Chẩn đoán vết nứt trong thanh, dầm đàn hồi bằng hàm đáp ứng tần số tt tt tieengs anh

The oscillation parameters commonly used in structural failure diagnosis are specific frequencies and patterns of oscillations or frequency response functions.. In order to avoid the err

ABSTRACT OF DOCTOR THESIS

IN MECHANICAL ENGINEERING AND ENGINEERING

MECHANICS

HANOI - 2019

The thesis has been completed at: Graduate University of Science and Technology - Vietnam Academy of Science and Technology

Supervisions:

1: Prof.DrSc Nguyen Tien Khiem

2: Assoc.Prof.Dr Nguyen Viet Khoa

Reviewer 1:

Reviewer 2:

Reviewer 3:

Thesis is defended at Graduate University of Science and Technology

- Vietnam Academy of Science and Technology at…, on date…month…2019

Hardcopy of the thesis be found at:

- Library of Graduate University of Science and Technology

- Vietnam National Library

INTRODUCTION

1 Significance of the study

Damage in structures, especially cracks, can cause the construction to collapse if not detected in time This is proved

by the results of studies of accidents that have occurred in important projects such as offshore rigs However, it is difficult

to determine the position and the extent of a crack in a structure, because the crack usually stays in the structures that the naked eye cannot detect Therefore, to diagnose cracks, people often use non-destructive testing methods One of these methods, which is comprehensive and applicable to complex construction, is based on measuring the oscillation parameters

of a building to determine the position and extent of the damage

in construction

The oscillation parameters commonly used in structural failure diagnosis are specific frequencies and patterns of oscillations or frequency response functions These parameters are characteristics which are quite comprehensive for the technical condition of a building without depending on external stimuli However, identifying these characteristics from measurement data (often understood as measurement) is also an important issue This is the problem of Modal Testing Technique The specific oscillation frequency is the first parameter to be used and is still being used in the evaluation of structural health monitoring As the specific frequency of oscillations is associated with the overall properties of the structure (such as mass, hardness), it is easy to measure accurately The biggest obstacle of using specific frequencies that are still being addressed is that we only measure very few specific frequencies while the number of failures is often unknown If the natural frequency is a numerical characteristic,

then the specific oscillation pattern of the structure is a function feature in space, which can give us more detailed information about the position of the failure There have been many publications using both frequency and specific patterns to diagnose the damage in the structure, but the existing problem

is the difficulty in measuring the oscillation patterns separately

In order to be able to measure specific oscillations, a lot of transducers are required and a specific method of determining the oscillation patterns accurately from the measurement data (due to the non-unique nature of the specific oscillation patterns)

As mentioned above, both the frequency and the specific patterns of oscillations are determined from the measurement data of the frequency response function Determining frequencies and specific patterns from frequency response functions also encounter many errors that are still being studied

In order to avoid the errors in processing the above measurement data, many experts have suggested using the frequency response function for the diagnosis of structural damage In addition, the frequency response function is also a function characteristic in the frequency domain that allows us not only to define a specific frequency, its own oscillation patterns, but also to show the behavior of the structure in the vicinity of the frequency (approximate frequency) This potential of the frequency response function that has not yet been exploited and applied in diagnosing structural damage

2 Aims of the study

The aims of this study are to develop and apply the method of using frequency response functions to diagnose cracks in elastic bar and beams structure The contents of the study includes: building models of cracked elastic bar and

beams structure; studying the changes of oscillation parameters, mainly frequency response functions due to cracks; conducting experimental studies to measure the oscillation parameters of cracked elastic bar and beams structure in the laboratory and proposing some algorithms to diagnose cracks in the structure based on the built model and experimental measurements

3 The main contents of the study

(1) Study the change of axial oscillation nodes in the bar and the bending oscillation of the beam due to the appearance

of cracks in order to diagnose cracks

(2) Experimental study of elastic bar and beam structure containing many cracks by measuring frequency response functions Since then, we analyze and process the measurement data of frequency response functions to find specific experimental frequencies

(3) Construct an explicit frequency response function in the bar structure, thereby combining with experimental measurement data and using CSM (Crack Scanning Method) to solve the diagnostic problem in the cracked bar

(4) Using Rayleigh formula and CSM to set up and solve the problem of crack diagnosis from experimental frequencies

This thesis includes an introduction, 5 chapters and a conclusion, in which chapter 1 presents an overview of literature; chapter 2 presents the theory of multi-cracked bars and beams; chapter 3 presents the changes in the oscillation nodes; chapter 4 presents the experimental study and chapter 5 presents the algorithms and results of bar and beam structural diagnosis based on the frequency response function and particular frequency

CHAPTER 1: LITERATURE OVERVIEW

1.1 Questions of damage diagnosis

With a technical object, there are always two questions: the forward question, studying behavior of the structure; the diagnostic question, in fact is an inverse question, which aims

to detect damage in the structure from the measurement data based on the analysis of the forward problem Specifically for a mechanical system, it is often described by a diagram:

Figure 1.1 Mechanical diagram of mechanics

with: X: input, external impact,

∑: modeling, describing the structure and characteristics

of the system,

Y: output, the response of the system

Mechanical systems can be represented by a mathematical equation:

A crack is a typical form of failure in the structure of buildings and machinery The crack is generally described by its position and size in the structure The appearance of cracks in the structure degrades the hardness of the structure in the vicinity of the crack

The diagnosis of cracks in the composition of the structure has attracted many researchers over the past two decades as indicated in the general reports of Doebling et al in

1996, Salawu in 1997 and Sohn et al in 2004

In the diagnosis of damage of the structure in general as well as the cracks in particular, people often use dynamic characteristics The specific oscillation frequencies, specific

oscillation patterns and frequency response functions (and related characteristics such as the hardness and the softness) are often used

The diagnosis of damage in general and the cracks in particular of the structure based on the frequency change usually only detects the appearance of the crack without determining the crack position Meanwhile, the cracks affect locally Therefore the crack information is based on the specific patterns considered in the diagnostic problem

From domestic and foreign studies, it has been shown that specific forms can be used to determine the position of cracks However, if only the specific form is used for this purpose, it is necessary to have accurate measurement data, which is not always practical in practice Meanwhile, the response function contains information of both frequency and specific patterns that can be used to analyze the effect of cracks

on structural response Measuring frequency response functions

is simple and gives accurate results Therefore, the development

of methods of application of frequency response functions in crack diagnosis is very necessary due to its superiority

1.2 Frequency response functions in diagnosing structural damage

In the measurement data of oscillation characteristics, it was found that using the frequency response functions, which is usually measured directly as input for the diagnosis of damage

is better than using frequency and specific patterns This is due

to the remarkable advantages of measured frequency response function data:

• The external frequency response function provides information about the specific frequency (resonant frequency),

which can also provide additional information about the response of the structure at distant resonant frequencies

• Using the frequency response function will avoid the error of processing the measurement data for frequency separation and the specific form of the measured data (the frequency response function is the input in the separate format analysis)

• In addition, important information such as the position

of the measurement point and of the force set can be found in the frequency response functions

In recent years the use of a frequency response function

to diagnose the damage in structures can be mentioned as in

2005 proposal of Araujo dos Santos et al - a method of determining damage based on the sensitivity of frequency response functions They pointed out that the damage detection results would be better if we measured low frequencies and stimulus nodes, not cracked nodes Therefore, there is a wide range of the possibilities of exploiting more information from the frequency response functions In 2012 Huang et al identified the damage of the five-storey house structure in the structural control problem based on the change of the frequency response functions and the dampers Here they have shown that with greater noise than 10% it is impossible to determine the damage

1.3 Reviews and research questions

The method of measuring the oscillation characteristics

of structures to diagnose the damage is currently the most effective method However, no matter how we directly analyze the measurement signal or use the model to diagnose the damage, the following two problems still exist One is that the easy-to-measure characteristics are less sensitive to damage and

the second is the measurement error may be greater than the effect of the damage Therefore, finding other oscillation characteristics which is not sensitive to measurement errors, but

is sensitive to the damage to diagnose the damage in the construction is still an unsolved problem In the oscillation characteristics: frequency and specific oscillation patterns, the drag coefficient and the frequency response function, the frequency and the frequency response function are easily measured and the most accurate However, the frequency response function is an aggregate feature, including all three previous features (frequency, specific patterns and drag coefficient) and describes the spectral structure of the system Therefore, the interaction between the vibrational forms and their sensitivity makes the sensitivity of the frequency response function to failure very complex and difficult to identify This is

an obstacle to the use of a frequency response function in diagnosing structural failure The majority of published works

in the world for crack diagnosis by impulse response function are based on finite element method, which does not allow determining the exact position of the crack Therefore, it is necessary to develop methods aimed at utilizing the precise measurement of the frequency and the frequency response functions in the diagnosis of the damage, which is finding its representations through damage parameters This allows us to study the frequency sensitivity and frequency response functions for damage and therefore can apply to the structural damage diagnosis

The questions of this thesis are as follows:

Study the change of axial oscillation nodes in the bar, bending oscillation of the beam due to the appearance of cracks

in order to diagnose the cracks

Experimental study of elastic bar and beam structure containing many cracks by measuring the frequency response function Since then, we can analyze and process measurement data of frequency response functions in order to find experimental specific frequencies

Constructing the explicit frequency response function in the bar structure, thereby combining with experimental measurement data and using CSM (Crack Scanning Method) to solve the diagnostic problem in the bar containing cracks Using Rayleigh formula and CSM to set up and solve the problem of crack diagnosis from experimental frequency

CHAPTER 2 THE OSCILLATION OF CRACKED BAR

AND BEAM STRUCTURES

2.1 Model of cracks in elastic bar and beam structures The crack, generally understood as an interface in a solid object, causes the state of deformation stress at that interface to

be interrupted The appearance of cracks in the structure changes the dynamic characteristics Usually cracks are characterized by parameters: position, size and shape

For elastic bars and beams, cracks are considered as changes in the cross section in a segment of very small length b with the depth a It is precisely the crack pattern opened in the form of a saw which is called The V-shaped crack The concept

of the crack depth and the beginning of the crack is clearly described Furthermore, it is calculated that the decrease in hardness (or increase in softness) of the bar - beam at the crack-containing cross-section has led to the idea of modeling the crack with a spring which is equivalent to the hardness K at the section containing the crack Thus, it is possible to describe

cracks in elastic beams with a spring that links the two sides of the crack with the hardness determined by experiment and destructive mechanical theory

Figure 2.1 Crack pattern and replacement springs (bending -

pulling compressors)

2.2 Axial oscillation of cracked elastic bars

The specific oscillation patterns of the elastic bar has the parameters (E, ρ, A, L), which is defined from the equation:

/ ,

/ ),

1 , 0 ( , 0 ) ( )

at the crack is:

2.1.1 Transmission matrix method

solutions of oscillation equations, they can be expressed in the form of:

nm

xx

A

m m

ij m

m

njeee

ee

ee

j j j j

j

j j j

j j j

j

cossin1

sin

coscos

sin1

0)

(

; ) (cos )

(

; ) (sin )

(

; ) (cos )

(

1 1

1 1 1

1

0 0

0 0 0

q q

q x q

q q

q

x p

p p

p x p

p p

p

x

x S

S x

x C

C

x

x S

S x

x C

,/),

()()(

(

0

0 0

Doing the integral on the right and applying the last boundary condition, we get the general expression of the frequency response function:

) 1 ( )

1 (

)] ( )

( )[

1 ( ) ( ) , , (

0

1 0 0 )

0 0 0 0

j

j p j p

n

j

j j p

e K L

e x K x

L x h x x h a x x H

Figure 2.2 Influence of crack position on FRF1 frequency response function of the two-ends free rod (30% crack depth)