CN102928247B - Equivalent modal strain energy damage identification method - Google Patents

Abstract

The invention provides an equivalent modal strain energy damage identification method. The method comprises the following steps of: respectively solving corresponding modal strain energy by using a modal shape generated before and after being damaged; and then judging the damage position and the damage degree of the unit by using an strain energy equivalent index of each damage unit; if an index value is approximate to zero or has a negative value, expressing that no damage exists; and if the index value is a positive value, expressing that the unit has the damage, wherein the damage degree of the unit is the size of the equivalent index value. Compared with the strain energy variation rate method, a strain energy equivalent index method has the advantage of quantitative identification; and compared with the strain energy dissipation rating method, the strain energy equivalent index method has the advantage of higher identification precision.

Description

A kind of equivalent modalities strain energy damnification recognition method

Technical field

The present invention relates to the damage detecting method of fabric structure, be specifically related to a kind of equivalent modalities strain energy damnification recognition method.

Background technology

The major injury of structure can cause collapsing of buildings or lose efficacy, thus causes huge economy or the loss of human life.Therefore, be international study hotspot to the Study of recognition of structural damage always.Damnification recognition method based on modal strain energy is comparatively effective a kind of damnification recognition method, (the Shi Z Y such as Shi Z L, Law S S and Zhang L M.Structural damagelocalization from modal strain energy change [J] .Journal of Sound and Vibration, 1998, 218 (5): 825-844.) non-destructive tests of structure has been carried out in the change of range site modal strain energy, and consider modal data there is incomplete factor, propose a kind of modal strain energy rate of change method and carry out non-destructive tests, but the method cannot carry out quantitative judge, (the Sazonov E such as Sazonov E, Klinkhachorn P.Optimal spatial sampling interval for damage detectionby curvature or strain energy mode shapes.Journal of Sound and Vibration, 2005,285 (4-5): 783-801.) then make use of strain energy mode and have studied vibration base damnification recognition method, and have studied the sampling interval duration problem of optimization.But the method also cannot carry out the quantitative judge damaged.(the Liu Hui such as Liu Hui, Qu Weilian, Yuan Runzhang. based on the Structural Damage Identification [J] of modal strain energy dissipative shock wave theory. vibration and impact, 2004,23 (2): 118-121.) dissipation issues of strain energy is then considered, propose a kind of recognition methods based on strain energy dissipative shock wave theory, but the process employs unmarred stiffness matrix instead of damage after matrix.This simplification reduces the precision of identification, therefore the damage quantitative accuracy of identification of the method is not high.(the Hu Huiwen such as Hu Huiwen, Wang Bor-Tsuen, Lee Cheng-Hsin et al.Damage detection ofsurface cracks in composite laminates using modal analysis and strain energy method.CompositeStructures, 2006, 74 (4): 399-405.Hu Huiwen, Wu Chengbo.Development of scanning damageindex for the damage detection of plate structures using modal strain energy method.MechanicalSystems and Signal Processing, 2009, 23 (2): 274-287) then make use of modal analysis method and the strain energy technique study surface crack identification problem of composite panel, first it utilize modal analysis method to obtain condition shape, then make use of differential quadrature method and calculate strain energy, but the method can only be applied to the identification problem of the single surface crack damage of composite panel, be difficult to solve poly-injury problem.Therefore this research is by the basis of above research, proposes a kind of strain energy equivalent merit damnification recognition method.The method will directly utilize the stiffness matrix after damage to calculate the modal strain energy after damage, and derives corresponding active balance equation, thus sets up a new signatures for damage detection, i.e. strain energy equivalent merit.This new index not only can improve the precision of non-destructive tests, and can carry out Study of recognition to poly-injury.

To sum up, mainly there is following defect in existing strain energy damage identification technique:

One is the quantitative judge being difficult to carry out Multiple Damaged Locations in Structures; Two is not high for the accuracy of identification of damage.

Summary of the invention

For prior art above shortcomings, the object of the invention is to propose a kind of new strain energy damage identification technique, not only can solve the quantitative judge problem of poly-injury, and the precision of Damage Assessment Method can be improved.

Realize above-mentioned purpose, the present invention adopts following technical scheme: a kind of equivalent modalities strain energy damnification recognition method, it is characterized in that, utilize the Mode Shape produced before and after damage to obtain corresponding modal strain energy respectively, recycle the strain energy equivalent merit of each damage unit to judge damage position and the degree of this unit; Wherein, if this desired value is 0 or occurs negative value, mean not damage, when this value on the occasion of time then mean that damage appears in this unit, the degree of injury of unit is exactly the size of this equivalent desired value; Specifically comprise the steps:

1) extraction of raw data: according to concrete structure, extracts the elastic modulus E of material, density p, sectional dimension A, cross sectional moment of inertia I and these master datas of component length l;

2) basic stiffness matrix is generated: first according to member structure Form generation element stiffness matrix, then be translated into the stiffness matrix under global coordinate system, and be integrated into global stiffness matrix K; Wherein, the element stiffness matrix of bar element is:

In formula, E-elastic modulus, A-sectional dimension, I-cross sectional moment of inertia, l-component length, density p;

3), adopt feature vector method to extract the original vibration shape mode Ф of structure, its secular equation extracting mode is

KΦ _i＝ω _i ²MΦ _i

In formula, K-stiffness matrix, ω _i-the i-th rank characteristic frequency, M-mass matrix; Ф _ibe the i-th original vibration shape mode in rank;

4) the basic strain energy of Raw Data Generation is utilized: utilize the transposed vector premultiplication of original vibration shape mode with element stiffness matrix, then Mode Shape vector is multiplied by the right side, thus the basic strain energy of generation unit; Like this, the strain energy of the front m rank mode of jth unit is ${\mathrm{MSE}}_j^u=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i;$

5) strain energy after the vibration shape mode after measuring damage also generates damage: the vibration shape mode structure employing excitation method after damage being motivated to structure, and adopt displacement sensor to go out corresponding vibration shape mode Ф d, the strain energy of the front m rank mode of jth unit after finally utilizing the rear vibration shape generation of damage to damage

6) calculate the strain energy before and after the damage of jth unit, calculate the strain energy equivalent merit of jth unit;

$c_j=\frac{{\mathrm{MSE}}_j^d-\sqrt{{\mathrm{MSE}}_j^u\×{\mathrm{ESE}}_j^d}}{{\mathrm{MSE}}_j^d};$

Wherein, the modal strain energy before damage, it is the modal strain energy after damage;

7) judged position and the degree of structural damage by strain energy equivalent merit: the damage criterion calculating each unit successively, thus position and the degree of each damage unit can be obtained.

The present invention starts with from the change of strain energy and the equivalence principle of energy dissipation, thus the energy-balance equation that must make new advances, and draw strain energy equivalent merit and corresponding damnification recognition method thereof further.Make a concrete analysis of as follows:

1, the change of strain energy:

Recognition methods based on modal strain energy is comparatively effective non-destructive tests method, and these class methods can be utilized to carry out quantitative and qualitative analysis identification, a known jth unit and the modal strain energy of the i-th rank mode corresponding to damage front and back as follows:

$\begin{array}{cc}{\mathrm{MSE}}_{\mathrm{ij}}^u={\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i& {\mathrm{MSE}}_{\mathrm{ij}}^d={\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j{\mathrm{\Φ}}_i^d\end{array}---(1a,b)$

When considering front m rank mode, before the structure corresponding to a jth unit, the modal strain energy of m rank mode before and after damage is

$\begin{array}{cc}{\mathrm{MSE}}_j^u=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i& {\mathrm{MSE}}_j^d=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j{\mathrm{\Φ}}_i^d\end{array}---(2a,b)$

Due to the modal strain energy after damage with all have employed the stiffness matrix before damage and replace the stiffness matrix after damaging, therefore have impact on the accuracy of identification of corresponding recognition methods.Therefore this research to give more accurate modal strain energy expression formula as follows:

A jth unit and the modal strain energy of the i-th rank mode corresponding to before and after damage are

$\begin{array}{cc}{\mathrm{MSE}}_{\mathrm{ij}}^u={\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i& {\mathrm{MSE}}_{\mathrm{ij}}^{\mathrm{dd}}={\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j^d{\mathrm{\Φ}}_i^d\end{array}---(3a,b)$

In formula, for jth unit stiffness matrix after injury, for damaging the accurate expression of rear modal strain energy, this formula is different from formula (1b).

When structural damage, stiffness matrix and i-th displacement modes of its jth unit can be expressed as follows

K _j ^d=K _j-c _jk _j; Φ _i ^d=Φ _i-△ Φ _iin (4a, b) formula, c _jfor the Damage coefficient of a jth unit, its span is (0≤c _j≤ 1).△ Φ _ifor the displacement modes knots modification after structural damage.Then before and after damage, the strain energy knots modification of a jth unit and the i-th rank displacement modes is

${\mathrm{MSEC}}_{\mathrm{ij}}={\mathrm{MSE}}_{\mathrm{ij}}^{\mathrm{dd}}-{\mathrm{MSE}}_{\mathrm{ij}}^u=(1-c_j){\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j{\mathrm{\Φ}}_i^d-{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i---\left(5\right)$

If m rank mode before considering, then before the structure corresponding to a jth unit, the accurate modal strain energy expression formula of m rank mode before and after damage is

$\begin{array}{cc}{\mathrm{MSE}}_j^u=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i& {\mathrm{MSE}}_j^{\mathrm{dd}}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j^d{\mathrm{\Φ}}_i^d\end{array}---(6a,b)$

In order to equation expression for simplicity, can make

$\begin{array}{cc}{u}_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i& d_j=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^{\mathrm{dT}}{K}_j{\mathrm{\Φ}}_i^d\end{array}---(7a,b)$

Then before and after damage, the knots modification of a jth element modal strain energy is

MSEC _j＝(1-c _j)d _j-u _j(8)

2, dissipation of energy:

The damage of structure also can be described to energy dissipation process, then at the energy absorbing device of t be

In formula, σ and ε is stress and strain vector respectively, and V is the volume of structure.Then the energy absorbing device of a jth damage unit is

When moment t=0, not damaged occurs, then c _j(0)=0; At moment t=t ^dtime, damage occurs, and hypothesis c _jt () and t. are linear relationships, then derivative for constant.A jth unit generation size as fruit structure is c _jdamage, then the energy dissipation of a jth unit of this damaged structure is:

3, Energy Equivalent equation and strain energy equivalent merit:

Because the energy dissipation of structure and the changing value of damage front and back strain energy should be equivalent, therefore formula (8) should be equal with (11), then

$\left|(1-c_j)d_j{-u}_j\right|=\left|u_j\frac{-c_j}{1-c_j}\right|---\left(12\right)$

Above formula can be reduced to equivalent equation

$d_j^2{c}_j^4+{2d}_j(u_j-{2d}_j)c_j^3+{6d}_j(d_j-u_j)c_j^2+2(u_j-2d_j)(d_j-u_j)c_j+{(d_j-u_j)}^2=0---\left(13\right)$

Solve this equation by the single order biquadratic equation solution of Ferrari, and consider constraint condition and adopt modal strain energy (MSE) form to represent, then the damage criterion obtaining a jth unit is as follows:

$c_j=\frac{{\mathrm{MSE}}_j^d-\sqrt{{\mathrm{MSE}}_j^u\×{\mathrm{MSE}}_j^d}}{{\mathrm{MSE}}_j^d}---\left(14\right)$

Calculate the damage criterion of each unit successively, thus position and the degree of each damage unit can be obtained.Like this, Study on Damage Identification can be carried out by this damage criterion.This damage criterion is called as strain energy equivalent merit, and the damnification recognition method based on this index is called as strain energy equivalent merit method, and this damnification recognition method can carry out the quantitative judge damaged more accurately.

Compared to existing technology, strain energy equivalent merit method of the present invention has following beneficial effect:

1, relative to strain energy change rate method, this strain energy equivalent merit method has the advantage can carrying out quantitative judge.

2, relative to strain energy dissipative shock wave method, this strain energy equivalent merit method has the higher advantage of accuracy of identification.

3, relative to other two benches quantitative and qualitative analysis recognition methodss, this strain energy equivalent merit method can simultaneously to structure

Poly-injury carry out quantitative and qualitative analysis identification, method is simple, and accuracy of identification is high, has suitable practical value.

Accompanying drawing explanation

Fig. 1 is equivalent modalities strain energy damnification recognition method process flow diagram of the present invention;

Fig. 2 is the three-dimensional truss structural drawing of one embodiment of the invention;

Recognition result when Fig. 3 is unit 5,9,22 damage;

Recognition result when Fig. 4 is unit 11,21,45 damage.

Embodiment

As shown in Figure 1, equivalent modalities strain energy damnification recognition method of the present invention mainly adopts strain energy equivalent merit to carry out Study on Damage Identification, what first utilize the Mode Shape produced before and after damage obtains corresponding modal strain energy respectively, recycles the strain energy equivalent merit of each damage unit to judge damage position and the degree of this unit.Wherein, if this desired value close to 0 or occur negative value, means not damage, when this value on the occasion of time then mean that damage appears in this unit, the degree of injury of unit is exactly the size of this equivalent desired value.

Specific embodiment can adopt a three-dimensional structure to verify, considers a three-dimensional truss structure as shown in Figure 2.Its basic parameter is: elastic modulus E=72GPa, density of material ρ=2800kg/m ³, as shown in the figure, unit sectional area is 0.001m to rod member length ².Suppose there are two kinds of degree of impairments, the first situation, damage at unit 5,9 and 22, rigidity reduces by 20%, 20% and 15% respectively, the second situation, and damage at unit 11,21,45, rigidity reduces by 20%, 30% and 10% respectively.Utilize the strain energy equivalent merit of front 3 rank modal data computation structures, and if the Damage coefficient desired value calculated is less than 0, then this value of mandatory provision is 0.The strain energy equivalent merit method then adopting this patent to propose carries out non-destructive tests, and contrasts with another strain energy dissipative shock wave method.

Example 1: when damage occurs unit 5,9 and 22, the strain energy equivalent merit method adopting strain energy dissipative shock wave method and the present invention to propose respectively carries out Study on Damage Identification, and the result of calculation of two kinds of methods as shown in Figure 3.Can find from Fig. 3, two kinds of methods can effectively identify damage unit, but strain energy dissipative shock wave method is not high for the accuracy of identification of degree of injury, the method is for unit 5, 9 and 22 impairment values calculated are respectively 0.357, 0.353 and 0.276, differ larger with actual value, the strain energy equivalent merit method that the present invention proposes then can determine the degree damaged more accurately, for unit 5, 9 and 22 values calculated are respectively 0.198, 0.195 and 0.149, this desired value is very close with the degree truly damaged, therefore, strain energy equivalent merit method can the degree of identification of damage more accurately.

Example 2: when damage occurs unit 11,21 and 45, have employed strain energy dissipative shock wave method equally and strain energy equivalent merit method has carried out Study on Damage Identification, and the result of calculation of two kinds of methods as shown in Figure 4.Can find from Fig. 4, two kinds of methods effectively can identify the position of damage unit, but strain energy dissipative shock wave method is not high for the accuracy of identification of degree of injury.The impairment value that strain energy dissipative shock wave method calculates for unit 11,21 and 45 is respectively 0.355,0.506 and 0.13, differs larger with actual value.The strain energy equivalent merit method that the present invention proposes then can determine the degree damaged more accurately, the value calculated for unit 11,21 and 45 is respectively 0.197,0.297 and 0.067, this desired value is very close with the degree truly damaged, therefore, strain energy equivalent merit method can the degree of more accurately identification of damage.

From above two example analyses, strain energy dissipative shock wave method is difficult to accurately determine degree of injury, and the method is often bigger than normal for the calculated value of degree of injury.And strain energy equivalent merit method not only can determine the position of damage preferably, and the degree of damage can be determined more accurately.This is mainly due to when derivation strain energy equivalent merit formula, modal strain energy after structural damage is calculated, stiffness matrix before the method does not simply adopt damage removes the stiffness matrix after substituting damage, but have employed the element stiffness matrix after damage to calculate and the strain energy equivalent merit made new advances of deriving.Therefore the quantitative judge result of strain energy equivalent merit method of the present invention to structural damage is more accurate.Concrete example also shows, strain energy equivalent merit method more accurately can carry out the quantitative and qualitative analysis identification damaged, and the accuracy of identification of the method is obviously better than the methods such as strain energy dissipative shock wave.

What finally illustrate is, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although with reference to preferred embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, can modify to technical scheme of the present invention or equivalent replacement, and not departing from aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of right of the present invention.

Claims (1)

1. an equivalent modalities strain energy damnification recognition method, it is characterized in that, utilize the Mode Shape produced before and after damage to obtain corresponding modal strain energy respectively, recycle the strain energy equivalent merit of each damage unit to judge damage position and the degree of this unit; Wherein, if this desired value is 0 or occurs negative value, mean not damage, when this value on the occasion of time then mean that damage appears in this unit, the degree of injury of unit is exactly the size of this equivalent desired value; Specifically comprise the steps:

1) extraction of raw data: according to concrete structure, extracts the elastic modulus E of material, density p, sectional dimension A, cross sectional moment of inertia I and these master datas of component length l;

2) basic stiffness matrix is generated: first according to member structure Form generation element stiffness matrix, then be translated into the stiffness matrix under global coordinate system, and be integrated into global stiffness matrix K; Wherein, the element stiffness matrix of bar element is:

In formula, E-elastic modulus, A-sectional dimension, I-cross sectional moment of inertia, l-component length;

3) adopt feature vector method to extract the original vibration shape mode Ф of structure, its secular equation extracting mode is

KΦ _i＝ω _i ²MΦ _i

In formula, K-stiffness matrix, ω _i-the i-th rank characteristic frequency, M-mass matrix; Ф _ibe the i-th original vibration shape mode in rank;

4) the basic strain energy of Raw Data Generation is utilized: utilize the transposed vector premultiplication of original vibration shape mode with element stiffness matrix, then Mode Shape vector is multiplied by the right side, thus the basic strain energy of generation unit; Like this, the strain energy of the front m rank mode of jth unit is ${\mathrm{MSE}}_j^u=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Φ}}_i^T{K}_j{\mathrm{\Φ}}_i;$

5) strain energy after the vibration shape mode after measuring damage also generates damage: the vibration shape mode structure employing excitation method after damage being motivated to structure, and adopt displacement sensor to go out corresponding vibration shape mode Ф ^d, the strain energy of the front m rank mode of jth unit after finally utilizing the rear vibration shape generation of damage to damage

6) calculate the strain energy before and after the damage of jth unit, calculate the strain energy equivalent merit of jth unit;

$c_j=\frac{{\mathrm{MSE}}_j^d-\sqrt{{\mathrm{MSE}}_j^u\×{\mathrm{MSE}}_j^d}}{{\mathrm{MSE}}_j^d};$

Wherein, the modal strain energy before damage, it is the modal strain energy after damage;

7) judged position and the degree of structural damage by strain energy equivalent merit: the damage criterion calculating each unit successively, thus position and the degree of each damage unit can be obtained.