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CN109709150B - Laminated rubber vibration isolation support damage identification method based on piezoelectric impedance information - Google Patents

Laminated rubber vibration isolation support damage identification method based on piezoelectric impedance information Download PDF

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CN109709150B
CN109709150B CN201811595124.3A CN201811595124A CN109709150B CN 109709150 B CN109709150 B CN 109709150B CN 201811595124 A CN201811595124 A CN 201811595124A CN 109709150 B CN109709150 B CN 109709150B
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damage
resonance frequency
origin
substructure
admittance
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CN109709150A (en
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朱宏平
张莹
翁顺
雷鹰
袁涌
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Huazhong University of Science and Technology
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Abstract

本发明公开了一种基于压电阻抗信息的叠层橡胶隔震支座损伤识别方法，属于土木工程结构检测领域。该方法包括：(1)建立单一损伤和无损伤的单耦合周期结构的原点反共振频率特征方程；(2)叠层橡胶隔震支座简化为有限单耦合周期结构，计算无损伤状态下的无量纲原点反共振频率；(3)计算无量纲原点反共振频率对基本周期单元剪切刚度变化的敏感度，建立敏感性识别方程组；(4)采集损伤前后的导纳信号，提取结构原点反共振频率；基于损伤前后原点反共振频率的变化率，求解敏感性识别方程组，完成损伤识别。本发明只需测得结构损伤前后的少数几个测点的原点反共振频率的变化，不需要原始结构的准确模型参数，就能较准确地进行周期结构多损伤识别。

Figure 201811595124

The invention discloses a damage identification method of a laminated rubber vibration isolation bearing based on piezoelectric impedance information, and belongs to the field of civil engineering structure detection. The method includes: (1) establishing the origin anti-resonance frequency characteristic equations of single-damaged and non-damaged single-coupled periodic structures; (2) simplifying the laminated rubber isolation bearing into a finite single-coupled periodic structure, and calculating the non-damaged state of the The dimensionless origin anti-resonance frequency; (3) Calculate the sensitivity of the dimensionless origin anti-resonance frequency to the shear stiffness change of the fundamental periodic element, and establish a sensitivity identification equation system; (4) Collect the admittance signals before and after damage, and extract the structural origin Anti-resonance frequency: Based on the change rate of the origin anti-resonance frequency before and after the damage, the sensitivity identification equations are solved to complete the damage identification. The invention only needs to measure the change of the origin anti-resonance frequency of a few measuring points before and after the structure damage, and does not need the accurate model parameters of the original structure, so that the periodic structure multi-damage identification can be more accurately performed.

Figure 201811595124

Description

Laminated rubber vibration isolation support damage identification method based on piezoelectric impedance information
Technical Field
The invention belongs to the field of civil engineering structure detection, and particularly relates to a method for identifying damage of a laminated rubber vibration isolation support based on piezoelectric impedance information.
Background
The shock isolation device bears a large amount of seismic energy consumption, the performance of the shock isolation device is continuously deteriorated under the long-term action of multiple factors such as load, environment and the like, and the shock isolation device is a key part which is most easily damaged in the seismic process. Among them, the laminated rubber vibration isolation support is one of the vibration isolation devices widely used at present. The laminated rubber shock-insulation support is generally formed by mutually staggering a layer of rubber and a layer of reinforcing steel plate through a special process by bonding and pressing, and can be regarded as a chain-shaped harmonious periodic structure system formed by connecting a plurality of repeated substructures (or called periodic units) end to end.
The anti-resonance of the structural system refers to the situation that under the harmonic excitation action of certain specific frequencies, harmonic reaction or zero dynamic compliance occurs at certain parts of the system in the elastic system. Compared with the traditional modal parameters, the anti-resonance frequency has the obvious advantages of representing the overall characteristics of the structure and reflecting the local physical parameter change of the structure. At present, anti-resonance is mainly applied to finite element model modification and dynamic modification of non-periodic structures, and is less applied to periodic structure damage identification.
Piezoelectric impedance (EMI) technology based on piezoelectric ceramic sensors/drivers (abbreviated as PZT) has great advantages in the aspect of identifying tiny damage, and is particularly suitable for local online monitoring and accurate damage identification of structures. The method is based on the basic principle that a high-strength adhesive is used for adhering the surface of the PZT structure or implanting the PZT structure into the structure, and the occurrence of damage is judged by monitoring the change of an electric admittance signal of the PZT self-driven sensor. Sensor damage and bond line defects can interfere with identification.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a laminated rubber vibration isolation support damage identification method based on piezoelectric impedance information, and aims to fully utilize the characteristic that the laminated rubber vibration isolation support is periodic along the axial direction, and solve the technical problem of multi-damage identification of the laminated rubber vibration isolation support based on PZT intelligent sensing monitoring data and according to the change of the original point anti-resonance frequency of a few measuring points before and after structural damage.
In order to achieve the above object, according to an aspect of the present invention, there is provided a method for identifying damage to a laminated rubber-vibration-isolated mount based on piezoelectric impedance information, comprising the steps of:
(1) constructing an original point anti-resonance frequency characteristic equation of a single-damage and non-damage single-coupling periodic structure;
(2) simplifying the laminated rubber shock-insulation support into a single-coupling periodic structure, wherein a basic periodic unit of the laminated rubber shock-insulation support is composed of a second-order shear beam and concentrated masses at two ends of the second-order shear beam, and calculating the dimensionless origin point anti-resonance frequency of the single-coupling periodic structure in a non-damage state;
(3) introducing the increase of the shear stiffness into the admittance of the damage unit, and calculating the sensitivity coefficient of the anti-resonance frequency of the dimensionless origin to the change of the shear stiffness of the basic period unit; establishing a sensitivity identification equation set according to approximate linear superposition of the change of the antiresonance frequency under multiple damages into the change caused by single damage;
(4) acquiring admittance signals before and after damage, and extracting the origin point anti-resonance frequency of the single-coupling periodic structure; and solving a sensitivity identification equation set based on the change rate of the original point anti-resonance frequency before and after the damage, and identifying the damage.
Further, the step (1) further comprises the following sub-steps:
(1.1) for a single-coupling periodic structure of N basic periodic units, setting a left boundary A to be fixed and a right boundary B to be free, and dividing the single-coupling periodic structure into a substructure I and a substructure II by taking the point C as a boundary point when an excitation force P acts on the point C;
(1.2) assuming that the excitation point C is at the node j, the substructure II has a damaged unit k, i.e. j < k; the substructure I is regarded as a healthy single-coupling periodic structure with j units and fixed at two ends; the substructure II is regarded as a single-coupling periodic structure with fixed left end and free right end and (N-j) units, wherein the unit k is damaged; the natural frequency characteristic equations of the substructure I and the substructure II are respectively as follows:
substructure I: 1-e-2jμ＝0
Substructure II: 1+ phi is 0
Figure BDA0001921173550000031
Figure BDA0001921173550000032
C0＝A0+αDDαwr-αEEαwt-αwtαwr
Figure BDA0001921173550000033
E0＝A0+αDDαwt-αEEαwr-αwtαwr
A0＝αDDαEE-αDEαED
Where Φ represents the reflected and transmitted wave displacements at C in substructure II
Figure BDA0001921173550000034
And
Figure BDA0001921173550000035
ratio of (a)DDand alphaEEfor direct admittance of the two ends of the damaged element, alphaEDand alphaDEfor indirect admittance between the ends of the damaged element, alphawtand alphawrcharacteristic wave susceptance, respectively of the transmitted wave and the reflected wave, having alpha for the symmetrical cellwt＝-αwr(ii) a μ is the wave propagation constant;
(1.3) based on the condition of occurrence of anti-resonance, that is, the excitation frequency is equal to a certain natural frequency of the substructure on the left or right of the excitation point, obtaining an origin anti-resonance frequency characteristic equation through the natural frequency characteristic equations of the substructures I and II in the step (1.2) as follows:
(1-e-2jμ)(1+Φ)＝0
(1.4) supposing that the excitation point C is at the node j, the substructure I has a damage unit k, i.e. j is more than or equal to k; the substructure I is regarded as a single-coupling periodic structure with j units and fixed at two ends, wherein the unit k is damaged; the substructure II is a healthy single-coupling periodic structure with fixed left end and free right end and (N-j) units; the natural frequency characteristic equations of the substructure I and the substructure II are respectively:
substructure I: 1+ Ψ ═ 0
Substructure II: 1+ e-2(N-j)μ＝0
Figure BDA0001921173550000036
In the formula, Ψ represents the displacement of the reflected wave and the transmitted wave at C in the substructure I
Figure BDA0001921173550000046
And
Figure BDA0001921173550000047
the ratio of (A) to (B);
(1.5) repeating the step (1.3) to obtain an origin anti-resonance frequency characteristic equation corresponding to the step (1.4) as follows:
[1+e-2(N-j)μ](1+Ψ)＝0
(1.6) under a non-damage state, degenerating an origin anti-resonance frequency characteristic equation of the single damage obtained in the steps (1.3) and (1.5) into:
[1+e-2(N-j)μ](1-e-2jμ)＝0。
further, the step (2) further comprises the following sub-steps:
(2.1) the direct admittance and the indirect admittance at the two ends of the rubber layer are:
Figure BDA0001921173550000041
Figure BDA0001921173550000042
in the formula, gammallAnd gammarrRespectively direct admittance of both ends of the rubber layer, gammalrAnd gammarlRespectively, the indirect admittance between two ends of the rubber layer, G is the shear modulus of the rubber, rho is the density of the rubber, L is the thickness of the rubber layer, A is the cross-sectional area of the rubber layer,
Figure BDA0001921173550000043
is a periodic structure wave number, omega is a circle frequency, and omega is ksL is a dimensionless frequency;
(2.2) admittance of the steel sheet is:
Figure BDA0001921173550000044
wherein β is the admittance of the steel plate, omega is the circular frequency,msthe mass of each layer of steel plate;
(2.3) the direct admittance and the indirect admittance of the composite periodic unit of the laminated rubber vibration isolation bearing and the propagation constants are respectively as follows:
Figure BDA0001921173550000045
Figure BDA0001921173550000051
Figure BDA0001921173550000052
in the formula, αlland alpharris a direct admittance across the composite periodic unit, alphalrand alpharlFor transfer admittance between the two ends of the composite periodic unit,
Figure BDA0001921173550000053
m is the mass ratio of rubber to steel platerRho AL is the rubber mass; μ is the wave propagation constant;
(2.4) direct admittance α of the healthy compound periodic unit of step (2.3)ll、αrrand transfer admittance αlr、αrlAnd (4) substituting the obtained result into the dimensionless origin point antiresonance frequency characteristic equation of the nondestructive single-coupling periodic structure in the step (1.6), and calculating the dimensionless origin point antiresonance frequency of the laminated rubber vibration-isolating support in the nondestructive state.
Further, the step (2.4) of calculating the anti-resonance frequency of the dimensionless origin in the non-damage state further comprises the following sub-steps:
(2.4.1) setting γ ═ μ i, and converting the origin antiresonance frequency characteristic equation in the non-invasive state obtained in step (1.6) into:
cos[(N-j)γ]sinγ＝0
the solution to the equation is:
Figure BDA0001921173550000054
or
Figure BDA0001921173550000055
In the formula:
Figure BDA0001921173550000056
is an imaginary unit, mu is a wave propagation constant;
(2.4.2) converting the wave propagation constant calculation formula of the step (2.3) into:
Figure BDA0001921173550000057
and (4) substituting the solution gamma obtained in the step (2.4.1) into the equation to calculate the dimensionless origin point anti-resonance frequency.
Further, the step (3) further comprises the following sub-steps:
(3.1) when the rubber is aged, the shear modulus of the corresponding rubber layer is increased, and a damage state characterization parameter is introduced, wherein the direct admittance and the indirect admittance of a damage unit are as follows:
Figure BDA0001921173550000061
Figure BDA0001921173550000062
Figure BDA0001921173550000063
Ω′＝k′L
wherein Δ G is the increase in unit shear modulus;
(3.2) shear modulus change rate xi of the damaged unit k before and after damagekAnd (3) evaluating the damage degree:
Figure BDA0001921173550000064
in the formula, ξkWhen 0, unit k is intact;
(3.3) the rate of change of the antiresonance frequency of the nth order dimensionless origin of the excitation point j before and after the damage is as follows:
Figure BDA0001921173550000065
in the formula:
Figure BDA0001921173550000066
respectively representing dimensionless origin point anti-resonance frequencies before and after damage, wherein the superscript u represents an undamaged state, and the superscript d represents a damaged state;
(3.4) based on the perturbation theory and the sensitivity analysis principle, obtaining the sensitivity of the n-th order dimensionless origin point anti-resonance frequency of the excitation point j to the k-th unit damage
Figure BDA0001921173550000067
Figure BDA0001921173550000068
In the formula:
Figure BDA0001921173550000069
representing the origin antiresonant frequency characteristic equation of a single lesion by steps (1.3) and (1.5)
Figure BDA0001921173550000071
Paxi xikpartial derivatives of (c), then make xi in the expression of resultk＝0；
(3.5) approximately linear superposition of the change of the dimensionless origin antiresonance frequency under multiple damages into the change caused by single damage, and accordingly, the vector of the total dimensionless origin antiresonance frequency change rate at the excitation point caused by multiple damages is established
Figure BDA0001921173550000072
and a damage state identification equation between the shear modulus change rate vector { ξ } of each layer of rubber:
Figure BDA0001921173550000073
Figure BDA0001921173550000074
in the formula, [ S ] is a sensitivity matrix of the dimensionless origin antiresonance frequency, p and q represent different nodes where the excitation point C is located, and p is 1, 2.
Further, the step (4) further comprises the following sub-steps:
(4.1) sticking PZT along the axial direction of the laminated rubber shock-insulation support, and collecting admittance signals Y before and after damage;
(4.2) separating the mechanical impedance Z of the single-coupling periodic structure from the PZT electric admittance signal Y according to the one-dimensional impedance models；
(4.3) velocity admittance H based on Single-coupling periodic StructurevAnd the displacement admittance HdIn relation to (3), the mechanical impedance Z of the single-coupled periodic structuresStructure displacement admittance H converted into single coupling periodd：
Figure BDA0001921173550000075
Extracting a valley value of the displacement admittance curve, namely the original point anti-resonance frequency of the structure;
and (4.4) obtaining the change rate of the original point anti-resonance frequency before and after damage based on the step (4.3), and thus carrying out damage identification on the laminated rubber vibration isolation support.
Further, step (4.2) separates the mechanical impedance Z of the structure from the PZT electrical admittance signal YsFurther comprising the substeps of:
(4.2.1) calculating the mechanical impedance Z of the PZT in the short-circuited statea：
Figure BDA0001921173550000081
Figure BDA00019211735500000812
In the formula (I), the compound is shown in the specification,
Figure BDA0001921173550000082
wave number of PZT, ω circular frequency of excitation frequency, la、ba、haRespectively the length, width and thickness of the PZT,
Figure BDA0001921173550000083
is the composite elastic modulus of PZT when the electric field is constant,
Figure BDA0001921173550000084
is the modulus of elasticity, η is the mechanical loss factor,
Figure BDA0001921173550000085
is a plurality of units;
(4.2.2) the PZT electrical admittance expression is:
Figure BDA0001921173550000086
Figure BDA0001921173550000087
in the formula (I), the compound is shown in the specification,
Figure BDA0001921173550000088
is the complex dielectric constant of PZT when the stress is constant,
Figure BDA0001921173550000089
for a real dielectric constant, δ is a dielectric loss factor, d31Is the piezoelectric strain coefficient of PZT;
further, the step (4.4) is used for identifying the damage of the laminated rubber vibration isolation support based on the measured change rate of the anti-resonance frequency of the original point before and after the damage, and further comprises the following substeps:
(4.4.1) calculating the change rate of the dimensionless origin point antiresonance frequency through the measured before and after damage:
Figure BDA00019211735500000810
in the formula (I), the compound is shown in the specification,
Figure BDA00019211735500000811
respectively representing the measured original point anti-resonance frequency before and after damage, the superscript u representing the undamaged state and the superscript d representing the damaged state;
(4.4.2) converting the equation set solving problem of step (3.5) to a non-negative least squares curve fitting problem based on damage such that the shear stiffness of the rubber increases:
Figure BDA0001921173550000091
and (5) solving [ S ] according to the fitting result of the formula to finish the damage identification.
In order to achieve the above object, the invention also provides a laminated rubber vibration-isolating support damage identification device based on piezoelectric impedance information, which comprises a processor and a damage identification program module; and the damage identification program module executes any one of the above-mentioned laminated rubber vibration-isolating support damage identification methods when being called by the processor.
In general, compared with the prior art, the technical scheme of the invention combines the periodic characteristics of the laminated rubber vibration isolation support and the high sensitivity of the PZT technology to tiny damage, so that the following beneficial effects can be obtained:
1) the periodic characteristic of the laminated rubber shock-insulation support is considered, and the multi-damage identification and accurate positioning of the laminated rubber support is realized. Preferably, relatively many frequency variation data can be obtained using the origin anti-resonance frequency: when periodic structure damage identification is carried out through the structure natural frequency, the order of the available frequency is less and is generally smaller than the structure period number. And damage identification is carried out by utilizing the origin point anti-resonance frequency, one structure can be provided with a plurality of driving points, and each driving point can obtain the multi-order origin point anti-resonance frequency.
2) And the original point anti-resonance frequency of the laminated rubber vibration-isolating support is obtained from the measured PZT electric admittance signals, so that the direct measurement of the original point anti-resonance frequency is avoided.
Drawings
FIG. 1 is a schematic flow chart of main steps of a laminated rubber vibration-isolating support damage identification method based on piezoelectric impedance information;
FIG. 2 is a schematic diagram of an experiment for identifying damage to a laminated rubber-vibration-isolating support in accordance with a preferred embodiment of the present invention;
FIG. 3(a) is a schematic diagram of a period system of a laminated rubber vibration-isolating support;
FIG. 3(b) is a schematic diagram of a basic periodic unit of laminated rubber vibration isolation;
FIG. 4(a) is a schematic diagram of single-coupling periodic system wave propagation when the excitation point is on the left side of the damage unit;
FIG. 4(b) is a schematic diagram of single-coupling periodic system wave propagation when the excitation point is at the right side of the damage unit;
FIG. 5(a) is the anti-resonance frequency sensitivity coefficient of node 1;
FIG. 5(b) is the anti-resonance frequency sensitivity coefficient of the node 4;
FIG. 5(c) is the anti-resonance frequency sensitivity coefficient of node 7;
FIG. 5(d) is the anti-resonance frequency sensitivity coefficient of the node 10;
fig. 6 shows the result of lesion recognition.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a method for identifying damage to a laminated rubber-vibration-isolated bearing based on piezoelectric impedance information according to a preferred embodiment of the present invention includes the following steps:
(1) constructing an original point anti-resonance frequency characteristic equation of a single-damage and non-damage single-coupling periodic structure;
(1.1) a single-coupling periodic structure of N basic periodic units, wherein a left boundary A is fixed, a right boundary B is free, an excitation force P acts on a point C, the point C is used as a demarcation point, and the periodic structure is divided into a substructure I and a substructure II;
(1.2) assuming that the excitation point C is at the node j, the substructure II has a damaged unit k, i.e. j < k; the substructure I is a health cycle structure with j units and two fixed ends; the substructure II is regarded as a single-coupling periodic structure with fixed left end and free right end and (N-j) units, wherein the unit k is damaged; the natural frequency characteristic equations of the substructure I and the substructure II are respectively as follows:
substructure I: 1-e-2jμ＝0
Substructure II: 1+ phi is 0
Figure BDA0001921173550000101
Figure BDA0001921173550000111
C0＝A0+αDDαwr-αEEαwt-αwtαwr
Figure BDA0001921173550000112
E0＝A0+αDDαwt-αEEαwr-αwtαwr
A0＝αDDαEE-αDEαED
Where Φ represents the reflected and transmitted wave displacements at C in substructure II
Figure BDA0001921173550000113
And
Figure BDA0001921173550000114
ratio of (a)DDand alphaEEfor direct admittance of the two ends of the damaged element, alphaEDand alphaDEfor indirect admittance between the two ends of the lesion element, subscript D, E distinguishes between the two ends and the admittance direction, αwtand alphawrcharacteristic wave susceptance, respectively of the transmitted wave and the reflected wave, having alpha for the symmetrical cellwt＝-αwr(ii) a μ is the wave propagation constant;
(1.3) based on the condition of occurrence of anti-resonance, that is, the excitation frequency is equal to a certain natural frequency of the substructure on the left or right of the excitation point, obtaining an origin anti-resonance frequency characteristic equation through the natural frequency characteristic equations of the substructures I and II in the step (1.2) as follows:
(1-e-2jμ)(1+Φ)＝0
(1.4) supposing that the excitation point C is at the node j, the substructure I has a damage unit k, i.e. j is more than or equal to k; the substructure I is regarded as a single-coupling periodic structure with j units and fixed at two ends, wherein the unit k is damaged; the substructure II is a healthy single-coupling periodic structure with fixed left end and free right end and (N-j) units; the natural frequency characteristic equations of the substructure I and the substructure II are respectively:
substructure I: 1+ Ψ ═ 0
Substructure II: 1+ e-2(N-j)μ＝0
Figure BDA0001921173550000115
In the formula, Ψ represents the displacement of the reflected wave and the transmitted wave at C in the substructure I
Figure BDA0001921173550000116
And
Figure BDA0001921173550000117
the ratio of (A) to (B);
(1.5) repeating the step (1.3) to obtain an origin anti-resonance frequency characteristic equation corresponding to the step (1.4) as follows:
[1+e-2(N-j)μ](1+Ψ)＝0
(1.6) under a non-damage state, degenerating an origin anti-resonance frequency characteristic equation of the single damage obtained in the steps (1.3) and (1.5) into:
[1+e-2(N-j)μ](1-e-2jμ)＝0。
(2) the laminated rubber shock-insulation support is simplified into a limited single-coupling period structure, a basic period unit of the laminated rubber shock-insulation support is composed of a second-order shear beam and two end concentrated masses, and the dimensionless origin point anti-resonance frequency in a non-damage state is calculated;
(2.1) the direct admittance and the indirect admittance at the two ends of the rubber layer are:
Figure BDA0001921173550000121
Figure BDA0001921173550000122
in the formula, gammallAnd gammarrRespectively direct admittance of both ends of the rubber layer, gammalrAnd gammarlThe subscripts l and r are used for distinguishing the two ends and the admittance direction; g is the shear modulus of the rubber, ρ is the density of the rubber, L is the thickness of the rubber layer, A is the cross-sectional area of the rubber layer,
Figure BDA0001921173550000123
is a periodic structure wave number, omega is a circle frequency, and omega is ksL is a dimensionless frequency;
(2.2) admittance of the steel sheet is:
Figure BDA0001921173550000124
wherein β is the admittance of the steel plate, omega is the circular frequency, msThe mass of each layer of steel plate;
(2.3) the direct admittance and the indirect admittance of the composite periodic unit of the laminated rubber vibration isolation bearing and the propagation constants are respectively as follows:
Figure BDA0001921173550000125
Figure BDA0001921173550000131
Figure BDA0001921173550000132
in the formula, αlland alpharris a direct admittance across the composite periodic unit, alphalrand alpharlSubscripts l and r are used for distinguishing two ends and admittance directions for transfer admittance between two ends of the composite periodic unit;
Figure BDA0001921173550000133
m is the mass ratio of rubber to steel platerRho AL is the rubber mass; μ is the wave propagation constant;
(2.4) direct admittance α of the healthy compound periodic unit of step (2.3)ll、αrrand transfer admittance αlr、αrlAnd (4) substituting the obtained result into the dimensionless origin point antiresonance frequency characteristic equation of the nondestructive single-coupling periodic structure in the step (1.6), and calculating the dimensionless origin point antiresonance frequency of the laminated rubber vibration-isolating support in the nondestructive state.
(2.4.1) setting γ ═ μ i, and converting the origin antiresonance frequency characteristic equation in the non-invasive state obtained in step (1.6) into:
cos[(N-j)γ]sinγ＝0
the solution to the equation is:
Figure BDA0001921173550000134
or
Figure BDA0001921173550000135
In the formula:
Figure BDA0001921173550000136
is an imaginary unit, mu is a wave propagation constant;
(2.4.2) converting the wave propagation constant calculation formula of the step (2.3) into:
Figure BDA0001921173550000137
and (4) substituting the solution gamma obtained in the step (2.4.1) into the equation to calculate the dimensionless origin point anti-resonance frequency. The ratio of the dimensionless origin antiresonance frequency value omega to the structural period number N, the excitation point j and the mass of the rubber and the steel plate
Figure BDA0001921173550000138
And (4) relevant, independent of other geometrical and physical parameters.
(3) Introducing the increase of the shear stiffness into the admittance of the damage unit, and calculating the sensitivity coefficient of the anti-resonance frequency of the dimensionless origin to the change of the shear stiffness of the basic period unit; establishing a sensitivity identification equation set according to approximate linear superposition of the change of the dimensionless origin point antiresonance frequency under multiple damages into the change caused by single damage;
(3.1) when the rubber is aged, the shear modulus of the corresponding rubber layer is increased, and a damage state characterization parameter is introduced, wherein the direct admittance and the indirect admittance of a damage unit are as follows:
Figure BDA0001921173550000141
Figure BDA0001921173550000142
Figure BDA0001921173550000143
Ω′＝ks′L
wherein Δ G is the increase in unit shear modulus;
(3.2) shear modulus change rate xi of the damaged unit k before and after damagekAnd (3) evaluating the damage degree:
Figure BDA0001921173550000144
in the formula, ξkWhen 0, unit k is intact;
(3.3) the rate of change of the antiresonance frequency of the nth order dimensionless origin of the excitation point j before and after the damage is as follows:
Figure BDA0001921173550000145
in the formula:
Figure BDA0001921173550000146
respectively representing dimensionless origin point anti-resonance frequencies before and after damage, wherein the superscript u represents an undamaged state, and the superscript d represents a damaged state;
(3.4) based on the perturbation theory and the sensitivity analysis principle, obtaining the sensitivity of the n-th order dimensionless origin point anti-resonance frequency of the excitation point j to the k-th unit damage
Figure BDA0001921173550000147
Figure BDA0001921173550000148
In the formula:
Figure BDA0001921173550000151
representing the origin antiresonant frequency characteristic equation of a single lesion by steps (1.3) and (1.5)
Figure BDA0001921173550000152
Paxi xikpartial derivatives of (c), then make xi in the expression of resultk＝0；
(3.5) approximately linear superposition of the change of the dimensionless origin antiresonance frequency under multiple damages into the change caused by single damage, and accordingly, the vector of the total dimensionless origin antiresonance frequency change rate at the excitation point caused by multiple damages is established
Figure BDA0001921173550000153
and a damage state identification equation between the shear modulus change rate vector { ξ } of each layer of rubber:
Figure BDA0001921173550000154
Figure BDA0001921173550000155
in the formula, [ S ] is a sensitivity matrix of the dimensionless origin antiresonance frequency, p and q represent different nodes where the excitation point C is located, and p is 1, 2.
(4) Acquiring admittance signals before and after damage, and extracting the origin point anti-resonance frequency of the structure; and solving a sensitivity identification equation set based on the change rate of the original point anti-resonance frequency before and after the damage, and identifying the damage.
(4.1) sticking PZT along the axial direction of the laminated rubber shock-insulation support, and collecting admittance signals Y before and after damage;
(4.2) separating the mechanical impedance Z of the single-coupling periodic structure from the PZT electric admittance signal Y according to the one-dimensional impedance models；
(4.2.1) calculating the mechanical impedance Z of the PZT in the short-circuited statea：
Figure BDA0001921173550000156
Figure BDA0001921173550000157
In the formula (I), the compound is shown in the specification,
Figure BDA0001921173550000161
wave number of PZT, ω circular frequency of excitation frequency, la、ba、haRespectively the length, width and thickness of the PZT,
Figure BDA0001921173550000162
is the composite elastic modulus of PZT when the electric field is constant,
Figure BDA0001921173550000163
is the modulus of elasticity, η is the mechanical loss factor,
Figure BDA0001921173550000164
is a plurality of units;
(4.2.2) the PZT electrical admittance expression is:
Figure BDA0001921173550000165
Figure BDA0001921173550000166
in the formula (I), the compound is shown in the specification,
Figure BDA0001921173550000167
is the complex dielectric constant of PZT when the stress is constant,
Figure BDA0001921173550000168
for a real dielectric constant, δ is a dielectric loss factor, d31Is the piezoelectric strain coefficient of PZT;
(4.3) velocity admittance H based on Single-coupling periodic StructurevAnd the displacement admittance HdIn relation to (3), the mechanical impedance Z of the single-coupled periodic structuresStructure displacement admittance H converted into single coupling periodd：
Figure BDA0001921173550000169
Extracting a valley value of the displacement admittance curve, namely the original point anti-resonance frequency of the structure;
and (4.4) obtaining the change rate of the original point anti-resonance frequency before and after damage based on the step (4.3), and thus carrying out damage identification on the laminated rubber vibration isolation support.
(4.4.1) calculating the change rate of the dimensionless origin point antiresonance frequency through the measured before and after damage:
Figure BDA00019211735500001610
in the formula (I), the compound is shown in the specification,
Figure BDA00019211735500001611
respectively representing the measured original point anti-resonance frequency before and after damage, the superscript u representing the undamaged state and the superscript d representing the damaged state;
(4.4.2) converting the equation set solving problem of step (3.5) to a non-negative least squares curve fitting problem based on damage such that the shear stiffness of the rubber increases:
Figure BDA0001921173550000171
and (5) solving [ S ] according to the fitting result of the formula to finish the damage identification.
The damage identification process based on the periodic structure theory is described below by taking the laminated rubber vibration isolation bearing experimental model shown in fig. 2 as an object. FIG. 3(a) is a schematic diagram of a period system of a laminated rubber vibration-isolating support, and the model consists of 10 nodes and 10 units. FIG. 3(b) is a schematic diagram of basic cycle units, with the following parameters: the shear modulus of the rubber was 8X 105N/m2The density of the rubber is 1000kg/m3The thickness of the rubber layer was 3.14mm, and the cross-sectional area of the rubber layer was 0.16m2The steel sheet had a mass of 2.512 kg. Fig. 4(a) is a schematic diagram of single-coupling period system wave propagation when the excitation point is on the left side of the damage unit, and fig. 4(b) is a schematic diagram of single-coupling period system wave propagation when the excitation point is on the right side of the damage unit.
In order to verify the invention, a damage working condition is set for the laminated rubber vibration isolation support: the stiffness of cell 1 increased by 5% and the stiffness of cell 10 increased by 10%. And (3) pasting the PZT on the positions of the nodes 1, 4, 7 and 10 for measurement, converting PZT electric admittance signals into structural mechanical impedance signals, and extracting ninth-order antiresonance frequency. The anti-resonance frequency sensitivity coefficients of the nodes 1, 4, 7, 10 obtained by the above-described method according to the present invention are shown in fig. 5(a) to 5 (d). Based on the antiresonance frequency change rate before and after the damage, the sensitivity identification equation set is solved, and the comparison between the identification result obtained by solving and the actual damage is shown in fig. 6. Therefore, the damage identification result of the method is very close to the actual damage, and the damage position and the damage degree can be accurately identified.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (4)

1.一种基于压电阻抗信息的叠层橡胶隔震支座损伤识别方法，其特征在于，包括以下步骤：1. a method for identifying damage to a laminated rubber vibration isolation bearing based on piezoelectric impedance information, is characterized in that, comprises the following steps: (1)构建单一损伤和无损伤的单耦合周期结构的原点反共振频率特征方程；(1) Construct the origin anti-resonance frequency characteristic equations of single-damaged and non-damaged single-coupled periodic structures; (2)将叠层橡胶隔震支座简化为单耦合周期结构，其基本周期单元由二阶剪切梁和二阶剪切梁两端的集中质量构成，计算单耦合周期结构在无损伤状态下的无量纲原点反共振频率；(2) The laminated rubber isolation bearing is simplified as a single-coupled periodic structure, and its basic periodic element is composed of a second-order shear beam and the concentrated masses at both ends of the second-order shear beam. Calculate the single-coupled periodic structure in a damage-free state The dimensionless origin anti-resonance frequency of ; (3)将剪切刚度增加量引入损伤单元的导纳中，计算无量纲原点反共振频率对基本周期单元剪切刚度变化的敏感度系数；视多损伤下反共振频率变化为单损伤引起变化的近似线性叠加，建立敏感性识别方程组；(3) The increase in shear stiffness is introduced into the admittance of the damaged element, and the sensitivity coefficient of the anti-resonance frequency at the dimensionless origin to the change of the shear stiffness of the basic periodic element is calculated; The approximate linear superposition of , establishes the sensitivity identification equation system; (4)采集损伤前后的导纳信号，提取单耦合周期结构的原点反共振频率；基于损伤前后原点反共振频率的变化率，求解敏感性识别方程组，进行损伤识别；(4) Collect the admittance signals before and after the damage, and extract the origin anti-resonance frequency of the single-coupled periodic structure; based on the rate of change of the origin anti-resonance frequency before and after the damage, solve the sensitivity identification equations to identify the damage; 所述步骤(1)进一步包括以下子步骤：Described step (1) further comprises the following sub-steps: (1.1)对于N个基本周期单元的单耦合周期结构，设左边界A固定，右边界B自由，激励力P作用于C点，则以C点作为分界点，将该单耦合周期结构划分为子结构I和子结构II；(1.1) For a single-coupled periodic structure with N basic periodic units, suppose the left boundary A is fixed, the right boundary B is free, and the excitation force P acts on point C, then point C is used as the boundary point, and the single-coupled periodic structure is divided into Substructure I and Substructure II; (1.2)假定激励点C在节点j，子结构II有损伤单元k，即j＜k；子结构I视为两端固定、有j个单元的健康单耦合周期结构；子结构II视为左端固定、右端自由、有(N-j)个单元的单耦合周期结构，其中单元k发生损伤；子结构I与子结构II的固有频率特征方程分别为：(1.2) Assume that the excitation point C is at node j, and substructure II has damaged unit k, that is, j<k; substructure I is regarded as a healthy single-coupled periodic structure with fixed ends and j units; substructure II is regarded as the left end Fixed, right-hand free, single-coupled periodic structure with (N-j) elements, where element k is damaged; the natural frequency characteristic equations of substructure I and substructure II are: 子结构I：1-e-2jμ＝0Substructure I: 1-e- 2jμ = 0 子结构II：1+Φ＝0Substructure II: 1+Φ=0
Figure FDA0002430101210000021
Figure FDA0002430101210000021
Figure FDA0002430101210000022
Figure FDA0002430101210000022
 C0＝A0+αDDαwr-αEEαwt-αwtαwr C 0 =A 0 +α DD α wr -α EE α wt -α wt α wr
Figure FDA0002430101210000028
Figure FDA0002430101210000028
 E0＝A0+αDDαwt-αEEαwr-αwtαwr E 0 =A 0 +α DD α wt -α EE α wr -α wt α wr A0＝αDDαEE-αDEαED A 0 =α DD α EE -α DE α ED 式中，Φ表示子结构II中C处反射波和传递波位移
Figure FDA0002430101210000023
和
Figure FDA0002430101210000024
的比值，αDD和αEE为损伤单元两端的直接导纳，αED和αDE为损伤单元两端之间的间接导纳，αwt和αwr分别为传递波和反射波的特征波导纳，对于对称单元有αwt＝-αwr；μ为波传播常数；In the formula, Φ represents the displacement of reflected and transmitted waves at C in substructure II
Figure FDA0002430101210000023
and
Figure FDA0002430101210000024
The ratio of α DD and α EE is the direct admittance between the two ends of the damaged element, α ED and α DE are the indirect admittance between the two ends of the damaged element, α wt and α wr are the characteristic waveguide admittance of the transmitted wave and the reflected wave, respectively , α wt =-α wr for symmetric unit; μ is the wave propagation constant; (1.3)基于发生反共振的条件，即激励频率等于激励点左边或右边子结构的某一固有频率，通过步骤(1.2)的子结构I和II的固有频率特征方程，得到原点反共振频率特征方程为：(1.3) Based on the condition that anti-resonance occurs, that is, the excitation frequency is equal to a certain natural frequency of the sub-structure on the left or right side of the excitation point, through the natural frequency characteristic equations of sub-structures I and II in step (1.2), the origin anti-resonance frequency characteristic is obtained The equation is: (1-e-2jμ)(1+Φ)＝0(1-e- 2jμ )(1+Φ)=0 (1.4)假定激励点C在节点j处，子结构I有损伤单元k，即j≥k；子结构I视为两端固定、有j个单元的单耦合周期结构，其中单元k发生损伤；子结构II视为左端固定、右端自由、有(N-j)个单元的健康单耦合周期结构；子结构I和子结构II的固有频率特征方程分别为：(1.4) Assuming that the excitation point C is at the node j, the substructure I has a damaged unit k, that is, j≥k; the substructure I is regarded as a single-coupled periodic structure with fixed ends and j units, where the unit k is damaged; Substructure II is regarded as a healthy single-coupled periodic structure with fixed left end, free right end, and (N-j) units; the natural frequency characteristic equations of substructure I and substructure II are: 子结构I：1+Ψ＝0Substructure I: 1+Ψ=0 子结构II：1+e-2(N-j)μ＝0Substructure II: 1+e −2(Nj)μ =0
Figure FDA0002430101210000025
Figure FDA0002430101210000025
 式中，Ψ表示子结构I中C处反射波和传递波位移
Figure FDA0002430101210000026
和
Figure FDA0002430101210000027
的比值；In the formula, Ψ represents the displacement of reflected and transmitted waves at C in substructure I
Figure FDA0002430101210000026
and
Figure FDA0002430101210000027
ratio; (1.5)重复步骤(1.3)，得到步骤(1.4)对应的原点反共振频率特征方程为：(1.5) Repeat step (1.3) to obtain the characteristic equation of the origin anti-resonance frequency corresponding to step (1.4): [1+e-2(N-j)μ](1+Ψ)＝0[1+e -2(Nj)μ ](1+Ψ)=0 (1.6)在无损伤状态下，将步骤(1.3)和(1.5)得到的单一损伤的原点反共振频率特征方程退化为：(1.6) In a non-damaged state, degenerate the characteristic equation of the origin anti-resonance frequency of a single damage obtained in steps (1.3) and (1.5) into: [1+e-2(N-j)μ](1-e-2jμ)＝0；[1+e -2(Nj)μ ](1-e- 2jμ )=0; 所述步骤(2)进一步包括以下子步骤：Described step (2) further comprises the following sub-steps: (2.1)橡胶层两端的直接导纳和间接导纳为：(2.1) The direct and indirect admittances at both ends of the rubber layer are:
Figure FDA0002430101210000031
Figure FDA0002430101210000031
Figure FDA0002430101210000032
Figure FDA0002430101210000032
 式中，γll和γrr分别为橡胶层两端的直接导纳，γlr和γrl分别为橡胶层两端之间的间接导纳，G为橡胶的剪切模量，ρ为橡胶的密度，L为橡胶层的厚度，A为橡胶层的截面积，
Figure FDA0002430101210000033
为周期结构波数，ω为圆频率，Ω＝ksL为无量纲频率；where γll and γrr are the direct admittances at both ends of the rubber layer, γlr and γrl are the indirect admittances between the two ends of the rubber layer, G is the shear modulus of the rubber, and ρ is the density of the rubber , L is the thickness of the rubber layer, A is the cross-sectional area of the rubber layer,
Figure FDA0002430101210000033
is the periodic structure wave number, ω is the circular frequency, Ω=k s L is the dimensionless frequency; (2.2)钢板的导纳为：(2.2) The admittance of the steel plate is:
Figure FDA0002430101210000034
Figure FDA0002430101210000034
 式中，β为钢板的导纳，ω为圆频率，ms为每层钢板的质量；where β is the admittance of the steel plate, ω is the circular frequency, and m s is the mass of each layer of steel plate; (2.3)叠层橡胶隔震支座的复合周期单元的直接和间接导纳以及传播常数分别为：(2.3) The direct and indirect admittances and propagation constants of the composite periodic element of the laminated rubber isolator are:
Figure FDA0002430101210000035
Figure FDA0002430101210000035
Figure FDA0002430101210000036
Figure FDA0002430101210000036
Figure FDA0002430101210000041
Figure FDA0002430101210000041
 式中，αll和αrr为复合周期单元两端的直接导纳，αlr和αrl为复合周期单元两端之间的传递导纳，
Figure FDA0002430101210000042
为橡胶与钢板的质量之比，mr＝ρAL为橡胶质量；μ为波传播常数；where α ll and α rr are the direct admittances at both ends of the compound periodic element, α lr and α rl are the transfer admittances between the two ends of the compound periodic element,
Figure FDA0002430101210000042
is the mass ratio of rubber to steel plate, m r =ρAL is the mass of rubber; μ is the wave propagation constant; (2.4)将步骤(2.3)中的健康复合周期单元的直接导纳αll、αrr和传递导纳αlr、αrl代入步骤(1.6)中的无损伤单耦合周期结构的无量纲原点反共振频率特征方程中，计算叠层橡胶隔震支座无损伤状态下的无量纲原点反共振频率；所述步骤(3)进一步包括以下子步骤：(2.4) Substitute the direct admittance α ll , α rr and transfer admittance α lr , α rl of the healthy compound periodic element in step (2.3) into the dimensionless origin inversion of the damage-free single-coupled periodic structure in step (1.6) In the resonance frequency characteristic equation, the dimensionless origin anti-resonance frequency of the non-damaged state of the laminated rubber isolation bearing is calculated; the step (3) further includes the following sub-steps: (3.1)当橡胶老化时，相应橡胶层的剪切模量增大，引入损伤状态表征参数，损伤单元的直接和间接导纳为：(3.1) When the rubber ages, the shear modulus of the corresponding rubber layer increases, and the damage state characterization parameter is introduced. The direct and indirect admittances of the damaged unit are:
Figure FDA0002430101210000043
Figure FDA0002430101210000043
Figure FDA0002430101210000044
Figure FDA0002430101210000044
Figure FDA0002430101210000045
Figure FDA0002430101210000045
 Ω′＝ks′LΩ′=k s ′L 式中，ΔG为单元剪切模量的增加量；where ΔG is the increase in unit shear modulus; (3.2)以损伤单元k在损伤前后的剪切模量变化率ξk评估损伤程度：(3.2) The damage degree is evaluated by the shear modulus change rate ξ k of the damaged unit k before and after damage:
Figure FDA0002430101210000046
Figure FDA0002430101210000046
 式中，ξk＝0时表示单元k无损伤；In the formula, when ξ k = 0, it means that the unit k has no damage; (3.3)损伤前后激励点j的第n阶无量纲原点反共振频率变化率为：(3.3) The rate of change of the nth-order dimensionless origin anti-resonance frequency of excitation point j before and after damage is:
Figure FDA0002430101210000047
Figure FDA0002430101210000047
 式中：
Figure FDA0002430101210000051
分别表示损伤前后的无量纲原点反共振频率，上标u表示未损伤状态，上标d表示损伤状态；where:
Figure FDA0002430101210000051
Respectively represent the dimensionless origin anti-resonance frequency before and after the damage, the superscript u represents the undamaged state, and the superscript d represents the damaged state; (3.4)基于摄动理论与敏感性分析原理，获得激励点j的第n阶无量纲原点反共振频率对第k单元损伤的敏感度
Figure FDA0002430101210000052
(3.4) Based on the perturbation theory and sensitivity analysis principle, the sensitivity of the n-th dimensionless origin anti-resonance frequency of the excitation point j to the damage of the k-th element is obtained
Figure FDA0002430101210000052
Figure FDA0002430101210000053
Figure FDA0002430101210000053
 式中：
Figure FDA0002430101210000054
表示通过步骤(1.3)和(1.5)中的单一损伤的原点反共振频率特征方程求
Figure FDA0002430101210000055
对ξk的偏导，再在结果表达式中令ξk＝0；where:
Figure FDA0002430101210000054
represents the origin antiresonance frequency characteristic equation obtained by the single damage in steps (1.3) and (1.5)
Figure FDA0002430101210000055
For the partial derivative of ξ k , let ξ k = 0 in the resulting expression; (3.5)视多损伤下的无量纲原点反谐振频率变化为单损伤引起变化的近似线性叠加，据此建立多损伤引起的激励点处总无量纲原点反共振频率变化率向量
Figure FDA0002430101210000056
与各层橡胶剪切模量变化率向量{ξ}之间的损伤状态辨识方程：(3.5) The dimensionless origin anti-resonance frequency change under multiple damages is regarded as an approximate linear superposition of the changes caused by a single damage, and based on this, the total dimensionless origin anti-resonance frequency change rate vector at the excitation point caused by multiple damages is established.
Figure FDA0002430101210000056
The damage state identification equation between the shear modulus change rate vector {ξ} of each layer of rubber:
Figure FDA0002430101210000057
Figure FDA0002430101210000057
Figure FDA0002430101210000058
Figure FDA0002430101210000058
 式中，[S]为无量纲原点反共振频率的敏感性矩阵，p、q表示激励点C所处的不同节点，p＝1,2,...,N,q＝1,2,...,N；In the formula, [S] is the sensitivity matrix of the dimensionless origin anti-resonance frequency, p, q represent the different nodes where the excitation point C is located, p=1,2,...,N,q=1,2,. ..,N; 所述步骤(4)进一步包括以下子步骤：Described step (4) further comprises the following sub-steps: (4.1)沿叠层橡胶隔震支座轴向粘贴PZT，采集损伤前后的导纳信号Y；(4.1) Paste PZT along the axial direction of the laminated rubber isolation bearing, and collect the admittance signal Y before and after the damage; (4.2)根据一维阻抗模型，从PZT电导纳信号Y中分离出单耦合周期结构的机械阻抗Zs；(4.2) According to the one-dimensional impedance model, separate the mechanical impedance Z s of the single-coupling periodic structure from the PZT electrical admittance signal Y; (4.3)基于单耦合周期结构的速度导纳Hv与位移导纳Hd的关系，将单耦合周期结构的机械阻抗Zs转化为单耦合周期的结构位移导纳Hd：(4.3) Based on the relationship between the velocity admittance H v and the displacement admittance H d of the single-coupling periodic structure, the mechanical impedance Z s of the single-coupling periodic structure is converted into the displacement admittance H d of the single-coupling periodic structure:
Figure FDA0002430101210000061
Figure FDA0002430101210000061
 提取位移导纳曲线的谷值即为结构的原点反共振频率；The valley value of the extracted displacement admittance curve is the origin anti-resonance frequency of the structure; (4.4)基于步骤(4.3)获得损伤前后原点反共振频率的变化率，从而对叠层橡胶隔震支座进行损伤识别。(4.4) Based on step (4.3), the rate of change of the anti-resonance frequency at the origin before and after the damage is obtained, so as to identify the damage of the laminated rubber isolation bearing. 2.如权利要求1所述的一种基于压电阻抗信息的叠层橡胶隔震支座损伤识别方法，其特征在于，步骤(2.4)计算无损伤状态下的无量纲原点反共振频率进一步包括以下子步骤：2. a kind of damage identification method of laminated rubber vibration isolation bearing based on piezoelectric impedance information as claimed in claim 1, is characterized in that, step (2.4) calculating the dimensionless origin anti-resonance frequency under the non-damage state further comprises The following substeps: (2.4.1)设γ＝μi，将步骤(1.6)得到的无损伤状态下的原点反共振频率特征方程转化为：(2.4.1) Set γ=μi, and transform the characteristic equation of the origin anti-resonance frequency in the non-damaged state obtained in step (1.6) into: cos[(N-j)γ]sinγ＝0cos[(N-j)γ]sinγ=0 方程的解为：The solution to the equation is:
Figure FDA0002430101210000062
或
Figure FDA0002430101210000063
Figure FDA0002430101210000062
or
Figure FDA0002430101210000063
 式中：
Figure FDA0002430101210000064
为虚数单位，μ为波传播常数；where:
Figure FDA0002430101210000064
is an imaginary unit, and μ is the wave propagation constant; (2.4.2)根据γ＝μi将步骤(2.3)的波传播常数计算公式转化为：(2.4.2) According to γ=μi, the wave propagation constant calculation formula in step (2.3) is converted into:
Figure FDA0002430101210000065
Figure FDA0002430101210000065
 将步骤(2.4.1)得到的解γ代入上述方程，计算出无量纲原点反共振频率。Substitute the solution γ obtained in step (2.4.1) into the above equation to calculate the dimensionless origin anti-resonance frequency. 3.如权利要求1所述的一种基于压电阻抗信息的叠层橡胶隔震支座损伤识别方法，其特征在于，步骤(4.2)从PZT电导纳信号Y中分离出结构机械阻抗Zs进一步包括以下子步骤：3. a kind of damage identification method of laminated rubber vibration isolation bearing based on piezoelectric impedance information as claimed in claim 1, is characterized in that, step (4.2) separates structural mechanical impedance Z s from PZT electric admittance signal Y It further includes the following sub-steps: (4.2.1)计算短路状态下PZT的机械阻抗Za：(4.2.1) Calculate the mechanical impedance Z a of the PZT in the short-circuit state:
Figure FDA0002430101210000071
Figure FDA0002430101210000071
Figure FDA0002430101210000072
Figure FDA0002430101210000072
 式中，
Figure FDA0002430101210000073
为PZT的波数，ω为激励频率的圆频率，la、ba、ha分别为PZT的长度、宽度和厚度，
Figure FDA0002430101210000074
是电场为常数时PZT的复合弹性模量，
Figure FDA0002430101210000075
为实弹性模量，η为机械损失因子，
Figure FDA0002430101210000076
为虚数单位；In the formula,
Figure FDA0002430101210000073
is the wave number of the PZT, ω is the circular frequency of the excitation frequency, la , b a and ha are the length, width and thickness of the PZT, respectively,
Figure FDA0002430101210000074
is the composite elastic modulus of PZT when the electric field is constant,
Figure FDA0002430101210000075
is the real elastic modulus, η is the mechanical loss factor,
Figure FDA0002430101210000076
is an imaginary unit; (4.2.2)PZT电导纳表达式为：(4.2.2) The expression of PZT conductance is:
Figure FDA0002430101210000077
Figure FDA0002430101210000077
Figure FDA0002430101210000078
Figure FDA0002430101210000078
 式中，
Figure FDA0002430101210000079
是应力为常数时PZT的复合介电常数，
Figure FDA00024301012100000710
为实介电常数，δ为介电损失因子，d31为PZT的压电应变系数。In the formula,
Figure FDA0002430101210000079
is the complex permittivity of PZT when the stress is constant,
Figure FDA00024301012100000710
is the real dielectric constant, δ is the dielectric loss factor, and d 31 is the piezoelectric strain coefficient of PZT. 4.如权利要求3所述的一种基于压电阻抗信息的叠层橡胶隔震支座损伤识别方法，其特征在于，步骤(4.4)基于测得的损伤前后原点反共振频率的变化率，对叠层橡胶隔震支座进行损伤识别，进一步包括以下子步骤：4. a kind of damage identification method of laminated rubber vibration-isolating bearing based on piezoelectric impedance information as claimed in claim 3, is characterized in that, step (4.4) is based on the rate of change of origin anti-resonance frequency before and after the measured damage, The damage identification of the laminated rubber isolation bearing further includes the following sub-steps: (4.4.1)通过测得的损伤前后原点反共振频率，计算无量纲原点反共振频率变化率：(4.4.1) Calculate the change rate of the dimensionless origin anti-resonance frequency through the measured origin anti-resonance frequency before and after the damage:
Figure FDA00024301012100000711
Figure FDA00024301012100000711
 式中，
Figure FDA00024301012100000712
分别表示测得的损伤前后的原点反共振频率，上标u表示未损伤状态，上标d表示损伤状态；In the formula,
Figure FDA00024301012100000712
Respectively represent the measured origin anti-resonance frequencies before and after the damage, the superscript u represents the undamaged state, and the superscript d represents the damaged state; (4.4.2)基于损伤使得橡胶的剪切刚度增大，将步骤(3.5)的方程组求解问题转化为非负最小二乘曲线拟合问题：(4.4.2) Based on the increase of the shear stiffness of the rubber due to the damage, the equation solving problem in step (3.5) is transformed into a non-negative least squares curve fitting problem:
Figure FDA0002430101210000081
Figure FDA0002430101210000081
 根据上式的拟合结果求解[S]，完成损伤识别。According to the fitting result of the above formula, solve [S] to complete the damage identification.
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