AAE556 lecture 16 Dynamics and Vibrations

integrating aerodynamics, structures, controls and actuation to create unbeatable systems Aeroelasticity – the challenge the shapes to come New systems, vehicles, shapes, environments &

AAE 556 Aeroelasticity Lecture 16

Dynamics and Vibrations

integrating aerodynamics, structures, controls and actuation to

create unbeatable systems

Aeroelasticity – the challenge the

shapes to come

New systems, vehicles, shapes, environments &

challenges

In the future

• Future aircraft will be

• Multi-purpose and robust

• Automated and robotic

• Semi-to-fully autonomous

• Able to change state

• Aircraft will be able to

• Cope with environmental

change, both man-made

and due to nature

Penetrating Configuration direct radar energy away from frontal threats

Compromised Configuration

Tailored Survivability

Loitering Configuration directs radar energy away from side threats

Penetrating Configuration direct radar energy away from frontal threats

Compromised Configuration

Tailored Survivability

…but the challenges loom large

• Conceptual design of highly integrated

systems with distributed power and actuation

• Redefining aeroelastic stability concepts for structures that lock and unlock, move, stay fixed and then move again

• Calculating loads and transient response

• Developing test plans for multi-dimensional structural configurations

• Assigning risk

Low speed and high-speed flutter

Handley Page O/400

Gloster Grebe

16-5

Unusual flutter has become usual

16-6

Flutter is a dynamic instability

it involves energy extraction

16-7

measured at the shear center from static

equilibrium position

Understanding the origin - Typical section

equations of motion - 2 DOF

Coupled Equations (EOM) are dynamically coupled but elastically uncoupled

Prove it! Lagrange steps up to the plate



 h x x

z(t) is the downward displacement

of a small potion of the airfoil at a

position x located aft of the shear

center

16-10

Kinetic energy integral simplifies

m is the total mass S q is called the static unbalance

Iq is called the airfoil mass moment of inertia – has 2

Equations of motion for the unforced

Diff Eqn trial solution -separable

st

e

h t

t h

substitute into coupled differential eqns.

The eventual result

Natural frequencies change value when

the c.g position changes

I

o o

0.50 0.25

0.00 0 5 10 15 20 25 30 35 40

Natural frequencies vs.

But – we have a derivation first collect terms into a single 2x2 matrix

( )

(

) (

)

(

2 2

2

2

st T

K I

s mx

s

mx s

K m

divide by exponential time term

Matrix equations for free vibration

The time dependence term is factored out

) (

) (

) (

)

(

22

22

T

h

K I

s mx

s

mx s

K m

Determinant of dynamic system matrix

set determinant to zero (characteristic equation)

 s m K2  h   s I2   KT    s mx2    s mx2    0

16-17

2 2

2 2

s I

K s

2 2

2 2

s s

Solution for natural frequencies

2 4

b s

Solution for exponent s

h

2

2 2 2

2 2

solutions for w are complex

2

2

o

o o

o

mx

mr mr

mx

I I

o

x I





16-21

Example configuration

b c

40 0

Natural frequencies change value when

the c.g position changes

I

o o

0.50 0.25

0.00 0 5 10 15 20 25 30 35 40

Natural frequencies vs.