 10 years or 10,000 flying

hours Using a scatter factor of 2.0, the fatigue life of this

electronic system will be designed for an operational time

of 20,000 hours

R n = 0.091 + 0.501 + 0.182 = 0.774 (35)The cumulative damage ratio is less than 1.0, so the elec-

tronic design is acceptable

3 MIL-Handbook-5A, Metallic Materials And Elements For

Aerospace Vehicle Structures, Department of Defense,

Washington, DC

4 R.E Peterson, Stress Concentration Design Factors J Wiley, NY

1959.

5 D.S Steinberg, Mach Design Mag., May 25, 1989.

6 D.S Steinberg, Mach Design Mag., March 24, 1977.

VIBRATIONAL DAMPING, DESIGN

This article discusses the phases of a damping design

ef-fort The basic steps in a damping design effort are

identi-cal for either a passive or active damping concept The steps

in this general approach are summarized in Table 1 The

first four steps in this design process ensure that the

de-signer completely defines the problem to be solved During

these steps, the designer verifies that the problem is the

result of a resonant vibration, defines the vibrational

char-acteristics of the structure under consideration, defines the

environmental conditions in which the structure operates,

and defines the level of damping required to solve the

prob-lem These parameters are obviously needed because an

effective design for the candidate damping concept (either

active or passive) depends on the level of damping required,

the frequency and mode shape, and the operational

tem-perature range of the vibrating system Based on these

parameters, the problem is completely defined, and the

designer can make a logical choice of appropriate ing concepts to be evaluated that lead to the final design(1–3)

damp-Although this design approach identifies individualsteps, these steps are not independent A successful damp-ing design project is a systems engineering problem andmust be solved using a concurrent engineering process.Most unsuccessfully damping designs are the direct result

of not addressing all of the critical issues in a timely ner The following paragraphs detail the critical tasks con-tained in each of the process steps and present examplesfrom actual case histories of the way various issues wereaddressed

man-DYNAMIC PROBLEM IDENTIFICATION

The proper initial step in solving any problem always

is first completely defining the problem This fact holdstrue when attempting to solve a vibration-induced prob-lem by using damping technology Therefore, the first step

in this damping design approach is to substantiate that theproblem to be solved results from structural resonance Ifthe vibration problem is not due to structural resonance,then a damping design will not be effective

In a new structural system design, the designer mustobtain the anticipated force input or excitatory environ-ment for the system and correlate the frequency content

of this information with the results of a natural frequencyanalysis of the structure (4) If there are natural frequen-cies within the frequency band of the excitation expected,the designer has identified the potential for dynamics prob-lems These dynamic problems must be evaluated to deter-mine if the vibrations will keep the system from fulfillingthe intended purpose

If a problem develops in an existing part, the designermight choose one of the following approaches to identifythe problem

When a component cracked, a crack analysis should berun to verify that the crack is a high cycle fatigue failure

An instrumented operational test of the component shouldalso be run to identify the frequencies and vibrationallevels of the problem Operational deflection patterns alsocan be defined to support the identification of the modeshapes encountered This operational test can be run usingstrain gauges or accelerometers for measurements Theuse of thermocouples enables one to obtain peak vibra-tional levels and corresponding temperature data, as well

as maximum operating temperature data

If the problem under consideration is a high-noise diative problem, an operating evaluation should be done

ra-to determine both the frequencies and magnitudes ofthe noise being radiated and the source of radiation (5)

An unacceptable vibrational level environment problemshould be attacked in the same basic manner as the noiseproblem

As a result of these investigations, the designer has termined the operating dynamic cause of the problem andthe resonant frequencies that are developing the high dy-namic response

de-Table 1 General Approach Steps

1 Verify that the problem is resonant vibration induced

2 Complete dynamic analysis of the system determining resonant frequencies,

mode shapes, and system damping

3 Define the environmental conditions in which the system operates

4 Define the system damping required to eliminate the problem

5 Select the appropriate damping concept and basic damping configuration

6 Develop the required design from the data collected

7 Prototype the design and complete laboratory verification tests

8 Develop tooling and manufacturing methods and complete field validation tests

DYNAMIC CHARACTERISTICS

A successful damping design is developed from a complete

understanding of the dynamic behavior of the structural

system and the component to be damped Generally, a

fre-quency range across which dynamic information is needed

is defined from the analysis completed during the first

step The dynamic range can be defined from operational

testing or can be determined from knowledge of the

sys-tem under consideration For example, problems such as

a component where the excitation forces are known to be

engine-order related, low frequency excitation from road

roughness to the suspension system, or acoustic excitation

to aircraft fuselage components due to jet engine exhaust

all enable rapid determination of the excitatory frequency

range Once a frequency range is defined for the problem,

a complete dynamic structural characterization must be

completed One must accurately determine all of the

reso-nant frequencies, corresponding structural mode shapes,

and inherent modal damping values that occur in the

re-quired frequency range This data can be obtained

analyt-ically or experimentally

If a prototype is available in the early structural design

stages, the optimum solution for data acquisition is

experi-mental analysis of the prototype structure used to refine

analytical models These models are then used for further

component damping design evaluation (6)

Often, when a damping application is used as a

re-design approach, the necessary dynamic characterization

can be acquired efficiently by using modern experimental

methods Experimental methods can quickly determine the

data needed for a highly complex structural system;

how-ever, measurements on operating systems can often be

ex-tremely difficult and costly

The Fourier analyzer is a powerful experimental tool

available to do the experimental work; however,

holo-graphic methods for determining mode shapes and

stan-dard sine sweep methods for resonant frequencies and

modal damping values are extremely useful (7–9) The

de-signer must choose the most expedient method for

deve-loping the required data

ENVIRONMENTAL DEFINITION

A major data point needed in the quest for an optimally

designed damping application is the operational

environ-ment that the design will see This data, at first thought,

might seem to be a rather simple task, but the importance

of accurate information cannot be overstressed This datamust cover the entire life of the damping concept from fab-rication through operation

A broad-brush approach to temperature, such as thestandard temperature range of −65 to 250% for opera-tion of many aircraft components, is not the answer Thisrange may be the maximum range seen by the component;however, it will not generally be necessary to provide highdamping across this entire range The engineer must de-termine the specific temperature range across which thedamage is occurring and design his application for thatrange while maintaining a total awareness of the requiredsurvivability temperature range Time-related recordings

of vibration and temperature data from operating testsare used to determine the temperature range across whichdamaging vibrational levels occur Operating tests can alsosupply the necessary maximum temperature limits to beused in the design If temperature data from a large num-ber of different operating tests are available, a statisti-cal study of the data will reveal the temperature range inwhich the majority of operating time is spent An example

of this type of data is shown in Fig 1 illustrating minimumand maximum temperatures along with the percentage oftotal operating time spent in each temperature range It

is easy to see the value of this type of data, particularly

if vibrational level and temperature data cannot be taneously obtained for operating conditions

simul-In the early stages of system design, complete operatingtemperature data may not be available Then, data from

35302520151050

Temperature

Figure 1 Percentage of flight time spent in various temperature

ranges during 500 flight hours.

similar systems should be reviewed, and the best estimates

of temperature should be developed and used in the design

procedure

Temperature is not the only environmental factor that

must be considered The engineer must know if the

appli-cation will come in contact with contaminants such as salt

water, gasoline, jet engine fuel, hydraulic fluid, or any other

substance that might affect the performance or longevity

of the candidate damping concepts (10,11)

When the damping concept will be integrated into the

structural system and installed during the structural

sys-tem manufacturing process, the damping concept

compo-nents must be able to survive manufacturing processing,

including temperatures, pressures, and processing

REQUIRED DAMPING INCREASE

The remaining question to be answered before a damping

design can be started is “How much damping is needed to

eliminate the problem?” In the “fix-it” damping business,

the general approach found in the literature is to design

an optimum damping system and test it in service If the

failures are eliminated, the problem is solved In reality,

the designer wants the minimum value of system damping

that will eliminate the vibrational problem If the damped

design accomplishes just the minimum required damping

using an optimum damping system, the design also should

be optimized from the standpoints of weight, size, and cost

The method for determining the minimum required

sys-tem damping depends on the problem to be solved The

inherent system damping has been determined from the

dynamic characterization The corresponding vibrational

problem (high dynamic stress, noise level radiated, high

dynamic amplitude response, etc.) is directly related to the

inherent damping Quick calculations can be made to

de-termine the required increase in system damping to

elim-inate the vibrational problem Basically, if a 20% decrease

of system response is needed, then the system damping

needs to be increased 20% If an analytical model has been

developed, an analysis can be conducted to verify the value

of system damping needed to eliminate the vibrational

problem

Table 2 presents values of typical system and material

damping for various structural systems and structural

ma-terials (4)

DAMPING CONCEPT SELECTION AND

APPLICATION DESIGN

Until this point, the primary function of the designer has

been to develop an accurate and complete definition of the

resonant vibrational problem Now, it becomes a simple

matter to determine which resonant modes of the

compo-nent are creating the vibrational problem This

informa-tion defines the frequencies that need to be damped, the

corresponding mode shapes, and the undamped modal loss

factors The required level of damping and the

environmen-tal conditions complete the data required to start defining

appropriate damping concepts and analyzing the

effective-ness of the concepts

Table 2 Typical Damping Values at Room Temperature

Systems/Materials Loss Factor Welded metal structure 0.001 to 0.0001 Bolted metal structure 0.01 to 0.001

Often, the temperature range for effective damping andthe survivability temperature limits are evaluated first Ifthe survival temperature is above 400◦F, most organic pas-sive damping materials and many of the piezoelectric ma-terials are eliminated from consideration Therefore, if youhad a requirement for damping in the 100◦–300◦F rangeand a survival temperature of 600◦F, most constrainedlayer and free layer damping materials and piezoelectricmaterials would be ruled out

The next consideration is the mode shapes of the nant frequencies that must be damped Free-layer andconstrained-layer passive damping concepts and inducedstrain actuation active damping concepts are effective fordamping “plate-like” modes that have large areas of bend-ing deformation Highly localized strain distribution willnegate the effectiveness of these damping concepts An ex-ample of the localized strain condition is discussed in (12).The high-cycle fatigue cracks initiated in the corner areas

reso-on the antenna are shown in Fig 2 For the mode rating the failure, all of the strain was concentrated in thecorners, and the rest of the cone area was moving in arigid body motion As a result, layered passive concepts andpiezoelectric induced strain active concepts were notapplicable The displacements of the mount were such that

gene-a displgene-acement-sensitive concept such gene-as gene-a pgene-assive tuneddamper or an active reaction mass concept could eliminatethe problem In this case, a passive design was used

High strain area

Figure 2 Cross section of the antenna base showing high strain

areas.

Structure without damping

Structure with damping

Forced vibration analysis Adjust damping parameters

Assess compliance data

Figure 3 Basic damping design flow chart.

From the environmental conditions and the dynamic

characteristics, the designer can choose the appropriate

classes of damping concepts for the starting point to design

the specific application for the structure under

investiga-tion The basic principles of passive and active damping

concepts and analysis methods are given in (13–18)

Various design analysis methods are often appropriate

for problems; however, a successful design can be

devel-oped only after all of the basic information discussed

pre-viously is obtained A design flow chart appropriate for

any of the design analysis techniques is given in Fig 3

The dynamic and temperature data are the inputs, and

the output is the structural loss factor The process loops

through the design analysis step until the proper loss

fac-tor is achieved

1.00E+021.00E+031.00E+04

1.00000010.000000

Figure 4 Y966 damping material properties as a function of temperature.

Note also that any successful design must use rent engineering principles and consider, from the begin-ning, the manufacturing methods that will be used to inte-grate the damping concept into the structural system andthe maintenance processes for the damping concept

concur-PROTOTYPE FABRICATION AND LABORATORY VERIFICATION

Once the design is complete, the next step is to fabricate thedesign prototype and verify the design in the laboratory.The fabrication processes used for the prototype should bescaliable to production processes, whenever possible Theseprocesses must not degrade the function of the dampingconcept in any way

Generally, the laboratory test setup is some scaled sion of the total structural system The primary consider-ation in the laboratory test is that the test article has thesame dynamic characteristics as the full structural systemand that the laboratory test environment simulates thecritical operating conditions

ver-The laboratory validation test results should verify theanalytical method used to develop the design Any varia-tion in the comparison of the test results and the modelresults should be evaluated and the test or the model,whichever is found in error, modified After satisfactorycomparisons are obtained, critical analysis for the fieldevaluation test should be conducted

PRODUCTION TOOLING AND FIELD VALIDATION

Production tooling and processes should be refined fromthe process used to fabricate and install the prototypedamping system All lessons learned from the laboratorytesting should be applied to the field test effort

Restating the importance of the problem definition is

appropriate at this point Inaccurate temperature range

data will eliminate any beneficial effects of the damping

concept For passive systems, this effect can be seen in

Fig 4 (dynamic properties of 3M Y-966) where a

temper-ature shift of 100◦F causes a significant reduction in the

material loss factor If the survival temperature limits

are incorrect, the damping concept may well provide the

necessary reduction in the vibration levels, but the concept

will be destroyed by the first overtemperature condition

(19) Guesses at temperature data will invariably lead to

failure of the damping design

The other major area where accurate data are necessary

is the dynamic characteristics of the structural system

un-der investigation Placing a strain-sensitive damping

con-cept on a portion of the structure which is not undergoing

significant strain for a particular mode is as ineffective as

placing a displacement-sensitive concept on a node line of

the mode that you wish to control

As in any design project, successful results require

ac-curate information upon which to base the design

Opera-tional data and dynamic characteristics are the two prime

factors that must be meticulously defined to obtain good

damping design results

BIBLIOGRAPHY

1 S.E Olson, et al., SPIE Smart Struct Mater 1994, Vol 2190.

2 A.J Bronowicki, et al., SPIE Smart Struct Mater 1994,

Vol 2190.

3 M.L Drake, et al 1999 USAF Aircraft Struct Integrity

Program Conf.

4 J Soovere and M.L Drake, Aerospace Structures Technology

Damping Design Guide, Vol 2-Design, Guide,

8 K.A Ramsey, “Effective Measurements for Structural

Dynam-ics Testing,” Sound Vib November 24–35 (1975).

9 M.L Drake and J.P Henderson, “An Investigation of the sponse of a Damped Structure Using Digital Techniques,”

Re-Shock Vib Bull 45 (Part 5): 1975.

10 Flora et al., “Dynamic Analysis and Testing of Damped termodule Plates for the Sigma Laser Device,” ASIAC Report

In-No 1182.1A, November 1982.

11 M.L Drake, ed., University of Dayton Vibration Damping Short Course, Section 4.

12 D.I.G Jones, J.P Henderson, 1/Lt G.H Burns, 13th Ann Air

Force Sci Eng Symp., Arnold Air Force Station, Tennessee, September 27–29, 1966.

13 C.T Sun and Y.P Lu, Vibration Damping of Structural ments Prentice Hall, (1995).

Ele-14 J Soovere and M.L Drake, Aerospace Structures Technology Damping Design Guide Vol 1, 2, and 3, AFWAL-TR-84-3089,

December 1985.

15 A.D Nashif et al., Vibration Damping J Wiley, NY, 1985.

16 C.R Fuller et al., eds Active Control of Vibration Academic

Mechanics, Inc, WIT Press, 2000.

19 M.L Drake, ed., University of Dayton Vibration Damping Short Course, Section 11.

The term Smart Window was introduced in the mid 1980s

by Claes Granqvist to describe optically switchable

elec-trochromic glazings These devices exemplify the

funda-mental characteristic of all “smart windows”: controllable

variation in the optical transmittance of the window The

variation in optical transmittance of electrochromic smart

windows occurs through the simultaneous injection of

elec-trons and ions (usually H+ or Li+ ions) into an

elec-trochromic material such as WO3 In WO3, this leads to

the development of either a broad absorption band or a

reflection edge (depending on the details of the material

preparation) that leads to a low transmittance state The

process is (ideally!) reversible; extraction of the ions and

electrons returns the material to a transparent state The

control of the process is accomplished by applying a small

voltage (1–2 V) (or passing a small current) that controls

ion injection and extraction Since the initial discovery of

electrochromism in thin film WO3 by Deb (1) in 1969, an

enormous amount of research has been directed toward

the goal of large area switchable windows for architectural

applications This initially focused on electrochromic

sys-tems that covered a wide range of materials and device

structures However, during the 1980s and subsequently,

several alternate optical switching systems were developed

that fall into the general category of smart windows These

include other electrically activated systems such as

sus-pended particle devices (2) and phase dispersed liquid

crys-tals (3), temperature controlled switchable devices such as

thermochromic (4) and thermotropic devices (5), and

re-cently developed gasochromic devices that are controlled

by using reducing or oxidizing gas mixtures in a window

unit (5)

ARCHITECTURAL GLAZING APPLICATIONS FOR

SMART WINDOWS

The potential reductions in heating, cooling, and lighting

energy use that can result from using switchable glazings

in buildings has provided the impetus for the majority of

this research More than 675 U.S patents have been filed

in this field since 1976 It is now well established that

re-duced energy consumption of up to 50% is possible from the

use of electrochromic glazings in commercial buildings, and

savings of 20–30% are obtainable in most climatic tions This is also the primary application for thermochro-mic and thermotropic windows that change transmittance

condi-as a function of temperature and therefore can reducetransmittance of infrared radiation (i.e., heat) when thetemperature is high However, some of the other “smart”windows, such as the polymer dispersed liquid crystal(PDLC) devices, do not provide significant energy savingsbut are used as privacy screens To understand the role ofswitching in a smart window, it is necessary to understandthe nature of glazings and the way the optical properties

of a window affect its performance and utility

Physics of Windows

Common to all applications of glazing materials is theneed for transmission of light, and in most applications,reflectivity is also very important To quantify the lighttransmission properties, the transmittance and reflectance

spectra, T ( λ) and R (λ) can be measured and used to define

several different average transmittance and reflectancequantities The most important of these are the solar andvisible transmittance and reflectance:

Tsol=

∞

0

T (λ)ϕsol(λ)dλ

∞

0

R(λ)ϕsol(λ)dλ

∞

0

ϕsol(λ)dλ

,

Tvis=

770370

T (λ)ϕvis(λ)dλ

770370

R(λ)ϕvis(λ)dλ

770370

ϕvis(λ)dλ

,

whereϕsol andϕvisare the solar spectrum and visible sponse of the human eye, respectively Usually, the air mass1.5 solar spectrum is used to define the solar averages, al-though it is not necessarily the most appropriate at alllocations, and there can be significant differences betweendifferent solar spectra (6) The difference in the spectralranges forϕsol,ϕvis, illustrated in Fig 1, immediately givesrise to the concept of spectral selectivity, which is central

re-to many advanced window glazing systems This refers re-tothe ability of a window to transmit, for example, visible

radiation (high Tvis) but to reflect heat (low Tsol and high

Rsol) This is fully explained in Granqvist (7) Therefore,

1134