CN106156441A - The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches - Google Patents

Abstract

A kind of grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches, by the Classical lamination theory of composite, construct the constitutive equation of grand fibrous composite, the correlation theory utilizing the mechanics of materials calculates the size being used as power, the practical function by grand fiber piezo-electricity composite material piezoelectric patches that can be directly perceived, easy is equivalent to four mid-side node load of piezoelectric patches, facilitates the finite element dynamic analysis of grand fiber piezo-electricity composite material piezoelectric patches.The present invention carries out piezoelectric modeling in the finite element software without piezoelectric unit, is applied in the piezoelectric unit modeling of finite element software, compensate for part Finite Element Method and can not carry out dynamic (dynamical) deficiency being used as power and identifying.

Description

The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches

Technical field

The invention belongs to piezo-electricity composite material, a kind of grand fiber piezo-electricity composite material piezoelectric patches kinetics start Power recognition methods, is applied in the piezoelectric unit modeling of finite element software.

Background technology

Piezo-electricity composite material is a kind of new material that recent decades grows up, be widely used in intelligent sensing, pulse- The fields such as echo transducer, acceleration transducer, vibration and noise control.Piezo-electricity composite material is main as fields such as sensors Application is the direct piezoelectric effect of piezo-electricity composite material, and carry out that vibration and noise controls main application as actuator is pressure The inverse piezoelectric effect of composite.

Grand fiber piezo-electricity composite material piezoelectric patches be by piezoelectric fabric and high molecular polymer according to certain connected mode, Certain volume or mass ratio and certain geometric distribution are composited.Piezoelectric fabric is laid along work surface direction, polarization side To along fibre length direction, and using interdigital electrode, this special configuration of electrodes makes actuator make full use of outside Added electric field direction can produce the longitudinal piezoelectric effect (d of maximum mechanical response₃₃Constant) produce higher being used as power and displacement, and And the piezoelectric fabric cross section that grand fiber piezo-electricity composite material piezoelectric patches uses is rectangular cross section.

The operation principle of grand fiber piezo-electricity composite material piezoelectric patches actuator is: execute on the electrode to grand fibrous composite Making alive, produces strain in the work surface of grand fibrous composite, at basal body structure surface mount or the grand fiber of internal embedment Composite, owing to the constraint of basal body structure can react on matrix one counter-force, makes matrix produce strain, thus makees kinetoplast.

The current grand fiber piezo-electricity composite material piezoelectric patches method that is used as power mainly has two kinds of thinkings, and one is to use thermoelastic ratio Plan method, by longitudinal piezoelectric effect constant d₃₃It is converted into thermoelastic coefficient, converts voltage to temperature, calculated by thermoelastic effect and make The size of power；Another kind is the Classical lamination theory using composite, constructs the constitutive equation of grand fibrous composite, The correlation theory utilizing the mechanics of materials calculates the size being used as power.Retrieve domestic and international Patents, be designed into grand fiber piezoelectricity The patent of composite piezoelectric patches is all the preparation about piezo-electricity composite material, for grand fiber piezo-electricity composite material piezoelectric patches The computational methods that are used as power are not mentioned.And at home and abroad in pertinent literature, Xue Xiaomin is at Journal of The Study on electric-delivered in Intelligent Material Systems and Structure Piezo-electricity composite material is led to by mechanical hysteretic model of Macro-Fiber Composite actuator After electricity, some material behaviors of piezoelectricity and the relation of voltage are stated in produced strain as, do not have the size that explanation is used as power；Breathe out Master's thesis " Active Vibration Control based on piezoelectric intelligent composite material " P1 type of the having derived grand fiber pressure of your shore polytechnical university The start Bending Moment Equations in composite plate of composite piezoelectric patches.

Summary of the invention

For overcoming part Finite Element Method in prior art can not carry out dynamic (dynamical) deficiency being used as power and identifying, the present invention Propose a kind of grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches.

The detailed process of the present invention is:

Step 1: intercept the analytic unit of piezoelectric patches.

Surface mount grand fiber piezo-electricity composite material piezoelectric patches at cantilever beam, and make this grand fiber piezo-electricity composite material pressure Electricity sheet is near the clamped end side of cantilever beam.The position pasting grand fiber piezo-electricity composite material piezoelectric patches on described cantilever beam is cut Take off, obtain analytic unit

Step 2: divide finite element unit

The described cantilever beam pasting grand fiber piezo-electricity composite material piezoelectric patches is divided finite element unit, and checks grand fibre The dimension finite element interstitial content on piezo-electricity composite material piezoelectricity length of a film limit and having of this grand fiber piezo-electricity composite material piezoelectric patches minor face Limit unit interstitial content.

Step 3: determine grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship.

Described grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship is:

$\left\{\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\τ}}_{12}\end{array}\right\}=\[Q\]\left\{\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right\}---\left(3\right)$

In formula: Q is the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches.ε₁、ε₂It is respectively 1 side of material principal direction To, the principal strain in 2 directions.σ₁、σ₂It is respectively 1 direction of material principal direction, the principal stress in 2 directions in the mechanics of materials；τ₁₂For material 1 direction of material principal direction and the shearing stress in the 1-2 plane of 2 direction compositions.γ₁₂1 direction of material principal direction and 2 direction compositions 1-2 plane in shear strain.

Step 4: determine the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches.

The stiffness matrix of grand fiber piezo-electricity composite material piezoelectric smart material is:

$\[Q\]=\left[\begin{array}{ccc}{Q}_{11}& Q_{12}& 0\\ Q_{12}& Q_{22}& 0\\ 0& 0& Q_{66}\end{array}\right]=\left[\begin{array}{ccc}\frac{E_1}{1-v_{12}{v}_{21}}& \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& 0\\ \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& \frac{E_2}{1-v_{12}{v}_{21}}& 0\\ 0& 0& G_{12}\end{array}\right]---\left(4\right)$

Q_ijIn subscript i, j represent the dimension of Stiffness Matrix；v₁₂With v₂₁Respectively represent material principal direction 1 direction just should The deformation coefficient in 1 direction that the direct stress in the deformation coefficient in 2 directions that power causes and 2 directions of material principal direction causes；E₁With E₂ Direction represents 1 direction of material principal direction and the elastic modelling quantity in 2 directions respectively；G₁₂Represent 1 direction and 2 directions of material principal direction Composition 1-2 plane in modulus of shearing.

Step 5, determines power and the moment on four limits of grand fiber piezo-electricity composite material piezoelectric patches under unit voltage；

Power matrix N suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches and moment matrix under the unit voltage determined M is respectively as follows:

N=[Q] × d × E_d×t_p (6)

$M=\frac{1}{2}\[Q\]\×d\×E_d\×t_p\×(t_p+t)---\left(7\right)$

D is piezoelectric effect constant matrices, t_pPiezoelectric patches thickness, t is cantilever beam thickness, and N is grand fiber piezo-electricity composite material Moment battle array suffered by four limits of piezoelectric patches, M is the moment matrix suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches.

Step 6, by the power suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches under unit voltage and moment equivalence For nodal force:

The power in x, y, z three direction that described nodal force is calculated by formula (8) forms with the moment in x, y, z three direction.

$\begin{array}{c}Npw=\[\begin{array}{cc}N\left(1\right)*wp/a/2N\left(3\right)*wp/a/2& 0\end{array}\]\\ Mpw=\[\begin{array}{cc}0& M\left(1\right)*wp/a/2-M\left(3\right)*wp/a/2\end{array}\]\\ Npl=\[\begin{array}{cc}N\left(3\right)*lp/b/2N\left(3\right)*lp/b/2& 0\end{array}\]\\ Mpl=\[\begin{array}{cc}-M\left(2\right)*lp/b/2M\left(3\right)*lp/b/2& 0\end{array}\]\end{array}---\left(8\right)$

In formula: Npw is the moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectric patches broadside；Npl The moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectricity length of a film limit；Mpw is grand fiber Piezoelectric anisotropy The moment matrix in x, y, z three direction suffered by material piezoelectric patches broadside；Mpl is grand fiber piezo-electricity composite material piezoelectricity length of a film limit The moment matrix in suffered x, y, z three direction；Wp is the width of grand fiber piezo-electricity composite material piezoelectric patches；A is width Nodes；Lp is the length of grand fiber piezo-electricity composite material piezoelectric patches；B is the nodes of length direction.

Step 7: nodal force will be carried out Coordinate Conversion.

The nodal force of the equivalence obtained is carried out Coordinate Conversion；Nodal force after coordinate transformation is:

$F=\left[\begin{array}{c}\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\\ \[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\end{array}\right]---\left(11\right)$

When the nodal force of the described equivalence to obtaining carries out Coordinate Conversion, coordinate conversion matrix is:

$lamda=\left[\begin{array}{ccc}cos\left(alpha\right)& -sin\left(alpha\right)& 0\\ sin\left(alpha\right)& \cos \left(alpha\right)& 0\\ 0& 0& 1\end{array}\right]---\left(9\right)$

$T=\left[\begin{array}{cc}lamda& 0\\ 0& lamda\end{array}\right]---\left(10\right)$

Lamda is direction cosine matrix；T is coordinate conversion matrix；Alpha grand fiber piezo-electricity composite material piezoelectric patches local Coordinate and the angle of global coordinate system.

Step 8, cantilever beam dynamic test；

Step 9, revises the modal damping system of the cantilever beam FEM (finite element) model pasting grand fiber piezo-electricity composite material piezoelectric patches Number: make each width of the test value of the intermediate value of each amplitude voltage of setting and this setting obtained by cantilever beam dynamic test The error of the simulation value of threshold voltage is in 1%.

The described modal damping coefficient revising the cantilever beam FEM (finite element) model pasting grand fiber piezo-electricity composite material piezoelectric patches Detailed process be:

Repeat step 5～7, calculate described grand fiber respectively being positioned in step 8 intermediate value of each amplitude voltage arranged The nodal force of each node on piezo-electricity composite material piezoelectric patches.Each node on the grand fiber piezo-electricity composite material piezoelectric patches that will obtain Nodal force is sequentially inputted in the load boundary of FEM (finite element) model, and inputs displacement boundary conditions；Described displacement boundary conditions Degree of freedom for all nodes of clamped end of cantilever beam is all set to 0.Give material properties to this FEM (finite element) model, and mode is set Damped coefficient, carries out finite element analysis.Obtain the displacement amplitude of cantilever beam free end under this amplitude voltage, this width that will obtain The displacement amplitude of the cantilever beam free end under threshold voltage intermediate value records the cantilever under this amplitude voltage intermediate value with step 8 test The carrying out of the displacement amplitude of beam free end contrasts, if error is more than 1%, adjusts modal damping coefficient and carries out finite element analysis again, Until error, within 1%, determines the modal damping coefficient of this FEM (finite element) model, this modal damping coefficient is solid in subsequent calculations Fixed constant.

If each amplitude voltage intermediate value of described setting has two, the most arbitrarily taking one, described node is grand fiber pressure All nodes on four limits of composite piezoelectric patches.

Step 10, the grand fiber piezo-electricity composite material piezoelectric patches dynamic (dynamical) piezoelectric effect constant identification of arbitrary amplitude voltage:

By the formula (12) piezoelectricity to the grand fiber piezo-electricity composite material piezoelectric patches under described each amplitude voltage effect Effect constant d_aBeing modified, subscript a of piezoelectric effect constant d represents that signal projector output signal is AC signal.

$d_a=\frac{w_3}{w_4}\×d_{33}---\left(12\right)$

w₃For the cantilever beam free end travel amplitude of the described amplitude voltage intermediate value that test records, w₄For simulation calculation The cantilever beam free end travel amplitude of this amplitude voltage intermediate value.

To the grand fiber piezo-electricity composite material piezoelectric patches under each amplitude voltage effect arranged obtained described in step 9 Piezoelectric effect constant d_aCarry out curve fitting, obtain grand fiber piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage dynamic (dynamical) Piezoelectric effect constant d_an。

Step 10 one, the dynamic (dynamical) identification that is used as power of grand fiber piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage:

The piezoelectric effect constant d of the grand fiber piezo-electricity composite material piezoelectric patches under the arbitrary amplitude voltage that will obtain_anSubstitute into In formula (6), formula (7), and repeat step 5～7, it is thus achieved that under arbitrary amplitude voltage, grand fiber piezo-electricity composite material piezoelectric patches is dynamically made Power.

The present invention carries out piezoelectric modeling in the finite element software without piezoelectric unit, is applied to finite element soft In the piezoelectric unit modeling of part, to make up the deficiency of part finite element software.

Compared with the prior art, advantages of the present invention:

In traditional finite element analysis software, in addition to ansys and abaqus, the most all there is no piezoelectric unit, these Piezoelectric unit existing in finite element software is not suitable for grand fiber piezo-electricity composite material piezoelectric patches yet, needs to carry out Piezoelectric analysis Shi Tongchang uses other complex methods such as thermoelastic analogy.The present invention proposes a kind of grand fiber piezo-electricity composite material piezoelectricity Sheet kinetics is used as power recognition methods, by the Classical lamination theory of composite, constructs the basis of grand fibrous composite Structure equation, utilizes the correlation theory of the mechanics of materials to calculate the size being used as power, it is possible to directly perceived, easy is multiple by grand fiber piezoelectricity The practical function of condensation material piezoelectric patches is equivalent to four mid-side node load of piezoelectric patches, facilitates grand fiber piezo-electricity composite material piezoelectric patches Finite element dynamic analysis.

The present invention can carry out piezoelectric modeling in the finite element software without piezoelectric unit, and making up part has The deficiency of limit meta software, changes into the form of power and moment by piezoelectric effect.

Accompanying drawing explanation

Fig. 1 is the cantilever beam geometric graph pasting grand fiber piezo-electricity composite material piezoelectric patches；

Fig. 2 is that structure upper surface pastes grand fiber piezo-electricity composite material piezoelectric patches schematic diagram；

Fig. 3 is the cantilever beam FEM (finite element) model pasting grand fiber piezo-electricity composite material piezoelectric patches；

Fig. 4 is the flow chart of the present invention.

The grandest fiber piezo-electricity composite material piezoelectric patches；2. cantilever beam；σ_x.x the direct stress in direction；σ_y.y the direct stress in direction； τ_xy. along the shearing stress in xy direction；τ_yx. along the shearing stress in yx direction, the termination of l. grand fiber piezo-electricity composite material piezoelectric patches is with outstanding The minimum distance of the clamped end of arm beam.

Detailed description of the invention

The present embodiment is to use grand fiber piezo-electricity composite material piezoelectric patches finite element modeling method, calculates one and pastes grand fibre The process of grand fiber piezo-electricity composite material piezoelectric patches modeling on the cantilever beam 2 of dimension piezo-electricity composite material piezoelectric patches 1 is concrete such as Fig. 1 Shown in, this cantilever beam 2 cross section is rectangle.A length of 390mm of described cantilever beam 2, a width of 64mm, thickness is 3mm, clamped end Clamping length is 30mm.A length of 85mm, a width of 57mm of described grand fiber piezo-electricity composite material piezoelectric patches 1, thickness is 0.3mm, makes the length direction of this grand fiber piezo-electricity composite material piezoelectric patches 1 with the length direction of cantilever beam 2 along identical during stickup Change in coordinate axis direction, and the minimum distance of the clamped end of the termination of grand fiber piezo-electricity composite material piezoelectric patches 1 and cantilever beam is 44mm. The material properties of described cantilever beam 2 is: elastic modelling quantity 70GPa, Poisson's ratio 0.3, density 2700kg/m³.Described grand fiber pressure The piezoelectric effect constant d of composite piezoelectric patches₃₃For 4e-7, d₃₁With d₃₂It is zero, the springform in 1 direction of material principal direction Amount E₁Elastic modulus E for 30.336GPa Yu 2 directions of material principal direction₂For 15.857GPa, 1 direction and 2 of material principal direction Shear modulus G in what direction formed 1-2 plane₁₂For 5.515GPa, the direct stress in 1 direction of material principal direction cause 2 The v of the deformation coefficient in direction₁₂It is 0.31.

1 direction of described material principal direction is the interior direction along fiber of composite fiber roofing, described material master 2 directions in direction are the interior direction perpendicular with fiber of composite fiber roofing, and 3 directions of described material principal direction are The direction perpendicular with composite fiber roofing.

The present embodiment to be embodied as step as follows:

Step 1: intercept the analytic unit of piezoelectric patches.

Surface mount grand fiber piezo-electricity composite material piezoelectric patches 1 at cantilever beam 2, and make this grand fiber piezo-electricity composite material Piezoelectric patches is near the clamped end side of cantilever beam；In the present embodiment, the termination of grand fiber piezo-electricity composite material piezoelectric patches and cantilever The minimum distance of the clamped end of beam is 44mm.The position pasting grand fiber piezo-electricity composite material piezoelectric patches on described cantilever beam is cut Take off, obtain analytic unit, as shown in Figure 2.This analytic unit by the position of the cantilever beam intercepted be pasted onto this position The grand fiber piezo-electricity composite material piezoelectric patches composition of upper surface.

Step 2: divide finite element unit

The described cantilever beam pasting grand fiber piezo-electricity composite material piezoelectric patches is divided finite element unit, and checks grand fibre The dimension finite element interstitial content on piezo-electricity composite material piezoelectricity length of a film limit and having of this grand fiber piezo-electricity composite material piezoelectric patches minor face Limit unit interstitial content.

In the present embodiment, the long limit finite element node number of piezoelectric patches is 10, and minor face finite element node number is 7.

Step 3: determine grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship.

The stress and strain relationship of grand fiber piezo-electricity composite material piezoelectric patches is plane stress problem:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\ϵ}}_3\\ {\mathrm{\γ}}_{23}\\ {\mathrm{\γ}}_{31}\\ {\mathrm{\γ}}_{12}\end{array}\right\}=\left[\begin{array}{cccccc}{S}_{11}& S_{12}& S_{13}& 0& 0& 0\\ S_{21}& S_{22}& S_{23}& 0& 0& 0\\ S_{31}& S_{32}& S_{33}& 0& 0& 0\\ 0& 0& 0& S_{44}& 0& 0\\ 0& 0& 0& 0& S_{55}& 0\\ 0& 0& 0& 0& 0& S_{66}\end{array}\right]\left\{\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\σ}}_3\\ {\mathrm{\τ}}_{23}\\ {\mathrm{\τ}}_{31}\\ {\mathrm{\τ}}_{12}\end{array}\right\}---\left(1\right)$

In formula: ε₁、ε₂、ε₃It is respectively the principal strain in 1 direction of material principal direction, 2 directions and 3 directions.γ₂₃For material master Shear strain in what 2 directions in direction and 3 directions formed 2-3 plane；γ₃₁3 directions and 1 direction composition for material principal direction 3-1 plane in shear strain；γ₁₂Shear strain in what 1 direction of material principal direction and 2 directions formed 1-2 plane.

S_ijFor Flexibility Matrix, subscript i, j are the dimension of Flexibility Matrix, i=1, and 2 ..., 6；J=1,2 ..., 6.σ₁、σ₂、σ₃Point Wei 1 direction of material principal direction in the mechanics of materials, the principal stress in 2 directions and 3 directions；τ₂₃For material principal direction in the mechanics of materials 2 directions with 3 directions composition 2-3 plane in shearing stress, τ₃₁The 3-1 formed with 1 direction for 3 directions of material principal direction Shearing stress in plane, τ₁₂1 direction and the shearing stress in the 1-2 plane of 2 direction compositions for material principal direction.

Due to 3 directions small-sized of grand fiber piezo-electricity composite material piezoelectric smart material principal direction, therefore regard this grand fiber Piezo-electricity composite material piezoelectric patches is one-way slabs, it may be assumed that

σ₃=τ₂₃=τ₃₁=0 (2)

The components of stress, grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship is represented by the components of strain For:

$\left\{\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\τ}}_{12}\end{array}\right\}=\[Q\]\left\{\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right\}---\left(3\right)$

In formula: Q is the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches.

Step 4: determine the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches.

Grand fiber piezo-electricity composite material piezoelectric patches is orthotropy one-way slabs.For orthotropy one-way slabs, Material principal direction and the x of one-way slabs, y-coordinate overlaps, then stiffness matrix is:

$\[Q\]=\left[\begin{array}{ccc}{Q}_{11}& Q_{12}& 0\\ Q_{12}& Q_{22}& 0\\ 0& 0& Q_{66}\end{array}\right]=\left[\begin{array}{ccc}\frac{E_1}{1-v_{12}{v}_{21}}& \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& 0\\ \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& \frac{E_2}{1-v_{12}{v}_{21}}& 0\\ 0& 0& G_{12}\end{array}\right]---\left(4\right)$

Q_ijIn subscript i, j represent the dimension of Stiffness Matrix；v₁₂With v₂₁Respectively represent material principal direction 1 direction just should The deformation coefficient in 1 direction that the direct stress in the deformation coefficient in 2 directions that power causes and 2 directions of material principal direction causes；E₁With E₂ Direction represents 1 direction of material principal direction and the elastic modelling quantity in 2 directions respectively；G₁₂Represent 1 direction and 2 directions of material principal direction Composition 1-2 plane in modulus of shearing.

Step 5: determine power and the moment on four limits of grand fiber piezo-electricity composite material piezoelectric patches under unit voltage.

First electric field intensity E under unit voltage is determined_dFor:

E_d=U/u (5)

In formula: U is voltage of electric field；U is electrode spacing.

Then under unit voltage, power matrix N suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches is divided with moment matrix M It is not:

N=[Q] × d × E_d×t_p (6)

$M=\frac{1}{2}\[Q\]\×d\×E_d\×t_p\×(t_p+t)---\left(7\right)$

D is piezoelectric effect constant matrices, t_pPiezoelectric patches thickness, t is cantilever beam thickness, and N is grand fiber piezo-electricity composite material Moment battle array suffered by four limits of piezoelectric patches, M is the moment matrix suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches.

Step 6: by the power suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches under unit voltage and moment equivalence On node.

By formula (8) by the power on four limits of grand fiber piezo-electricity composite material piezoelectric patches under described unit voltage and power Square is equivalent on each node of fiber piezo-electricity composite material piezoelectric patches grand in finite element, grand fibre in the finite element under unit voltage The equivalent nodal force of dimension four each nodes in limit of piezo-electricity composite material piezoelectric patches is:

$\begin{array}{c}Npw=\[\begin{array}{cc}N\left(1\right)*wp/a/2N\left(3\right)*wp/a/2& 0\end{array}\]\\ Mpw=\[\begin{array}{cc}0& M\left(1\right)*wp/a/2-M\left(3\right)*wp/a/2\end{array}\]\\ Npl=\[\begin{array}{cc}N\left(3\right)*lp/b/2N\left(3\right)*lp/b/2& 0\end{array}\]\\ Mpl=\[\begin{array}{cc}-M\left(2\right)*lp/b/2M\left(3\right)*lp/b/2& 0\end{array}\]\end{array}---\left(8\right)$

In formula: Npw is the moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectric patches broadside；Npl The moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectricity length of a film limit；Mpw is grand fiber Piezoelectric anisotropy The moment matrix in x, y, z three direction suffered by material piezoelectric patches broadside；Mpl is grand fiber piezo-electricity composite material piezoelectricity length of a film limit The moment matrix in suffered x, y, z three direction；Wp is the width of grand fiber piezo-electricity composite material piezoelectric patches；A is width Nodes；Lp is the length of grand fiber piezo-electricity composite material piezoelectric patches；B is the nodes of length direction.

The power in x, y, z three direction that described nodal force is calculated by formula (8) forms with the moment in x, y, z three direction.

The x-axis of the coordinate of described one-way slabs is the length direction of grand fiber piezo-electricity composite material piezoelectric patches, described list To the width that the y-axis of the coordinate of plate is grand fiber piezo-electricity composite material piezoelectric patches.

Step 7: nodal force will be carried out Coordinate Conversion.

The nodal force of the equivalence obtained is carried out Coordinate Conversion, and coordinate conversion matrix is:

$lamda=\left[\begin{array}{ccc}cos\left(alpha\right)& -sin\left(alpha\right)& 0\\ sin\left(alpha\right)& \cos \left(alpha\right)& 0\\ 0& 0& 1\end{array}\right]---\left(9\right)$

$T=\left[\begin{array}{cc}lamda& 0\\ 0& lamda\end{array}\right]---\left(10\right)$

Lamda is direction cosine matrix；T is coordinate conversion matrix；Alpha grand fiber piezo-electricity composite material piezoelectric patches local Coordinate and the angle of global coordinate system.

Nodal force after coordinate transformation is:

$F=\left[\begin{array}{c}\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\\ \[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\end{array}\right]---\left(11\right)$

In the present embodiment, the coordinate system of grand fiber piezo-electricity composite material piezoelectric patches is identical with global coordinate system, alpha=0.

Step 8: cantilever beam dynamic test.

The frequency of signal projector institute output signal and the amplitude voltage of signal projector institute output signal are set.Set The arbitrary value that amplitude voltage is the maximal work voltage less than described grand fiber piezo-electricity composite material piezoelectric patches.

The output signal of signal projector being accessed in high-voltage power amplifier, high-voltage power amplifier drives on cantilever beam Grand fiber piezo-electricity composite material piezoelectric patches, make cantilever beam move, gather different input voltage by data acquisition software Analysis of A Cantilever Beam Under free end travel amplitude, and record each amplitude voltage.

In the present embodiment, the first natural frequency that frequency is cantilever beam of described signal projector institute output signal, signal For sinusoidal signal, the amplitude voltage of setting is respectively 0.075V, 0.1V, 0.125V, 0.15V, 0.175V, 0.2V, high-voltage power Amplifier voltage amplification power is 200 times, and the data collecting system used is the smart office of M+P company.

Step 9: revise the modal damping system of the cantilever beam FEM (finite element) model pasting grand fiber piezo-electricity composite material piezoelectric patches Number.

Repeat step 5～7, be positioned in step 8 arrange each amplitude voltage intermediate value calculate described grand fiber pressure respectively The nodal force of each node on composite piezoelectric patches.The joint of each node on the grand fiber piezo-electricity composite material piezoelectric patches that will obtain Point power is sequentially inputted in the load boundary of the FEM (finite element) model shown in Fig. 3, and inputs displacement boundary conditions；Residing displacement limit Boundary's condition is that the degree of freedom of all nodes of clamped end of cantilever beam is all set to 0.Give material properties to this FEM (finite element) model, and set Put modal damping coefficient, carry out finite element analysis.Obtain the displacement amplitude of cantilever beam free end under this amplitude voltage, will obtain This amplitude voltage intermediate value under displacement amplitude and step 8 test of cantilever beam free end record under this amplitude voltage intermediate value The carrying out of displacement amplitude of cantilever beam free end contrast, if error is more than 1%, adjusts modal damping coefficient and carry out finite element again Analyzing, until error, within 1%, determines the modal damping coefficient of this FEM (finite element) model, this modal damping coefficient is at follow-up meter Calculation immobilizes.

If each amplitude voltage intermediate value of described setting has two, the most arbitrarily taking one, described node is grand fiber pressure All nodes on four limits of composite piezoelectric patches.

Step 10: arbitrary amplitude voltage grand fiber piezo-electricity composite material piezoelectric patches dynamic (dynamical) piezoelectric effect constant identification

By the formula (12) pressure to the grand fiber piezo-electricity composite material piezoelectric patches under described amplitude voltage intermediate value effect Electrical effect constant d_aBe modified, subscript a of piezoelectric effect constant d be signal projector output signal be AC signal.

$d_a=\frac{w_3}{w_4}\×d_{33}---\left(12\right)$

w₃For the cantilever beam free end travel amplitude of the described amplitude voltage intermediate value that test records, w₄For simulation calculation The cantilever beam free end travel amplitude of this amplitude voltage intermediate value.

By the above-mentioned work of step 10, obtain the piezoelectric effect constant d that amplitude voltage intermediate value is revised_a ¹。

Repeating step 5～7, the grand fiber piezoelectricity corresponding to the amplitude voltage arranged described in calculation procedure 8 is multiple respectively The nodal force of each node on condensation material piezoelectric patches.The nodal force of each node on the grand fiber piezo-electricity composite material piezoelectric patches that will obtain It is sequentially inputted in the load boundary of the FEM (finite element) model that step 9 determines, carries out finite element analysis.Counted successively by formula (12) The piezoelectric effect constant of the calculation grand fiber piezo-electricity composite material piezoelectric patches corresponding to each amplitude voltage arranged described in step 9 d_a.Piezoelectricity to the grand fiber piezo-electricity composite material piezoelectric patches under each amplitude voltage effect arranged obtained described in step 9 Effect constant d_aCarry out curve fitting, obtain d_aThe relational expression of covariant buckling:

d_an=1.72 × U+309.81 (13)

In formula, d_anThe piezoelectricity of the grand fiber piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage effect after expression matching Effect constant, U is the general name of arbitrary amplitude voltage.

Step 10 one: the dynamic (dynamical) identification that is used as power of grand fiber piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage

Step 10 has obtained arbitrary amplitude voltage grand fiber piezo-electricity composite material piezoelectric patches dynamic (dynamical) piezoelectric effect constant. The piezoelectric effect constant d of the grand fiber piezo-electricity composite material piezoelectric patches under the arbitrary amplitude voltage that will obtain_anSubstitution formula (6), formula (7) in, and step 5～7 is repeated, it is thus achieved that under arbitrary amplitude voltage, grand fiber piezo-electricity composite material piezoelectric patches is dynamically used as power.

Using amplitude voltage in the present embodiment is 50V.The voltage range of matching is 30V-80V.

In order to verify the accuracy of the method, again to cantilever beam FEM (finite element) model imposed load, described model is carried out Dynamic analysis, it is thus achieved that each amplitude voltage Analysis of A Cantilever Beam Under free end travel amplitude, result is as shown in table 1, according to described result pair The piezoelectric effect constant d of grand fiber piezo-electricity composite material piezoelectric patches_anBeing modified, correction result is as shown in table 1.And according to correction The piezoelectric effect constant d of result matching grand fiber piezo-electricity composite material piezoelectric patches_anRelational expression, calculate 90V Yu 100V grand fibre The piezoelectric effect constant d of dimension piezo-electricity composite material piezoelectric patches_an, it was predicted that simulation result, contrast with result of the test, it appeared that The method describes the practical function of grand fiber piezo-electricity composite material piezoelectric patches more accurately, it was demonstrated that this method should in reality It is feasible in.

Table 1 dynamic simulation and test displacement

Voltage/V	Test displacement/mm	Do not revise emulation displacement/mm	Do not revise phantom error/%	Revised dan
					30	1.15	1.29	12.17	356.5891
40	1.64	1.72	4.88	381.3953
					50	2.13	2.15	0.93	396.2791
60	2.7	2.58	4.44	418.6047
					70	3.24	3.01	7.1	430.5648
80	3.81	3.44	9.71	443.0233

Table 2 dynamic simulation predictive displacement result

Voltage/V	Test/mm	Predict the outcome/mm	Do not revise phantom error/%	Forecast error/%
					90	4.47	4.495	13.42	0.5
100	5.12	5.18	16.02	1.17

Claims (6)

1. The grandest dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches, it is characterised in that detailed process is:

   Step 1: intercept the analytic unit of piezoelectric patches；

   Surface mount grand fiber piezo-electricity composite material piezoelectric patches at cantilever beam, and make this grand fiber piezo-electricity composite material piezoelectric patches Clamped end side near cantilever beam；Under the position pasting grand fiber piezo-electricity composite material piezoelectric patches on described cantilever beam is intercepted Come, obtain analytic unit

   Step 2: divide finite element unit

   The described cantilever beam pasting grand fiber piezo-electricity composite material piezoelectric patches is divided finite element unit, and checks grand fiber pressure The finite element interstitial content on composite piezoelectricity length of a film limit and the finite element of this grand fiber piezo-electricity composite material piezoelectric patches minor face Interstitial content；

   Step 3: determine grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship；

   Step 4: determine the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches；

   Step 5, determines power and the moment on four limits of grand fiber piezo-electricity composite material piezoelectric patches under unit voltage；

   Step 6, is equivalent to joint by the power suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches under unit voltage and moment Point power:

   The power in x, y, z three direction that described nodal force is calculated by formula (8) forms with the moment in x, y, z three direction；

   $\begin{array}{c}Npw=\[\begin{array}{cc}N\left(1\right)*wp/a/2N\left(3\right)*wp/a/2& 0\end{array}\]\\ Mpw=\[\begin{array}{cc}0& M\left(1\right)*wp/a/2-M\left(3\right)*wp/a/2\end{array}\]\\ Npl=\[\begin{array}{cc}N\left(3\right)*lp/b/2N\left(2\right)*lp/b/2& 0\end{array}\]\\ Mpl=\[\begin{array}{cc}-M\left(2\right)*lp/b/2M\left(3\right)*lp/b/2& 0\end{array}\]\end{array}---\left(8\right)$

   In formula: Npw is the moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectric patches broadside；

   Npl is the moment battle array in x, y, z three direction suffered by grand fiber piezo-electricity composite material piezoelectricity length of a film limit；Mpw is grand fiber The moment matrix in x, y, z three direction suffered by piezo-electricity composite material piezoelectric patches broadside；Mpl is grand fiber piezo-electricity composite material pressure The moment matrix in electricity x, y, z three direction suffered by length of a film limit；Wp is the width of grand fiber piezo-electricity composite material piezoelectric patches；A is The nodes of width；Lp is the length of grand fiber piezo-electricity composite material piezoelectric patches；B is the nodes of length direction；

   Step 7: nodal force will be carried out Coordinate Conversion；

   The nodal force of the equivalence obtained is carried out Coordinate Conversion；Nodal force after coordinate transformation is:

   $F=\left[\begin{array}{c}\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\\ \[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npl& Mpl\end{array}\]*T\\ -\[\begin{array}{cc}Npw& Mpw\end{array}\]*T\end{array}\right]---\left(11\right)$

   Step 8, cantilever beam dynamic test；

   Step 9, revises the modal damping coefficient of the cantilever beam FEM (finite element) model pasting grand fiber piezo-electricity composite material piezoelectric patches: make The test value of the intermediate value of each amplitude voltage of the setting obtained by cantilever beam dynamic test and each amplitude electrical of this setting The error of the simulation value of pressure is in 1%；

   Step 10, the grand fiber piezo-electricity composite material piezoelectric patches dynamic (dynamical) piezoelectric effect constant identification of arbitrary amplitude voltage:

   By the formula (12) piezoelectric effect to the grand fiber piezo-electricity composite material piezoelectric patches under described each amplitude voltage effect Constant d_aBeing modified, subscript a of piezoelectric effect constant d represents that signal projector output signal is AC signal；

   $d_a=\frac{w_3}{w_4}\×d_{33}---\left(12\right)$

   w₃For the cantilever beam free end travel amplitude of the described amplitude voltage intermediate value that test records, w₄This width for simulation calculation The cantilever beam free end travel amplitude of threshold voltage intermediate value；

   Pressure to the grand fiber piezo-electricity composite material piezoelectric patches under each amplitude voltage effect arranged obtained described in step 9 Electrical effect constant d_aCarry out curve fitting, obtain the grand fiber dynamic (dynamical) pressure of piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage Electrical effect constant d_an；

   Step 11, the dynamic (dynamical) identification that is used as power of grand fiber piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage:

   The piezoelectric effect constant d of the grand fiber piezo-electricity composite material piezoelectric patches under the arbitrary amplitude voltage that will obtain_anSubstitution formula (6), in formula (7), and step 5～7 is repeated, it is thus achieved that the grand fiber dynamic start of piezo-electricity composite material piezoelectric patches under arbitrary amplitude voltage Power.
2. The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches the most as claimed in claim 1, its feature exists In, when the nodal force of the described equivalence to obtaining carries out Coordinate Conversion, coordinate conversion matrix is:

   $lamda=\left[\begin{array}{ccc}\cos \left(alpha\right)& -\sin \left(alpha\right)& 0\\ \sin \left(alpha\right)& \cos \left(alpha\right)& 0\\ 0& 0& 1\end{array}\right]---\left(9\right)$

   $T=\left[\begin{array}{cc}lamda& 0\\ 0& lamda\end{array}\right]---\left(10\right)$

   Lamda is direction cosine matrix；T is coordinate conversion matrix；Alpha grand fiber piezo-electricity composite material piezoelectric patches local coordinate Angle with global coordinate system.
3. The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches the most as claimed in claim 1, its feature exists In, under the unit voltage determined, the power matrix N suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches is with moment matrix M respectively For:

   N=[Q] × d × E_d×t_p (6)

   $M=\frac{1}{2}\[Q\]\×d\×E_d\×t_p\×(t_p+t)---\left(7\right)$

   D is piezoelectric effect constant matrices, t_pPiezoelectric patches thickness, t is cantilever beam thickness, and N is grand fiber piezo-electricity composite material piezoelectric patches Moment battle array suffered by four limits, M is the moment matrix suffered by grand four limits of fiber piezo-electricity composite material piezoelectric patches.
4. The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches the most as claimed in claim 1, its feature exists In, the concrete of the modal damping coefficient of the cantilever beam FEM (finite element) model of grand fiber piezo-electricity composite material piezoelectric patches is pasted in described correction Process is:

   Repeat step 5～7, calculate described grand fiber piezoelectricity respectively being positioned in step 8 the intermediate value of each amplitude voltage arranged The nodal force of each node on composite piezoelectric patches；The node of each node on the grand fiber piezo-electricity composite material piezoelectric patches that will obtain Power is sequentially inputted in the load boundary of FEM (finite element) model, and inputs displacement boundary conditions；Described displacement boundary conditions is outstanding The degree of freedom of all nodes of clamped end of arm beam is all set to 0；Give material properties to this FEM (finite element) model, and modal damping is set Coefficient, carries out finite element analysis；Obtain the displacement amplitude of cantilever beam free end under this amplitude voltage, this amplitude electrical that will obtain The displacement amplitude of the cantilever beam free end under pressure intermediate value records the cantilever beam under this amplitude voltage intermediate value with step 8 test The carrying out of the displacement amplitude of free end contrasts, if error is more than 1%, adjusts modal damping coefficient and carries out finite element analysis again, directly To error within 1%, determining the modal damping coefficient of this FEM (finite element) model, this modal damping coefficient is fixing in subsequent calculations Constant；

   If each amplitude voltage intermediate value of described setting has two, the most arbitrarily taking one, described node is that grand fiber piezoelectricity is multiple All nodes on four limits of condensation material piezoelectric patches.
5. The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches the most as claimed in claim 1, its feature exists In, described grand fiber piezo-electricity composite material piezoelectric patches principal direction stress and strain relationship is:

   $\left\{\begin{array}{c}{\mathrm{\σ}}_1\\ {\mathrm{\σ}}_2\\ {\mathrm{\τ}}_{12}\end{array}\right\}=\[Q\]\left\{\begin{array}{c}{\mathrm{\ϵ}}_1\\ {\mathrm{\ϵ}}_2\\ {\mathrm{\γ}}_{12}\end{array}\right\}---\left(3\right)$

   In formula: Q is the stiffness matrix of grand fiber piezo-electricity composite material piezoelectric patches；ε₁、ε₂Be respectively 1 direction of material principal direction, 2 The principal strain in direction；σ₁、σ₂It is respectively 1 direction of material principal direction, the principal stress in 2 directions in the mechanics of materials；τ₁₂For material master 1 direction in direction and the shearing stress in the 1-2 plane of 2 direction compositions；γ₁₂The 1-that 1 direction of material principal direction forms with 2 directions Shear strain in 2 planes.
6. The grand dynamic (dynamical) recognition methods that is used as power of fiber piezo-electricity composite material piezoelectric patches the most as claimed in claim 1, its feature exists In, the stiffness matrix of described grand fiber piezo-electricity composite material piezoelectric smart material is:

   $\[Q\]=\left[\begin{array}{ccc}{Q}_{11}& Q_{12}& 0\\ Q_{12}& Q_{22}& 0\\ 0& 0& Q_{66}\end{array}\right]=\left[\begin{array}{ccc}\frac{E_1}{1-v_{12}{v}_{21}}& \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& 0\\ \frac{v_{12}{E}_2}{1-v_{12}{v}_{21}}& \frac{E_2}{1-v_{12}{v}_{21}}& 0\\ 0& 0& G_{12}\end{array}\right]---\left(4\right)$

   Q_ijIn subscript i, j represent the dimension of Stiffness Matrix；v₁₂With v₂₁Represent that the direct stress in 1 direction of material principal direction draws respectively The deformation coefficient in 1 direction that the direct stress in the deformation coefficient in 2 directions risen and 2 directions of material principal direction causes；E₁With E₂Direction Represent 1 direction of material principal direction and the elastic modelling quantity in 2 directions respectively；G₁₂Represent 1 direction and the 2 direction compositions of material principal direction 1-2 plane in modulus of shearing.