非线性压电效应下压电弯曲执行器的动力分析

研究压电弯曲执行器在强电场作用下的非线性动力行为．考虑电致伸缩和电致弹性的非线性压电效应,导出了压电悬臂执行器变刚度的弯曲振动控制方程．利用非定常振动的渐近理论,讨论了弯曲压电执行器的动力特征．根据目前的非线性模型可以计算压电悬臂执行器的固有共振频率与电场的变化关系．结果表明压电执行器端头挠度谐振幅度随作用电场振幅的增大而增大,以及力学品质因数随电场振幅的增大而减少,并且与实验结果非常吻合．通过数值比较得到在电场频率随时间变化非常缓慢的情况下非定常振动问题可以近似地用定常振动来处理．     

Approximate dynamic boundary conditions for a thin piezoelectric layer

Approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material. The approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer. All the expansion functions are then eliminated with the aid of the equations of motion and boundary/interface conditions of the layer. This results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions. The approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly. Numerical examples show that the approximate boundary conditions give good results for low frequencies and/or thin piezoelectric layers.     

粘贴压电层功能梯度材料Timoshenko梁的热过屈曲分析

研究了上下表面粘贴压电层的功能梯度材料Timoshenko梁在升温及电场作用下的过屈曲行为。在精确考虑轴线伸长和一阶横向剪切变形的基础上,建立了压电功能梯度Timoshenko层合梁在热-电-机械载荷作用下的几何非线性控制方程。其中,假设功能梯度的材料性质沿厚度方向按照幂函数连续变化,压电层为各向同性均匀材料。采用打靶法数值求解所得强非线性边值问题,获得了在均匀电场和横向非均匀升温场内两端固定Timoshenko梁的静态非线性屈曲和过屈曲数值解。并给出了梁的变形随热、电载荷及材料梯度参数变化的特性曲线。结果表明,通过施加电压在压电层产生拉应力可以有效地提高梁的热屈曲临界载荷,延缓热过屈曲发生。由于材料在横向的非均匀性,即使在均匀升温和均匀电场作用下,也会产生拉-弯耦合效应。但是对于两端固定的压电-功能梯度材料梁,在横向非均匀升温下过屈曲变形仍然是分叉形的。     

The dynamic behaviour of a piezoelectric actuator bonded to an anisotropic elastic medium

Surface-bonded piezoelectric actuators can be used to generate elastic waves for monitoring damages of composite materials. This paper provides an analytical and numerical study to simulate wave propagation in an anisotropic medium induced by surface-bonded piezocermic actuators under high-frequency electric loads. Based on a one-dimensional actuator model, the dynamic load transfer between a piezoceramic actuator and an anisotropic elastic medium under in-plane mechanical and electrical loading is obtained. The wave propagation induced by the surface-bonded actuator is also studied in detail by using Fourier transform technique and solving the resulting integral equations in terms of the interfacial shear stress. Typical examples are provided to show effects of the geometry, the material combination, the loading frequency and the material anisotropy of the composite upon the load transfer and the resulting wave propagation.     

Electromechanical behaviour of a finite piezoelectric layer under a flat punch

This paper solves the problem of a smooth and frictionless punch on a piezoelectric ceramic layer. Different electrical boundary conditions that employ conducting or insulating punches are presented. The stress and electric displacement intensity factors are used to characterize the electromechanical fields at the punch tip. The field intensity factors are obtained numerically for finite layer thickness. Effects of the thickness of the piezoelectric layer on the stress and electric displacement, and the stress and electric displacement intensity factors at the punch tip are discussed. Solution technique for two identical and collinear surface punches on the piezoelectric layer is also provided and the effect of relative distance between the punches is investigated. Numerical results for some interesting special cases, such as conducting punch and insulating punch, and infinite piezoelectric layer thickness, are presented.     

On the dynamic behaviour of a piezoelectric laminate with multiple interfacial collinear cracks

This paper investigates the dynamic behaviour of a piezoelectric laminate containing multiple interfacial collinear cracks subjected to steady-state electro-mechanical loads. Both the permeable and impermeable boundary conditions are examined and discussed. Based on the use of integral transform techniques, the problem is reduced to a set of singular integral equations, which can be solved using Chebyshev polynomial expansions. Numerical results are provided to show the effect of the geometry of interacting collinear cracks, the applied electric fields, the electric boundary conditions along the crack faces and the loading frequency on the resulting dynamic stress intensity and electric displacement intensity factors.     

The effect of variable properties on laminar boundary layer flow

The influence of temperature dependent fluid properties on laminar boundary layer flows is examined for wedge flows (Falkner-Skan). An asymptotic expansion for small heat transfer rates is applied under the boundary conditionsT _w= const andq _w=const. Linear deviations from the zero order solution (constant properties) can be given in a form known as the property ratio method. As a consequence this method is no longer an empirical one.     

Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment

Free vibration of statically thermal postbuckled functionally graded material （FGM） beams with surface-bonded piezoelectric layers subject to both temperature rise and voltage is studied. By accurately considering the axial extension and based on the Euler-Bernoulli beam theory, geometrically nonlinear dynamic governing equations for FGM beams with surface-bonded piezoelectric layers subject to thermo-electro- mechanical loadings are formulated. It is assumed that the material properties of the middle FGM layer vary continuously as a power law function of the thickness coordinate, and the piezoelectric layers are isotropic and homogenous. By assuming that the amplitude of the beam vibration is small and its response is harmonic, the above mentioned non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations. One is for the postbuckling, and the other is for the linear vibration of the beam superimposed upon the postbuckled configuration. Using a shooting method to solve the two sets of ordinary differential equations with fixed-fixed boundary conditions numerically, the response of postbuckling and free vibration in the vicinity of the postbuckled configuration of the beam with fixed-fixed ends and subject to transversely nonuniform heating and uniform electric field is obtained. Thermo-electric postbuckling equilibrium paths and characteristic curves of the first three natural frequencies versus the temperature, the electricity, and the material gradient parameters are plotted. It is found that the three lowest frequencies of the prebuckled beam decrease with the increase of the temperature, but those of a buckled beam increase monotonically with the temperature rise. The results also show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and the natural frequency.     

Effect of imperfect bonding on the dynamic response of a pre-stressed sandwich plate-strip with elastic layers and a piezoelectric core

In this paper,we consider the dynamic response of a pre-stressed sandwich plate-strip with a piezoelectric core and elastic layers under the action of a time-harmonic force resting on a rigid foundation.The investigation is carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity.It is assumed that there is a shear-spring-type imperfect contact between the layers,but a complete contact between the plate-strip and the rigid foundation.A mathematical model of the problem is constructed,and the governing equations of motion are solved by employing the finite element method(FEM).Numerical results illustrating the influence of a change in the value of the shear-spring parameter on the dynamic response of the plate-strip are then presented.     

Swelling effect on the dynamic behaviour of composite cylindrical shells conveying fluid

This paper presents a semi‐analytical investigation of a fluid–structure system. Both isotropic and composite cylindrical shells filled with or subjected to a flowing fluid have been considered in this study. The structure may be uniform or non‐uniform in the circumferential direction. The hybrid finite element approach, shearable shell theory and velocity potential flow theory have been combined to establish the dynamic equations of the coupled system. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations. The linear potential flow theory is applied to describe the fluid effects that lead to the inertial, centrifugal and Coriolis forces. The axisymmetric, beam‐like and shell modes of vibrations in both cases of uniform and non‐uniform cylindrical shells are investigated. Fluid elastic stability of a structure subjected to a flowing fluid is also studied. This theory yields the high and the low eigenvalues and eigenmodes with comparably high accuracy. Reasonable agreement is found with other theories and experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem. These solutions can be reduced to the ones of an elastodynamic problem. Based on the effective medium method, these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters, which can be numerically solved by iteration. Theore...     

The dynamic behaviour of stiffened strings

Summary The small oscillation of a stiffened string about its static equilibrium configuration is studied. The solution requires both the static and dynamic shape of the rod to be determined and since the governing equations do not lend themselves to an analytical solution a Runge-Kutta integration technique was used. Experimental results for the natural frequencies are compared to the numerical solution for a particular stiffened string.

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Übersicht Es werden die kleinen Schwingungen eines versteiften Bandes um die statische Gleichgewichtslage untersucht. Dabei muß sowohl die statische wie auch die dynamische Form des Bandes bestimmt werden. Da eine analytische Lösung der Bewegungsgleichungen nicht möglich ist, wurde numerisch nach Runge-Kutta integriert. Für verschieden versteifte Bänder werden Versuchsergebnisse für die Eigenfrequenzen mit numerischen Lösungen verglichen.

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The authors would like to acknowledge the work of David Stredulinsky in the initial stages of this project and to thank the National Research Council for support under operating grant NRC A7514 (Faulkner).     

The dynamic behaviour of a tractor-vibrating subsoiler system and the effect of the virtual hitch point

In this report, the dynamic behaviour of a tractor-vibrating subsoiler system was analysed theoretically and experimentally. From a simulation using a mathematical model of this system and some field experiments, it was determined that the Virtual Hitch Point (VHP) is the parameter that most affects the vibrations of a tractor's body. By setting the VHP at an optimal position, the acceleration of a tractor's body was reduced considerably.     

Concentration of electric field near electrodes on piezoelectric layer

This paper aims at the study of electric field concentration near the edge of the electrodes for a piezoelectric layer. For simplicity, attention is focussed on a piezoelectric layer that is bonded to a rigid, conductive substrate and then covered by a pair of conductive electrodes on the surface. The analysis is performed within the scope of linear piezoelectricity. Fourier transform technique is applied to reduce the boundary value problem to a pair of dual integral equations. An analytical solution to the integral equations is obtained by using an iteration method. Numerical results for distributions of stresses and electric fields are displayed and discussed.     

Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid

Two problems will be studied in this contribution. First, we analyse some phenomena which take place in a laminated solid and are caused by a fluctuation of time-dependent boundary tractions. Second, we investigate the transient effect of initial displacement fluctuations on the behaviour of a laminate. To solve the above problems we propose a new macroscopic 3D model for investigations of initial-boundary value problems in elastodynamics of a laminated medium.     

Sample size effect on the dynamic torsional behaviour of the 2A12 aluminium alloy

In order to investigate the effect of sample size on the dynamic torsional behaviour of the 2A12 aluminium alloy. In this paper, torsional split Hopkinson bar tests are conducted on this alloy with different sample dimensions. It is found that with the decreasing gauge length and thickness, the tested yield strength increases. However, the sample inner/outer diameter has little effect on the dynamic torsional behaviour.Based on the finite element method, the stress states in the alloy with different sample sizes are analysed.Due to the effect of stress concentration zone(SCZ), the shorter sample has a higher yield stress.Furthermore, the stress distributes more uniformly in the thinner sample, which leads to the higher tested yield stress. According to the experimental and simulation analysis, some suggestions on choosing the sample size are given as well.     

The effect of dynamic impact and water potential on some surface soil properties

A direct shear test with a superimposed impact was used to simulate the action of a track on the soil surface and to study the effect on soil surface properties. Results showed that impact increased bulk density, reduced saturated hydraulic conductivity and decreased cone penetrometer resistance. An impact plus shear treatment reduced the residual shear strength to approximately 60 kPa compared with 85 kPa for a shear only treatment. Water tension also greatly influenced the changes measured with the order of greatest change being −5>−10>−60>t-100>−300 kPa. The results are discussed with respect to soil trafficability and soil structural change with vehicle passage.