Modeling of porous piezoelectric structures by the meshless local Petrov-Galerkin method

A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value problems of porous piezoelectric solids. Constitutive equations for porous piezoelectric materials possess a coupling between mechanical displacements and electric intensity vectors in both solid and fluid phases. Stationary and transient 2-D and 3-D axisymmetric problems are considered in this article. Nodal points are spread on the problem domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potentials for both phases is approximated by the moving least-squares scheme. After performing the spatial integration, one obtains a system of ordinary differential equations for certain nodal unknowns. The resulting system is solved numerically by the Houbolt finite-difference scheme as a time stepping method. The proposed method is applied to bending problems associated with a porous piezoelectric 2-D plate and 3-D axisymmetric cylinder under simply supported and clamped boundary conditions.     

FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials

We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme.We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.     

Numerical analysis for piezoelectric crack under varied boundary conditions by optimized hybrid element method

In this article, a piezoelectric hybrid element is presented and optimized by penalty equilibrium approach, and special crack surface element is suggested for exactly implementing the boundary conditions on crack surface. An iteration technique is used to treat one of the electric boundary conditions. Then, a piezoelectric material with crack is numerically studied by the optimized hybrid element method, and the results are compared with the analytical solutions. The stress and the electrical displacement fields with different crack surface conditions are studied, and the influence to those fields arisen by the far field mechanical and electric loading is also studied.     

A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.     

压电陶瓷变压器研究和发展现状

概述了压电陶瓷变压器的原理和分类，介绍了各种振动模式的压电陶瓷变压器，并重点叙述了两种电极设计精巧的压电陶瓷变压器，对体型和膜型压电陶瓷变压器的研究进展现状进行了分析。     

Modeling of piezoelectric transformers using finite‐element technique

Abstract

In this work, the modeling of piezoelectric transformers using the finite‐element technique is presented. A 3‐D finite element method solver, which employs 20‐node brick‐element formulation, is developed. Using the solver, the characteristics of piezoelectric transformers under different operating frequencies can be simulated. Also, the solver is capable of accounting for the effects of the electrical loadings attached to the output electrodes of piezoelectric transformers. The modeling results for two different types of piezoelectric transformers, the Rosen‐modal‐type and the unipoled‐disk‐type, are presented. For the Rosen‐modal‐type devices, the simulated voltage gains and the phase differences are validated with our measured results. Also, the simulated results of the unipoled‐disk‐type transformers agree with the measured results found in previously published literature. The effects of electrical loadings on these piezoelectric transformers are also discussed.     

Efficient charge recovery method for driving piezoelectric actuators with quasi-square waves

In this paper, an efficient charge recovery method for driving piezoelectric actuators with low frequency square waves in low-power applications such as mobile microrobots is investigated. Efficiency issues related to periodic mechanical work of the actuators and the relationship among the driving electronics efficiency, the piezoelectric coupling factor, and the actuator energy transmission coefficient are discussed. The proposed charge recovery method exploiting the energy transfer between an inductor and a general capacitive load is compared with existing techniques that lead to inherent inefficiencies. A charge recovery method is then applied to piezoelectric actuators, especially to bimorph ones. Unitary efficiency can be obtained theoretically for purely capacitive loads while intrinsic losses such as hysteresis necessarily lower the efficiency. In order to show the validity of the method, a prototype driving electronics consisting of an extended H-bridge is constructed and tested by experiments and simulations. Preliminary results show that 75% of charge (i.e., more than 56% of energy) can be recovered for bending actuators such as bimorphs without any component optimization at low fields.     

Characterization of elastic parameters for functionally graded material by a meshfree method combined with the NMS approach

This study aims to characterize the elastic parameters in a functionally graded material. To implement this work, a parameter identification algorithm is proposed by combining a meshless method with the Nelder–Mead simplex (NMS) approach. The meshless method is based on the method of fundamental solutions and a radial basis function approximation, while the NMS approach is adopted to minimize the objective function and at the same time to obtain the unknown parameters. The objective function in this study characterizes the difference between the observed and the numerically predicted displacements under the estimated parameters. The robustness and effectiveness of the proposed scheme are verified by three numerical examples.     

A meshless local boundary integral equation method for dynamic anti-plane shear crack problem in functionally graded materials

This paper presents a meshless local boundary integral equation method (LBIEM) for dynamic analysis of an anti-plane crack in functionally graded materials (FGMs). Local boundary integral equations (LBIEs) are formulated in the Laplace-transform domain. The static fundamental solution for homogeneous elastic solids is used to derive the local boundary–domain integral equations, which are applied to small sub-domains covering the analyzed domain. For the sub-domains a circular shape is chosen, and their centers, the nodal points, correspond to the collocation points. The local boundary–domain integral equations are solved numerically in the Laplace-transform domain by a meshless method based on the moving least–squares (MLS) scheme. Time-domain solutions are obtained by using the Stehfest's inversion algorithm. Numerical examples are given to show the accuracy of the proposed meshless LBIEM.     

3D analytical solution for a functionally graded transversely isotropic piezoelectric circular plate under tension and bending

A three-dimensional (3D) analysis of a functionally graded piezoelectric circular plate under tension and bending is carried out. A direct displacement method is developed, with analytical solutions obtained for plate with either free or simply-supported edge conditions. The material properties of the plate can vary arbitrarily along the thickness except that the strain-energy function should be positive definite as required for stable materials and certain integrable conditions are assumed valid during the derivation. The validity of the present solutions is discussed both analytically and numerically. Numerical analyses are made for a specific functionally graded material to show the influence of material heterogeneity on the piezoelastic field.     

Material properties of piezoelectric composites by BEM and homogenization method

Applications of boundary element method (BEM) to piezoelectric composites in conjunction with homogenization approach for determining their effective material properties are discussed in this paper. The composites considered here consist of inclusion and matrix phases. The homogenization model for composites with inhomogeneities is developed and introduced into a BE formulation to provide an effective means for estimating overall material constants of two-phase composites. In this model, a representative volume element (RVE) is used whose volume average stress and strain are calculated by the boundary tractions and displacements of the RVE. Thus BEM is suitable for performing calculations on average stress and strain fields of the composites. Numerical results for a piezoelectric plate with circular inclusions are presented to illustrate the application of the proposed micromechanics––BE formulation.     

Electrical and mechanical fully coupled theory and experimental verification of Rosen-type piezoelectric transformers

A piezoelectric transformer is a power transfer device that converts its input and output voltage as well as current by effectively using electrical and mechanical coupling effects of piezoelectric materials. Equivalent-circuit models, which are traditionally used to analyze piezoelectric transformers, merge each mechanical resonance effect into a series of ordinary differential equations. Because of using ordinary differential equations, equivalent circuit models are insufficient to reflect the mechanical behavior of piezoelectric plates. Electromechanically, fully coupled governing equations of Rosen-type piezoelectric transformers, which are partial differential equations in nature, can be derived to address the deficiencies of the equivalent circuit models. It can be shown that the modal actuator concept can be adopted to optimize the electromechanical coupling effect of the driving section once the added spatial domain design parameters are taken into account, which are three-dimensional spatial dependencies of electromechanical properties. The maximum power transfer condition for a Rosen-type piezoelectric transformer is detailed. Experimental results, which lead us to a series of new design rules, also are presented to prove the validity and effectiveness of the theoretical predictions.     

Simulation of piezoelectric devices by two- and three-dimensional finite elements

A method for the analysis of piezoelectric media based on finite-element calculations is presented in which the fundamental electroelastic equations governing piezoelectric media are solved numerically. The results obtained by this finite-element calculation scheme agree with theoretical and experimental data given in the literature. The method is applied to the vibrational analysis of piezoelectric sensors and actuators with arbitrary structure. Natural frequencies with related eigenmodes of those devices as well as their responses to various time-dependent mechanical or electrical excitations are computed. The theoretically calculated mode shapes of piezoelectric transducers and their electrical impedances agree quantitatively with interferometric and electric measurements. The simulations are used to optimize piezoelectric devices such as ultrasonic transducers for medical imaging. The method also provides deeper insight into the physical mechanisms of acoustic wave propagation in piezoelectric media.     

ECT Inversion Using a Knowledge-Based Forward Solver

In this paper, a new approach was proposed for crack reconstruction based on ECT technique and optimization theory. A newly developed fast forward solver was applied for predicting the impedance signals during the inversion procedure. Comparing with the conventional approaches, the scanning signal due to an arbitrary shaped crack can be calculated in a significantly reduced CPU time but with higher accuracy. The conjugate gradient algorithm was employed in the optimization of the crack parameters, with the gradient calculated numerically from the electric field in the crack region. The scheme was implemented for the shape reconstruction of EDM cracks from the measured impedance data having in mind possible applications in the inspection of steam generator tubing. Several cracks embedded in conducting tube or plate were reconstructed from the observed impedance data by concerning the benchmark models proposed by T. Takagiet al. Good reconstruction results were obtained within a short CPU time. Consequently, the validity of the new approach was verified.     

功能梯度压电层/压电半空间结构中Love波的传播:一种改进的拉盖尔多项式方法

使用传统的拉盖尔多项式方法求解层状半空间结构时,存在因层间材料差异所造成的应力、电位移不连续的现象。为了克服此方法的不足,提出了一种改进的拉盖尔多项式方法,研究了功能梯度压电层状半空间中Love波的传播特性。与文献中应用WKB法得到的结果进行对比,验证了该方法的正确性。计算和分析了相应的频散曲线、应力和电位移分布曲线。结果表明:该方法能够避免因层间材料差异所造成的应力、电位移不连续现象的出现;高频Love波的应力和电位移主要分布在功能梯度压电层中速度较低的一侧。该研究为基于Love波传感器的设计与优化奠定了一定的理论基础。     

基于虚拟介质方法数值模拟应力波穿透水舱

将虚拟介质方法推广到应力波与流固界面的相互作用,基于修正虚拟流体方法(MGFM)思想提出一种适用于流固界面应力波折射问题的界面状态计算法则。以此为基础,用Zwas格式和WENO格式分别离散固体和流体控制方程,数值模拟应力波穿透水舱。数值测试表明:虚拟介质方法推广到模拟流固界面上的应力波时,数值误差具有很好的收敛性;该研究提出的计算法则具有一阶精度。一维数值结果与理论解析解能很好地吻合,验证了用虚拟介质方法模拟应力波在流固界面处反射与透射的可行性。应力波穿透水舱的数值结果表明:虚拟介质方法与任意拉格朗日-欧拉(ALE)方法得到的数值结果相近;水舱加压后,透射波的强度也相应的增加;不同的水舱压力下,应力波在流固界面处的折射规律相近。该结论对舰船的防护设计有实际意义。     

Boundary element method for electroelastic interaction in piezoceramics

A boundary element formulation and its numerical realization for the analysis of electroelastic interaction in piezoelectric materials are presented and corroborated numerically. Based on the linear theory of piezoelasticity, the boundary integral equation is developed employing the mechanical displacement and the electric potential as the primary variables. A two-dimensional fundamental solution for transversely isotopic piezoelectric materials is obtained in closed form and numerically implemented using the spline boundary element method. As a numerical example, stress analysis is performed for an infinite piezoceramic medium (PZT-4) containing a cylindrical defect under several mechanical and electric loading conditions. Numerical results are shown to be in good agreement with an available solution.     

Extracting the electromechanical coupling constant of piezoelectric thin film by the high-tone bulk acoustic resonator technique

In this paper, a new approach is proposed to rapidly and accurately measure the electromechanical coupling constant K(t)(2) of thin film piezoelectric material, which is critically important for real-time quality control of the piezoelectric film growth in mass production. An ideal lossy bulk acoustic resonator (LBAR) model is introduced and the theory behind the method is presented. A high-tone bulk acoustic resonator (HBAR) was fabricated on a silicon wafer. The impedance response of the resonator was measured, from which the K(t)(2) of the piezoelectric material was extracted. To illustrate the potential of the proposed technique to extract material properties, two HBAR devices employing AlN as the piezoelectric material were fabricated using an RF sputter system with known good and bad deposition conditions; the extracted K(t)(2) values of the piezoelectric material are compared.     

压电陶瓷变压器的发展——回顾与展望

文章简要介绍了压电变压器的工作原理 ,给出了压电变压器几个重要工作特性的数学表达式 ,并对压电变压器的发展过程进行了简要的回顾。在此基础上 ,文章着重对压电变压器在研发过程中所涉及的五个方面的问题进行了详细的探讨与说明 ,作者讨论了压电变压器等效电路模型的改进措施及压电变压各个特性的研究状况 ,分析和对比了各种用于制作压电变压器的压电材料的优缺点及其性能的改进方法 ,探讨了各种振动模式作用于压电变压器的效果 ,总结了压电变压器的制作工艺及结构对其特性的影响效果 ,给出了压电变压器的具体应用的例子 ,并指出了压电变压器今后的发展方向及有待解决的问题     

基于压电材料的主动吸声降噪方法研究

提出了用压电材料进行主动吸声的方法。用压电材料作为主动吸声系统中的吸声材料,通过等间距布置于压电材料正前方的两个麦克风传感器,检测出平面入射声波与反射声波,利用压电材料的压电性能,在压电材料上加电压使得反射声波为零,从而达到主动吸声的目的。最后对不同频率入射的声波用matlab语言进行了仿真,仿真结果表明文中所提方法的可行性。