CN109709150A - Damage identification method of laminated rubber isolation bearing based on piezoelectric impedance information - Google Patents
Damage identification method of laminated rubber isolation bearing based on piezoelectric impedance information Download PDFInfo
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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。
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.
Description
Technical field
The invention belongs to civil engineering structure detection fields, more particularly, to a kind of folded based on Piezoelectric Impedance information
Rubber earthquake isolation support damnification recognition method.
Background technique
Earthquake isolating equipment assumes responsibility for a large amount of earthquake energy consumptions, and performance is continuous under the multifactor long term such as load, environment
Deterioration, is the key position for being easiest to destroy in seismic process.Wherein, laminated rubber damping bearing is to be widely used at present
One of earthquake isolating equipment.Laminated rubber damping bearing is usually interlaced through special by one layer of rubber one layer of reinforcement steel plate of superposition
The molding of technique adhering and pressing may be regarded as humorous by the end to end chain constituted by several repetitive substructures (or periodic unit)
Adjust periodic structure system.
Structural system antiresonance refer to elastic system under the harmonious incentive action of certain specific frequencies, the certain position meetings of system
There is the harmonious situation reacted or dynamic flexibility is zero.Compared to traditional modal parameter, antiresonant frequency has its significant advantage, can
The overall permanence of structure is characterized, and can reflect that structure partial physical parameter changes.Currently, antiresonance is mainly used in aperiodic knot
The FEM updating and Dynamic Modification of structure, it is less to be applied to periodic structure non-destructive tests.
Piezoelectric Impedance (EMI) technology based on piezoceramic transducer/driver (being abbreviated as PZT) is known to microlesion
Aspect does not have huge advantage, is particularly suitable for structure partial on-line monitoring and accurate non-destructive tests.Basic principle is using high-strength viscous
Agent is tied by inside PZT sticking structure surface or implant infrastructure, drives the variation of the electric admittance signal of sensor certainly by monitoring PZT
Judge the generation of damage.And sensor damage and bonding layer defects can interfere structure to identify.
Summary of the invention
In view of the drawbacks of the prior art or Improvement requirement, the present invention provides a kind of lamination rubbers based on Piezoelectric Impedance information
Glue shock isolating pedestal damnification recognition method is in periodic characteristics its object is to make full use of laminated rubber damping bearing edge axial,
Based on PZT intelligent sensing monitoring data, the driving point antiresonance frequency of a few measuring point before and after foundation structural damage
Variation, thus the technical issues of the poly-injury identification of solution laminated rubber damping bearing.
To achieve the above object, according to one aspect of the present invention, a kind of lamination based on Piezoelectric Impedance information is provided
Rubber earthquake isolation support damnification recognition method, comprising the following steps:
(1) the driving point antiresonance frequecy characteristic equation of single damage and undamaged single coupling period structure is constructed；
(2) laminated rubber damping bearing is reduced to single coupling period structure, basic cycle unit is by second order shear beam
It is constituted with the lumped mass at second order shear beam both ends, it is anti-to calculate dimensionless origin of single coupling period structure under not damaged state
Resonant frequency；
(3) shearing rigidity incrementss are introduced into the admittance of damage unit, calculate dimensionless driving point antiresonance frequency to base
The sensitivity coefficient of this periodic unit shearing rigidity variation；Regarding the variation of antiresonant frequency under poly-injury is that single injury causes to change
Sensibility identification equation group is established in approximately linear superposition；
(4) admittance signal of acquisition damage front and back extracts the driving point antiresonance frequency of single coupling period structure；Based on damage
The change rate of front and back driving point antiresonance frequency solves sensibility and identifies equation group, carries out non-destructive tests.
Further, the step (1) further comprises following sub-step:
(1.1) for single coupling period structure of N number of basic cycle unit, if left margin A is fixed, right margin B is free, swashs
It encourages power P and acts on C point, then using C point as separation, which is divided into minor structure I and minor structure II；
(1.2) assume that excitation point C has damage unit k, i.e. j < k in node j, minor structure II；It is solid that minor structure I is considered as both ends
Health list coupling period structure that is fixed, having j unit；Minor structure II is considered as left end and fixes, right end freedom, has (N-j) a unit
Single coupling period structure, wherein unit k is damaged；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Minor structure I:1-e-2jμ=0
Φ=0 minor structure II:1+
C0=A0+αDDαwr-αEEαwt-αwtαwr
E0=A0+αDDαwt-αEEαwr-αwtαwr
A0=αDDαEE-αDEαED
In formula, Φ indicates back wave and transmitting wave displacement at C in minor structure IIWithRatio, αDDAnd αEEFor
Damage the direct admittance at unit both ends, αEDAnd αDEFor the indirect admittance between damage unit both ends, αwtAnd αwrRespectively transmit wave
With the feature waveguide admittance of back wave, there is α for symmetrical cellwt=-αwr；μ is Propagation Constants；
(1.3) based on occur antiresonance condition, i.e., driving frequency be equal to excitation point the left side or the right minor structure it is a certain
Intrinsic frequency obtains driving point antiresonance frequecy characteristic by the intrinsic frequency characteristic equation of the minor structure I and II of step (1.2)
Equation are as follows:
(1-e-2jμ) (1+ Φ)=0
(1.4) excitation point C is assumed at node j, and minor structure I has damage unit k, i.e. j >=k；It is solid that minor structure I is considered as both ends
Single coupling period structure that is fixed, having j unit, wherein unit k is damaged；Minor structure II be considered as left end fix, right end freely,
There is the single coupling period structure of the health of (N-j) a unit；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Ψ=0 minor structure I:1+
Minor structure II:1+e-2(N-j)μ=0
In formula, Ψ indicates back wave and transmitting wave displacement at C in minor structure IWithRatio；
(1.5) step (1.3) are repeated, obtain the corresponding driving point antiresonance frequecy characteristic equation of step (1.4) are as follows:
[1+e-2(N-j)μ] (1+ Ψ)=0
(1.6) under not damaged state, the driving point antiresonance frequency for the single damage that step (1.3) and (1.5) are obtained
Characteristic equation is degenerated are as follows:
[1+e-2(N-j)μ](1-e-2jμ)=0.
Further, the step (2) further comprises following sub-step:
(2.1) the direct admittance and indirect admittance at rubber layer both ends are as follows:
In formula, γllAnd γrrThe respectively direct admittance at rubber layer both ends, γlrAnd γrlRespectively between rubber layer both ends
Indirect admittance, G be rubber modulus of shearing, ρ be rubber density, L be rubber layer thickness, A be rubber layer sectional area,For periodic structure wave number, ω is circular frequency, Ω=ksL is dimensionless frequency；
(2.2) admittance of steel plate are as follows:
In formula, β is the admittance of steel plate, and ω is circular frequency, msFor the quality of every layer of steel plate；
(2.3) the directly or indirectly admittance of the compounding period unit of laminated rubber damping bearing and propagation constant difference
Are as follows:
In formula, αllAnd αrrFor the direct admittance at compounding period unit both ends, αlrAnd αrlBetween compounding period unit both ends
Transfer admittance,For the mass ratio of rubber and steel plate, mr=ρ AL is rubber quality；μ is Propagation Constants；
(2.4) by the direct admittance α of the healthy compounding period unit in step (2.3)ll、αrrWith transfer admittance αlr、αrlGeneration
In the dimensionless driving point antiresonance frequecy characteristic equation for entering not damaged single coupling period structure in step (1.6), lamination is calculated
Dimensionless driving point antiresonance frequency under the not damaged state of rubber earthquake isolation support.
Further, step (2.4) calculate the dimensionless driving point antiresonance frequency under not damaged state further comprise with
Lower sub-step:
(2.4.1) sets γ=μ i, the driving point antiresonance frequecy characteristic equation under the not damaged state that step (1.6) is obtained
Conversion are as follows:
γ=0 sin cos [(N-j) γ]
Non trivial solution are as follows:
Or
In formula:For imaginary unit, μ is Propagation Constants；
(2.4.2) converts the Propagation Constants calculation formula of step (2.3) according to γ=μ i are as follows:
The solution γ that step (2.4.1) is obtained substitutes into above-mentioned equation, calculates dimensionless driving point antiresonance frequency.
Further, the step (3) further comprises following sub-step:
(3.1) when ageing of rubber, the modulus of shearing of corresponding rubber layer increases, and introduces faulted condition characterization parameter, damage
The directly or indirectly admittance of unit are as follows:
Ω '=k ' L
In formula, Δ G is the incrementss of unit modulus of shearing；
(3.2) to damage modulus of shearing change rate ξ of the unit k before and after damagekAssess degree of injury:
In formula, ξkIndicate that unit k is not damaged when=0；
(3.3) the n-th order dimensionless driving point antiresonance frequency change rate of damage front and back excitation point j are as follows:
In formula:The dimensionless driving point antiresonance frequency of damage front and back is respectively indicated, subscript u expression does not damage
State, subscript d indicate faulted condition；
(3.4) based on perturbation theory and sensitivity analysis principle, the n-th order dimensionless driving point antiresonance of excitation point j is obtained
The susceptibility that frequency damages kth unit
In formula:Indicate special by the driving point antiresonance frequency of step (1.3) and the single damage in (1.5)
Sign equation is askedTo ξkLocal derviation, then ξ is enabled in result expressionk=0；
(3.5) it regards the dimensionless origin variation in anti-resonant frequency under poly-injury and causes the approximately linear of variation folded as single injury
Add, establishes total dimensionless driving point antiresonance frequency change rate vector at the point of excitation caused by poly-injury accordinglyWith each layer rubber
Faulted condition between modulus of shearing change rate vector { ξ } recognizes equation:
In formula, [S] is the sensitivity matrix of dimensionless driving point antiresonance frequency, and p, q indicate difference section locating for excitation point C
Point, p=1,2 ..., N, q=1,2 ..., N.
Further, the step (4) further comprises following sub-step:
(4.1) PZT, the admittance signal Y of acquisition damage front and back are axially pasted along laminated rubber damping bearing；
(4.2) according to one-dimensional impedance model, the mechanical resistance of single coupling period structure is isolated from PZT electricity admittance signal Y
Anti- Zs；
(4.3) the velocity admittance H based on single coupling period structurevWith receptance HdRelationship, by single coupling period structure
Mechanical impedance ZsIt is converted into the displacement structure admittance H of single coupling periodd:
The valley for extracting receptance curve is the driving point antiresonance frequency of structure；
(4.4) based on step (4.3) obtain damage front and back driving point antiresonance frequency change rate, thus to laminated rubber every
It shakes support and carries out non-destructive tests.
Further, step (4.2) isolates structural mechanical impedance Z from PZT electricity admittance signal YsFurther comprise with
Lower sub-step:
(4.2.1) calculates the mechanical impedance Z of PZT under short-circuit conditiona:
In formula,For the wave number of PZT, ω is the circular frequency of driving frequency, la、ba、haRespectively PZT's
Length, width and thickness,Be electric field be constant when PZT complex elastic-modulus,For real elasticity modulus, η is mechanical damage
The factor is lost,For complex unit；
(4.2.2) PZT conductance receives expression formula are as follows:
In formula,Be stress be constant when PZT compound dielectric,For real dielectric constant, δ be dielectric absorption because
Son, d31For the piezoelectric strain coefficient of PZT；
Further, change rate of the step (4.4) based on driving point antiresonance frequency before and after the damage measured, to laminated rubber
Shock isolating pedestal carries out non-destructive tests, further comprises following sub-step:
(4.4.1) passes through driving point antiresonance frequency before and after the damage measured, calculates the variation of dimensionless driving point antiresonance frequency
Rate:
In formula,The driving point antiresonance frequency before and after the damage measured is respectively indicated, subscript u expression does not damage shape
State, subscript d indicate faulted condition；
(4.4.2) is based on damage so that the shearing rigidity of rubber increases, by the solving equations problem conversion of step (3.5)
For non-negative least square curve fitting problem:
[S] is solved according to the fitting result of above formula, completes non-destructive tests.
To achieve the goals above, the present invention also provides a kind of laminated rubber damping bearings based on Piezoelectric Impedance information
Non-destructive tests equipment, including processor and non-destructive tests program module；The non-destructive tests program module is by the processor
Any one foregoing laminated rubber damping bearing damnification recognition method is executed when calling.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, due to combining lamination
The periodic characteristics and PZT technology of rubber earthquake isolation support can achieve the following beneficial effects the high sensitivity characteristic of microlesion:
1) cyclophysis for considering laminated rubber damping bearing realizes accurate to the identification of laminated rubber bases poly-injury
Positioning.Preferably, relatively more frequency variation data can be obtained using driving point antiresonance frequency: by structural natural frequencies into
It is less using the order of frequency when row periodic structure non-destructive tests, generally less than structural cycle number.And utilize driving point antiresonance
Frequency carries out non-destructive tests, and a structure can have multiple driving points, and each driving point can get multistage driving point antiresonance frequency again
Rate.
2) the driving point antiresonance frequency that laminated rubber damping bearing is obtained from the PZT electricity admittance signal of measurement, to keep away
The direct measurement of driving point antiresonance frequency is exempted from.
Detailed description of the invention
Fig. 1 is a kind of the main of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information of the invention
Steps flow chart schematic diagram；
Fig. 2 is the laminated rubber damping bearing non-destructive tests experiment schematic diagram of the preferred embodiment of the present invention；
Fig. 3 (a) is laminated rubber damping bearing periodic system schematic diagram；
Fig. 3 (b) is laminated rubber shock insulation basic cycle cell schematics；
Fig. 4 (a) is excitation point when damaging the unit left side, and single coupling period system wave propagates schematic diagram；
Fig. 4 (b) is excitation point when damaging on the right of unit, and single coupling period system wave propagates schematic diagram；
Fig. 5 (a) is the antiresonant frequency sensitivity coefficient of node 1；
Fig. 5 (b) is the antiresonant frequency sensitivity coefficient of node 4；
Fig. 5 (c) is the antiresonant frequency sensitivity coefficient of node 7；
Fig. 5 (d) is the antiresonant frequency sensitivity coefficient of node 10；
Fig. 6 is non-destructive tests result.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
As shown in Figure 1, a kind of laminated rubber damping bearing damage based on Piezoelectric Impedance information of the preferred embodiment of the present invention
Hurt recognition methods to include the following steps:
(1) the driving point antiresonance frequecy characteristic equation of single damage and undamaged single coupling period structure is constructed；
(1.1) single coupling period structure of N number of basic cycle unit, left margin A are fixed, and right margin B is free, exciting force P
C point is acted on, using C point as separation, periodic structure is divided into minor structure I and minor structure II；
(1.2) assume that excitation point C has damage unit k, i.e. j < k in node j, minor structure II；It is solid that minor structure I is considered as both ends
It is fixed, there is the healthy periodic structure of j unit；Minor structure II be considered as left end fix, right end it is free, have single coupling of (N-j) a unit
Periodic structure is closed, wherein unit k is damaged；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Minor structure I:1-e-2jμ=0
Φ=0 minor structure II:1+
C0=A0+αDDαwr-αEEαwt-αwtαwr
E0=A0+αDDαwt-αEEαwr-αwtαwr
A0=αDDαEE-αDEαED
In formula, Φ indicates back wave and transmitting wave displacement at C in minor structure IIWithRatio, αDDAnd αEEFor
Damage the direct admittance at unit both ends, αEDAnd αDEFor the indirect admittance between damage unit both ends, subscript D, E is for distinguishing two
End and admittance direction；αwtAnd αwrThe feature waveguide admittance for respectively transmitting wave and back wave, has α for symmetrical cellwt=-αwr；
μ is Propagation Constants；
(1.3) based on occur antiresonance condition, i.e., driving frequency be equal to excitation point the left side or the right minor structure it is a certain
Intrinsic frequency obtains driving point antiresonance frequecy characteristic by the intrinsic frequency characteristic equation of the minor structure I and II of step (1.2)
Equation are as follows:
(1-e-2jμ) (1+ Φ)=0
(1.4) excitation point C is assumed at node j, and minor structure I has damage unit k, i.e. j >=k；It is solid that minor structure I is considered as both ends
Single coupling period structure that is fixed, having j unit, wherein unit k is damaged；Minor structure II be considered as left end fix, right end freely,
There is the single coupling period structure of the health of (N-j) a unit；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Ψ=0 minor structure I:1+
Minor structure II:1+e-2(N-j)μ=0
In formula, Ψ indicates back wave and transmitting wave displacement at C in minor structure IWithRatio；
(1.5) step (1.3) are repeated, obtain the corresponding driving point antiresonance frequecy characteristic equation of step (1.4) are as follows:
[1+e-2(N-j)μ] (1+ Ψ)=0
(1.6) under not damaged state, the driving point antiresonance frequency for the single damage that step (1.3) and (1.5) are obtained
Characteristic equation is degenerated are as follows:
[1+e-2(N-j)μ](1-e-2jμ)=0.
(2) laminated rubber damping bearing is reduced to limited single coupling period structure, and basic cycle unit is sheared by second order
Beam and both ends lumped mass are constituted, and calculate the dimensionless driving point antiresonance frequency under not damaged state；
(2.1) the direct admittance and indirect admittance at rubber layer both ends are as follows:
In formula, γllAnd γrrThe respectively direct admittance at rubber layer both ends, γlrAnd γrlRespectively between rubber layer both ends
Indirect admittance, subscript l, r is for distinguishing both ends and admittance direction；G is the modulus of shearing of rubber, and ρ is the density of rubber, L
For the thickness of rubber layer, A is the sectional area of rubber layer,For periodic structure wave number, ω is circular frequency, Ω=
ksL is dimensionless frequency；
(2.2) admittance of steel plate are as follows:
In formula, β is the admittance of steel plate, and ω is circular frequency, msFor the quality of every layer of steel plate；
(2.3) the directly or indirectly admittance of the compounding period unit of laminated rubber damping bearing and propagation constant difference
Are as follows:
In formula, αllAnd αrrFor the direct admittance at compounding period unit both ends, αlrAnd αrlBetween compounding period unit both ends
Transfer admittance, subscript l, r is for distinguishing both ends and admittance direction；For the mass ratio of rubber and steel plate,
mr=ρ AL is rubber quality；μ is Propagation Constants；
(2.4) by the direct admittance α of the healthy compounding period unit in step (2.3)ll、αrrWith transfer admittance αlr、αrlGeneration
In the dimensionless driving point antiresonance frequecy characteristic equation for entering not damaged single coupling period structure in step (1.6), lamination is calculated
Dimensionless driving point antiresonance frequency under the not damaged state of rubber earthquake isolation support.
(2.4.1) sets γ=μ i, the driving point antiresonance frequecy characteristic equation under the not damaged state that step (1.6) is obtained
Conversion are as follows:
γ=0 sin cos [(N-j) γ]
Non trivial solution are as follows:
Or
In formula:For imaginary unit, μ is Propagation Constants；
(2.4.2) converts the Propagation Constants calculation formula of step (2.3) according to γ=μ i are as follows:
The solution γ that step (2.4.1) is obtained substitutes into above-mentioned equation, calculates dimensionless driving point antiresonance frequency.Dimensionless
Driving point antiresonance frequency values Ω only with structural cycle number N, excitation point j and rubber and steel plate mass ratioIt is related, with it
Its geometric & physical property is unrelated.
(3) shearing rigidity incrementss are introduced into the admittance of damage unit, calculate dimensionless driving point antiresonance frequency to base
The sensitivity coefficient of this periodic unit shearing rigidity variation；Dimensionless driving point antiresonance frequency under poly-injury is regarded to change as single injury
Sensibility identification equation group is established in the approximately linear superposition for causing variation；
(3.1) when ageing of rubber, the modulus of shearing of corresponding rubber layer increases, and introduces faulted condition characterization parameter, damage
The directly or indirectly admittance of unit are as follows:
Ω '=ks′L
In formula, Δ G is the incrementss of unit modulus of shearing；
(3.2) to damage modulus of shearing change rate ξ of the unit k before and after damagekAssess degree of injury:
In formula, ξkIndicate that unit k is not damaged when=0；
(3.3) the n-th order dimensionless driving point antiresonance frequency change rate of damage front and back excitation point j are as follows:
In formula:The dimensionless driving point antiresonance frequency of damage front and back is respectively indicated, subscript u expression does not damage
State, subscript d indicate faulted condition；
(3.4) based on perturbation theory and sensitivity analysis principle, the n-th order dimensionless driving point antiresonance of excitation point j is obtained
The susceptibility that frequency damages kth unit
In formula:Indicate special by the driving point antiresonance frequency of step (1.3) and the single damage in (1.5)
Sign equation is askedTo ξkLocal derviation, then ξ is enabled in result expressionk=0；
(3.5) it regards the dimensionless origin variation in anti-resonant frequency under poly-injury and causes the approximately linear of variation folded as single injury
Add, establishes total dimensionless driving point antiresonance frequency change rate vector at the point of excitation caused by poly-injury accordinglyWith each layer rubber
Faulted condition between modulus of shearing change rate vector { ξ } recognizes equation:
In formula, [S] is the sensitivity matrix of dimensionless driving point antiresonance frequency, and p, q indicate difference section locating for excitation point C
Point, p=1,2 ..., N, q=1,2 ..., N.
(4) admittance signal of acquisition damage front and back, extracts the driving point antiresonance frequency of structure；It is anti-based on damage front and back origin
The change rate of resonant frequency solves sensibility and identifies equation group, carries out non-destructive tests.
(4.1) PZT, the admittance signal Y of acquisition damage front and back are axially pasted along laminated rubber damping bearing；
(4.2) according to one-dimensional impedance model, the mechanical resistance of single coupling period structure is isolated from PZT electricity admittance signal Y
Anti- Zs；
(4.2.1) calculates the mechanical impedance Z of PZT under short-circuit conditiona:
In formula,For the wave number of PZT, ω is the circular frequency of driving frequency, la、ba、haRespectively PZT's
Length, width and thickness,Be electric field be constant when PZT complex elastic-modulus,For real elasticity modulus, η is mechanical damage
The factor is lost,For complex unit；
(4.2.2) PZT conductance receives expression formula are as follows:
In formula,Be stress be constant when PZT compound dielectric,For real dielectric constant, δ be dielectric absorption because
Son, d31For the piezoelectric strain coefficient of PZT；
(4.3) the velocity admittance H based on single coupling period structurevWith receptance HdRelationship, by single coupling period structure
Mechanical impedance ZsIt is converted into the displacement structure admittance H of single coupling periodd:
The valley for extracting receptance curve is the driving point antiresonance frequency of structure；
(4.4) based on step (4.3) obtain damage front and back driving point antiresonance frequency change rate, thus to laminated rubber every
It shakes support and carries out non-destructive tests.
(4.4.1) passes through driving point antiresonance frequency before and after the damage measured, calculates the variation of dimensionless driving point antiresonance frequency
Rate:
In formula,The driving point antiresonance frequency before and after the damage measured is respectively indicated, subscript u expression does not damage shape
State, subscript d indicate faulted condition；
(4.4.2) is based on damage so that the shearing rigidity of rubber increases, by the solving equations problem conversion of step (3.5)
For non-negative least square curve fitting problem:
[S] is solved according to the fitting result of above formula, completes non-destructive tests.
Below using laminated rubber damping bearing experimental model shown in Fig. 2 as object, to describe based on periodic structure theory
Non-destructive tests process.Fig. 3 (a) is laminated rubber damping bearing periodic system schematic diagram, and the model is by 10 nodes, 10 lists
Member composition.Fig. 3 (b) is basic cycle cell schematics, and parameter is as follows: the modulus of shearing of rubber is 8 × 105N/m2, rubber it is close
Degree is 1000kg/m3, rubber layer with a thickness of 3.14mm, the sectional area of rubber layer is 0.16m2, the quality of steel plate is 2.512kg.
Fig. 4 (a) is that single coupling period system wave of the excitation point when damaging the unit left side propagates schematic diagram, and Fig. 4 (b) is that excitation point is damaging
Single coupling period system wave when hurting on the right of unit propagates schematic diagram.
For the verifying present invention, a kind of damage regime is arranged to the laminated rubber damping bearing: the rigidity of unit 1 increases by 5%,
And the rigidity of unit 10 increases by 10%.PZT is pasted on 1,4,7,10 position of node and is measured, by PZT electricity admittance signal
Structural mechanical impedance signal is converted to, and extracts the 9th rank antiresonant frequency.The node that the above method according to the invention obtains
1, shown in 4,7,10 antiresonant frequency sensitivity coefficient such as Fig. 5 (a)~5 (d).Antiresonant frequency variation based on damage front and back
Rate solves sensibility and identifies equation group, and the comparison of the recognition result and actual damage that solve is as shown in Figure 6.As can be seen that
The non-destructive tests result and actual damage of this method are very close, can accurately identify damage position and degree of injury.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (8)
1. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information, which is characterized in that including following
Step:
(1) the driving point antiresonance frequecy characteristic equation of single damage and undamaged single coupling period structure is constructed；
(2) laminated rubber damping bearing is reduced to single coupling period structure, basic cycle unit is by second order shear beam and two
The lumped mass at rank shear beam both ends is constituted, and calculates dimensionless driving point antiresonance of single coupling period structure under not damaged state
Frequency；
(3) shearing rigidity incrementss are introduced into the admittance of damage unit, calculate dimensionless driving point antiresonance frequency to substantially all
The sensitivity coefficient of phase unit shearing rigidity variation；Regard the approximation that antiresonant frequency variation under poly-injury causes variation as single injury
Linear superposition establishes sensibility identification equation group；
(4) admittance signal of acquisition damage front and back extracts the driving point antiresonance frequency of single coupling period structure；Based on damage front and back
The change rate of driving point antiresonance frequency solves sensibility and identifies equation group, carries out non-destructive tests.
2. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as described in claim 1,
It is characterized in that, the step (1) further comprises following sub-step:
(1.1) for single coupling period structure of N number of basic cycle unit, if left margin A is fixed, right margin B is free, exciting force
P acts on C point, then using C point as separation, which is divided into minor structure I and minor structure II；
(1.2) assume that excitation point C has damage unit k, i.e. j < k in node j, minor structure II；Minor structure I is considered as both ends and fixes, has
The single coupling period structure of the health of j unit；Minor structure II is considered as single coupling that left end is fixed, right end is free, has (N-j) a unit
Periodic structure is closed, wherein unit k is damaged；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Minor structure I:1-e-2jμ=0
Φ=0 minor structure II:1+
C0=A0+αDDαwr-αEEαwt-αwtαwr
E0=A0+αDDαwt-αEEαwr-αwtαwr
A0=αDDαEE-αDEαED
In formula, Φ indicates back wave and transmitting wave displacement at C in minor structure IIWithRatio, αDDAnd αEEFor damage
The direct admittance at unit both ends, αEDAnd αDEFor the indirect admittance between damage unit both ends, αwtAnd αwrRespectively transmitting wave and anti-
The feature waveguide admittance of ejected wave, has α for symmetrical cellwt=-αwr；μ is Propagation Constants；
(1.3) based on the condition that antiresonance occurs, i.e., driving frequency is equal to a certain intrinsic of the excitation point left side or the right minor structure
Frequency obtains driving point antiresonance frequecy characteristic equation by the intrinsic frequency characteristic equation of the minor structure I and II of step (1.2)
Are as follows:
(1-e-2jμ) (1+ Φ)=0
(1.4) excitation point C is assumed at node j, and minor structure I has damage unit k, i.e. j >=k；Minor structure I be considered as both ends fix,
There is single coupling period structure of j unit, wherein unit k is damaged；Minor structure II is considered as left end and fixes, right end freedom, has
(N-j) the single coupling period structure of the health of a unit；The intrinsic frequency characteristic equation of minor structure I and minor structure II is respectively as follows:
Ψ=0 minor structure I:1+
Minor structure II:1+e-2(N-j)μ=0
In formula, Ψ indicates back wave and transmitting wave displacement at C in minor structure IWithRatio；
(1.5) step (1.3) are repeated, obtain the corresponding driving point antiresonance frequecy characteristic equation of step (1.4) are as follows:
[1+e-2(N-j)μ] (1+ Ψ)=0
(1.6) under not damaged state, the driving point antiresonance frequecy characteristic for the single damage that step (1.3) and (1.5) are obtained
Equation is degenerated are as follows:
[1+e-2(N-j)μ](1-e-2jμ)=0.
3. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as described in claim 1,
It is characterized in that, the step (2) further comprises following sub-step:
(2.1) the direct admittance and indirect admittance at rubber layer both ends are as follows:
In formula, γllAnd γrrThe respectively direct admittance at rubber layer both ends, γlrAnd γrlBetween respectively between rubber layer both ends
Admittance is connect, G is the modulus of shearing of rubber, and ρ is the density of rubber, and L is the thickness of rubber layer, and A is the sectional area of rubber layer,For periodic structure wave number, ω is circular frequency, Ω=ksL is dimensionless frequency；
(2.2) admittance of steel plate are as follows:
In formula, β is the admittance of steel plate, and ω is circular frequency, msFor the quality of every layer of steel plate；
(2.3) the directly or indirectly admittance of the compounding period unit of laminated rubber damping bearing and propagation constant are respectively as follows:
In formula, αllAnd αrrFor the direct admittance at compounding period unit both ends, αlrAnd αrlFor the biography between compounding period unit both ends
Admittance is passed,For the mass ratio of rubber and steel plate, mr=ρ AL is rubber quality；μ is Propagation Constants；
(2.4) by the direct admittance α of the healthy compounding period unit in step (2.3)ll、αrrWith transfer admittance αlr、αrlSubstitute into step
Suddenly in the dimensionless driving point antiresonance frequecy characteristic equation of not damaged single coupling period structure in (1.6), laminated rubber is calculated
Dimensionless driving point antiresonance frequency under the not damaged state of shock isolating pedestal.
4. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as claimed in claim 3,
It is characterized in that, the dimensionless driving point antiresonance frequency that step (2.4) calculates under not damaged state further comprises following sub-step:
(2.4.1) sets γ=μ i, and the driving point antiresonance frequecy characteristic under the not damaged state that step (1.6) is obtained is equations turned
Are as follows:
γ=0 sin cos [(N-j) γ]
Non trivial solution are as follows:
Or
In formula:For imaginary unit, μ is Propagation Constants；
(2.4.2) converts the Propagation Constants calculation formula of step (2.3) according to γ=μ i are as follows:
The solution γ that step (2.4.1) is obtained substitutes into above-mentioned equation, calculates dimensionless driving point antiresonance frequency.
5. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as described in claim 1,
It is characterized in that, the step (3) further comprises following sub-step:
(3.1) when ageing of rubber, the modulus of shearing of corresponding rubber layer increases, and introduces faulted condition characterization parameter, damages unit
Directly or indirectly admittance are as follows:
Ω '=ks′L
In formula, Δ G is the incrementss of unit modulus of shearing；
(3.2) to damage modulus of shearing change rate ξ of the unit k before and after damagekAssess degree of injury:
In formula, ξkIndicate that unit k is not damaged when=0；
(3.3) the n-th order dimensionless driving point antiresonance frequency change rate of damage front and back excitation point j are as follows:
In formula:The dimensionless driving point antiresonance frequency of damage front and back is respectively indicated, subscript u indicates non-faulted condition,
Subscript d indicates faulted condition；
(3.4) based on perturbation theory and sensitivity analysis principle, the n-th order dimensionless driving point antiresonance frequency of excitation point j is obtained
To the susceptibility of kth unit damage
In formula:Indicate the driving point antiresonance frequecy characteristic equation by step (1.3) and the single damage in (1.5)
It asksTo ξkLocal derviation, then ξ is enabled in result expressionk=0；
(3.5) the approximately linear superposition that the dimensionless origin variation in anti-resonant frequency under poly-injury causes variation as single injury is regarded,
Total dimensionless driving point antiresonance frequency change rate vector at the point of excitation caused by poly-injury is established accordinglyIt is cut with each layer rubber
Faulted condition between shear modulu change rate vector { ξ } recognizes equation:
In formula, [S] is the sensitivity matrix of dimensionless driving point antiresonance frequency, and p, q indicate different nodes locating for excitation point C, p
=1,2 ..., N, q=1,2 ..., N.
6. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as claimed in claim 5,
It is characterized in that, the step (4) further comprises following sub-step:
(4.1) PZT, the admittance signal Y of acquisition damage front and back are axially pasted along laminated rubber damping bearing；
(4.2) according to one-dimensional impedance model, the mechanical impedance Z of single coupling period structure is isolated from PZT electricity admittance signal Ys；
(4.3) the velocity admittance H based on single coupling period structurevWith receptance HdRelationship, by the machine of single coupling period structure
Tool impedance ZsIt is converted into the displacement structure admittance H of single coupling periodd:
The valley for extracting receptance curve is the driving point antiresonance frequency of structure；
(4.4) change rate that damage front and back driving point antiresonance frequency is obtained based on step (4.3), thus to laminated rubber shock insulation branch
Seat carries out non-destructive tests.
7. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as claimed in claim 6,
It is characterized in that, step (4.2) isolates structural mechanical impedance Z from PZT electricity admittance signal YsFurther comprise following sub-step:
(4.2.1) calculates the mechanical impedance Z of PZT under short-circuit conditiona:
In formula,For the wave number of PZT, ω is the circular frequency of driving frequency, la、ba、haThe respectively length of PZT
Degree, width and thickness,Be electric field be constant when PZT complex elastic-modulus,For real elasticity modulus, η is mechanical loss
The factor,For complex unit；
(4.2.2) PZT conductance receives expression formula are as follows:
In formula,Be stress be constant when PZT compound dielectric,For real dielectric constant, δ is electrical dissipation factor,
d31For the piezoelectric strain coefficient of PZT.
8. a kind of laminated rubber damping bearing damnification recognition method based on Piezoelectric Impedance information as claimed in claim 5,
It is characterized in that, change rate of the step (4.4) based on driving point antiresonance frequency before and after the damage measured, to laminated rubber damping bearing
Non-destructive tests are carried out, further comprise following sub-step:
(4.4.1) passes through driving point antiresonance frequency before and after the damage measured, calculates dimensionless driving point antiresonance frequency change rate:
In formula,The driving point antiresonance frequency before and after the damage measured is respectively indicated, subscript u indicates non-faulted condition,
Subscript d indicates faulted condition；
(4.4.2) so that the shearing rigidity of rubber increases, is converted the solving equations problem of step (3.5) to non-based on damage
Negative least square curve fitting problem:
[S] is solved according to the fitting result of above formula, completes non-destructive tests.
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| US2913530A (en) * | 1953-07-03 | 1959-11-17 | Int Standard Electric Corp | Line identification in telecommunication systems |
| US20110260875A1 (en) * | 2010-04-21 | 2011-10-27 | Koninklijke Philips Electronics, N.V. | Alert device and method |
| CN103528778A (en) * | 2013-10-11 | 2014-01-22 | 南京航空航天大学 | Rapid damage detection method for three-layer-of-base shock isolation system on basis of incomplete measurement |
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