A Note on a Nonlinear Model of a Piezoelectric Rod

If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model.     

Nonlinear Behavior of Piezoceramic Actuators

Nonlinear behavior of piezoceramics is a well-known phenomenon. For large stresses and/or strong electric fields it is described by various hysteresis curves. Quasi-static experiments exhibited hysteresis relations between excitation voltage and strain as well as between excitation voltage and electric displacement. This behavior can be modeled by using the classical Preisach model. On the other hand, typical nonlinearities of Duffing type such as jump phenomena, multiple stable amplitude responses at the same excitation voltage and frequency, and the presence of superharmonics in response spectra can be observed when piezoceramic actuators are excited near resonance, even at weak electric fields. In this paper, different experimental results for both quasi-static and dynamic nonlinear behavior and corresponding models are presented and compared. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Antiplane Problem of Electroelasticity for a Hollow Piezoceramic Cylinder Excited by a System of Surface Electrodes

An antiplane mixed boundary-value problem of electroelasticity is considered for a hollow piezoceramic cylinder with an arbitrary system of active surface electrodes generating its harmonic vibrations. The problem is solved using a method elaborated earlier for investigating vibrations of a solid piezoceramic cylinder with a system of active surface electrodes. The scheme of numerical solution of the obtained singular integro-differential equations of the boundary-value problem is based on the quadrature method. Calculation results are presented that describe the amplitude-frequency characteristics of a hollow cylinder and the behavior of some mechanical and electric quantities both within the cylinder and on its boundary.     

Boundary Control of Physical Fields in a Piezoceramic Layer Having a Tunnel Hole with a System of Electrodes

An approach to the optimal (from the viewpoint of minimum energy consumption) control of the characteristics of coupled fields is illustrated with the example of an antiplane dynamic problem of electroelasticity for a piezoceramic layer with a tunnel hole. The vibrations in the layer are excited by time-dependent harmonic loads of two types: by the difference of electric potentials applied to a pair of infinitely long electrodes located on the surface of the hole and by shear forces or electric charges continuously distributed on the given sections of the layer base, which are assumed as control actions. The inverse problem is solved by using the solution of the corresponding direct mixed antiplane problem of electroelasticity, with the help of which the optimization problem is reduced to the -problem of moments. The functions of optimal control allowing one, for example, to disconnect the external circuit of the generator of electric voltage are given.     

Solution of an axisymmetric problem of free vibrations of piezoceramic hollow cylinders of finite length by the spline collocation method

An axisymmetric problem of longitudinal free vibrations of piezoceramic hollow cylinders for some types of boundary conditions on the end faces is considered. The lateral surfaces of the cylinder are covered with thin short-circuited electrodes. The polarization of piezoceramics is directed along the axis of the cylinder. Using the method of separation of variables and method of spline collocation along the length of the cylinder, we reduce the problem to a system of ordinary differential equations, which is solved by the method of step-by-step search. We present results of calculations for a PZT 4 piezoceramic cylinder.     

夹层压电材料中垂直于界面的共线双裂纹动力学问题分析

采用Schmidt方法分析了在简谐反平面剪切波作用下,两个半空间夹层压电材料中的共线裂纹的动力学行为．压电材料层内裂纹垂直于界面,电边界条件假设为可导通．通过Fourier变换,使问题的求解转换为两对三重积分对偶方程．通过数值计算,给出了裂纹的几何尺寸、压电材料常数、入射波频率等对于应力强度因子的影响．结果表明,在不同的入射波频率范围,动力场将阻碍或促使压电材料内裂纹的扩展．与不可导通电边界条件相比,导通裂纹表面的电位移强度因子比不可导通裂纹的电位移强度因子要小许多．     

Numerical Modeling Aspects of Dielectric Elastomer Actuators

In modern actuator technology dielectric elastomers are considered as new materials to realize smart actuators which are known as dielectric elastomer actuators (DEAs). In comparison to piezoceramics actuators, DEAs offer the possibility to achieve large deformations with low actuation forces. This property motivates the implementation as artificial muscles since the deformation-force behavior is similar. Other application fields are pumps, deformable surfaces in aerospace, robotics and haptic feedback. The present work introduces the fundamental concepts to describe the electromechanical coupling in the concept of continuum mechanics for finite deformations. As a benchmark a 3D sandwich actuator setup is taken into account to analyze the mechanical compression stability of the elastomer structure, see [1, 2]. This structure is also considered to study the influence of inhomogeneities in the deformation behavior. For this purpose piezoceramic and air inclusions are considered in the finite element mesh. As a last numerical example an elastomer tube with three pairs of electrodes is simulated numerically to motivate the use of dielectric elastomers as peristaltic pumps. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于扭转模态的角振动压电俘能器研究

以线性压电理论为基础,分析了压电陶瓷圆柱壳的扭转振动问题.由于压电陶瓷柱壳的扭转振动使得覆盖于柱壳两端的电极之间出现电势差,通过导线连接两电极与外负载,则圆柱壳在振动过程中所捕获的能量能有效地供给微电子器件工作.得到了输出电压、电流、能量、效率以及输出功率密度的解析表达式,并数值分析了这类压电俘能器的基本性能.结果表明,这种结构能够用作压电俘能器,将旋转机械能转化成为电能.     

不同功能梯度压电压磁层状介质中共线界面裂纹的动态性能分挝

对不同功能梯度压电压磁层状介质中,共线界面裂纹对简谐应力波作用下的动态问题,进行了分析.经Fourier变换,使问题的求解转换为求解以裂纹面上位移间断为未知量的三重对偶积分方程,三重对偶方程可以采用Schmidt方法来求解,进而分析了功能梯度参数、入射波频率和层状介质厚度对应力、电位移和磁通量强度因子的影响.     

A finite element model for nonlinear behaviour of piezoceramics under weak electric fields

It has been experimentally observed that piezoceramic materials exhibit different types of nonlinearities under different combinations of electric and mechanical fields. When excited near resonance in the presence of weak e to a Duffinor such as jump phenomena and presence of superharmonics in the response spectra. There has not been much work in the litrature to model these types of nonlinearities. Some authors have developed one-dimensional models for the above phenomenon and derived closed-form solutions for the displacement response of piezo-actuators. However, the generalized three-dimensional (3-D) formulation of electric enthalpy, the variational formulation and the FEM implementation have not yet been addressed, which are the focus of this paper. In this work, these nonlinearities have been modelled in a 3-D piezoelectric continuum using higher order quadratic and cubic terms in the generalized electric enthalpy density function. The coupled nonlinear finite element equations have been derived using variational formulation. A special linearization technique for assembling the nonlinear matrices and solution of the resulting nonlinear equations has been developed. The method has been used for simulating the nonlinear frequency response of a lead zirconate titanate plate excited near its first in-plane vibration resonance frequency with sinusoidal excitations of different electric field strengths. The results have been compared with those of the experiment.     

Free vibration of a functionally graded annular sector plate integrated with piezoelectric layers

Based on the first order shear deformation theory, free vibration behavior of functionally graded (FG) annular sector plates integrated with piezoelectric layers is investigated. The distribution of electric potential along the thickness direction of piezoelectric layers which is assumed to be a combination of linear and sinusoidal functions, satisfies both open and closed circuit electrical boundary conditions. Through a reformulation of governing equations and harmonic motion assumption, a novel decoupling method is suggested to transform the six second order coupled partial differential equations of motion into two eighth order and fourth order equations. A Fourier series method is then employed to present analytical solutions for free vibration of smart FG annular sector plates with simply supported radial edges and arbitrarily supported circular edges. The results, which can be used as a benchmark and suitable for design purposes, are verified with those reported in the literature. Finally, by presenting extensive ranges of frequencies, the effects of geometric parameters, power law index, FG and piezoelectric materials, electrical and mechanical boundary conditions as well as the piezoelectric layer thickness on vibration response of smart annular sector plates are discussed in detail.     

A moving thermal dielectric crack in piezoelectric ceramics with a shearing force applied on its surface

This article conducts an exact analysis of a thermal dielectric crack moving in piezoelectric materials. Self-generating thermal and electric loadings by the crack interior are exerted on the crack surfaces as well as various external loadings including a shearing force. Fundamental solutions of the thermal and electro-elastic coupling fields are given by determining a temperature function and a harmonic function with eigenvalues properties due to material properties considered. Analytical expressions are obtained benefiting evaluation of key parameters. Numerical analysis is done and some interesting observations are found. There is a critical crack velocity within and beyond which the electric loading exerts different influences on the thermal flux of crack interior and the thermal stress intensity factor.     

压电压磁复合材料中界面裂纹对弹性波的散射

利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题．经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式．数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同．     

Long-time behavior of solutions for quasilinear hyperbolic hemivariational inequalities with application to piezoelectricity problem

We consider quasilinear autonomous inclusions of hyperbolic type. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. The classes of mathematical models for piezoelectric fields containing the multidimensional law are studied. The conditions of the output of each weak solution for this problem at stationary states are given. We consider as a particular case the piezoelectric model for PZT-4 piezoceramics as one of the possible applications.     

Energy harvesting by coupled oscillators forced by excitations with harmonic and random components

We examine an energy harvesting system of two magnetopiezoelastic oscillators coupled by electric circuit and driven by a combination of harmonic and stochastic ambient disturbances. The effects of synchronization and escape from a single potential well are discussed. In the system with relative mistuning in the stiffness of the harvesting oscillators, we show the dependence of the voltage output for different noise levels and excitation frequency. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semi-analytical hybrid approach for the simulation of layered waveguide with a partially debonded piezoelectric structure

This paper presents an efficient semi-analytical hybrid approach for simulating the dynamic interaction of perfectly bonded or damaged piezoelectric structures with a layered elastic waveguide. In the proposed approach, the frequency domain spectral element method is utilized for the discretization of the finite-sized surface mounted piezoelectric structure, and the semi-analytical boundary integral method is employed for the evaluation of wave phenomena in the host laminate structure. While the spectral element method allows cost-effective simulation of dynamics of a complex-shaped transducer (e.g. curvilinear or with wrapped electrodes), the analytically-based technique reliably describes wave excitation and propagation in multi-layered structures. The coupling of these methods is achieved through the rigorous fulfillment of the boundary conditions at the area of waveguide-transducer contact. Three various combinations of approximation polynomials and surface-load interpolation functions are applied in order to obtain the solution in a frequency domain. The time-domain solution is evaluated employing the inverse Laplace transform. Convergence of the method is confirmed for different bonding conditions. The paper demonstrates the efficiency of the proposed method for the multi-parameter analysis of the dependence of the resonance characteristics on the debonding parameters and contact conditions. The approach can be used for such a crucial task as diagnosing failures of piezoelectric devices incorporated into a structural health monitoring system based on guided waves.     

Fundamental Solutions of Electroelasticity Equations for a Piezoceramic Layer in R3

Coupled electroelastic fields in a piezoceramic layer under the action of force and electric sources are determined analytically. The Fourier coefficients of the displacement and electric potential vectors and of the stress tensor are expressed in terms of the Macdonald cylindrical functions in a closed form. The solutions obtained can be used to consider the boundary-value problems of electroelasticity for a piezoceramic layer with tunnel heterogeneities.     

Excitation of Shear Waves in a Piezoceramic Medium with Two Tunnel Holes by a System of Surface Electrodes

An antiplane mixed dynamic problem of electroelasticity for an infinite piezoceramic medium weakened by two tunnel holes is considered. The conjugated fields are excited by the difference of electric potentials applied to a system of electrodes located on the surfaces of the holes. The boundary-value problem is reduced to a system of singular integrodifferential equations with discontinuous kernels, which is solved numerically by quadratures. The results of parametric investigations, characterizing the behavior of the electric field components on the boundary and in the region of the piecewise-homogeneous space, are presented.     

Diffraction of acoustoelectric waves by tunnel cavities in an unbounded piezoceramic medium

The steady wave process in a piezoceramic space with tunnel cavity-openings under plane deformation conditions in a plane parallel to the axis of symmetry of the material is investigated. The corresponding two-dimensional boundary-value problem of electroelasticity is reduced to a system of three singular integral equations of the second kind. The results of a numerical implementation of the algorithm illustrate the effect of the configuration of the openings, the type and frequency of the excitation and the effect of the connectedness of the mechanical and electric fields on the stress concentration.