Non-smooth model and numerical analysis of a friction driven structure for piezoelectric motors

In this contribution, typical friction driven structures are summarized and presented considering the mechanical structures and operation principles of different types of piezoelectric motors. A two degree-of-freedom dynamic model with one unilateral frictional contact is built for one of the friction driven structures. Different contact regimes and the transitions between them are identified and analyzed. Numerical simulations are conducted to find out different operation modes of the system concerning the sequence of contact regimes in one steady state period. The influences of parameters on the operation modes and corresponding steady state characteristics are also explored. Some advice are then given in terms of the design of friction driven structures and piezoelectric motors.     

Thermo-electro-mechanical contact behavior of a finite piezoelectric layer under a sliding punch with frictional heat generation

The thermal contact problem of a piezoelectric strip with heat supply generated by the frictional tangential traction under the action of a rigid sliding punch is investigated. The inertial effects are considered. It is convenient to introduce the Galilean transform. Whole cases of the root distribution of the corresponding characteristic equation are detailed. Appropriate fundamental solutions that can lead to real solutions of the thermo-electro-mechanical quantities are derived for the piezoelectric governing equation. The stated problem is reduced to Cauchy singular integral equation of the second kind finally. Numerical results are also presented. The solutions have a reduced dependence on the material properties. The singular behaviors at the edges of the punch are revealed. The stress distribution and temperature distribution above the punch with the variations of the relative sliding speed, the frictional coefficient and the thickness are plotted. The effects of the material constants on the stress distribution and temperature distribution above the punch are presented.     

A screw dislocation near a non-elliptical piezoelectric inhomogeneity with internal uniform electroelastic field

Conformal mapping and analytic continuation are employed to prove the existence of an internal uniform electroelastic field inside a non-elliptical piezoelectric inhomogeneity interacting with a screw dislocation. We focus specifically on the case when the piezoelectric matrix surrounding the inhomogeneity is subjected to uniform remote anti-plane mechanical and in-plane electrical loading and a constraint is imposed between the remote loading and the screw dislocation. The constraint can be expressed in a relatively simple decoupled form by utilizing orthogonality relationships between two corresponding eigenvectors. The internal uniform electroelastic field is found to be independent of the presence of the screw dislocation; moreover, it can be expressed in decoupled form.     

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.     

An analysis tool for piezoelectric gages

The Piezo-electric Gage Analysis System U.S. (pegasus) couples a two-dimensional dynamic structural finite element code to a two-dimensional electrostatics code for analysis of piezoelectric gages. The method has a sound theoretical basis and is built around two powerful finite element anlysis codes. The analysis codes provide the solution of the time dependent stress state in the gage and the solution of the electrostatic equation for each time step. pegasus provides the link between the two codes and the steps required to carry the analysis through to prediction of gage currents. Post-processing of the results allows visual interpretation of the the electric fields within the gage. Here we briefly describe the code and show that it can be a valuable tool for understanding the nature of piezoelectric gages. Received 6 May 1996 / Accepted 31 October 1996     

Asymptotic fields in the finite element analysis of electrically permeable interface cracks in piezoelectric bimaterials

Summary The interface crack problem for a piezoelectric bimaterial based on permeable conditions is studied numerically. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical and electrical loads, the complex stress intensity factor for an interface crack is obtained. The influence of the applied loads on the electromechanical fields near the crack tip is also studied. For a particular case of a short crack with respect to the bimaterial size, the numerical results are compared with the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.One author (V.G.) gratefully acknowledges the support provided by the Alexander von Humboldt Foundation of Germany.accepted for publication 7 June 2004     

Effective electroelastic constants for three-phase confocal elliptical cylinder model in piezoelectric quasicrystal composites

A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal (PQC) composites. Exact solutions of the phonon, phason, and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings. The effective electroelastic constants of several different composites made up of PQC, quasicrystal (QC), and piezoelectric (PE) materials are predicted by the generalized self-consistent method. Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion (or fiber) on the effective electroelastic constants of these composites. Compared with other micromechanical methods, the generalized selfconsistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.     

Pull-in voltage analysis of electrostatically actuated MEMS with piezoelectric layers: A size-dependent model

A size-dependent model for electrostatically actuated microbeam-based MEMS (micro-electro-mechanical systems) with piezoelectric layers attached is developed based on a modified couple stress theory. By using Hamilton's principle, the nonlinear differential governing equation and boundary conditions of the MEM structure are derived. In the newly developed model, the residual stresses, fringing-field and axial stress effects are considered for the fixed–fixed microbeam with piezoelectric layers. The results of the present model are compared with those from the classical model. The results show the size effect becomes prominent if the beam dimension is comparable to the material length scale parameter (MLSP). The effects of MLSP, the residual stresses and axial stress on the pull-in voltage are also studied. The study may be helpful to characterize the mechanical and electrostatic properties of small size MEMS, or guide the design of microbeam-based devices for a wide range of potential applications.     

压电质量传感器检测灵敏度分析

压电质量传感器是一种利用压电谐振器对质量的敏感性,通过谐振器吸附待测物后频率的变化实现对被测物质进行检测的传感器。由于附着物质引起的质量变化很小,因此测试精度将强烈依赖于结构频率对质量变化的敏感程度,而敏感程度与传感器感知部分的几何尺寸密切相关。本文主要研究压电材料悬臂梁式质量传感器的检测敏感度分析问题,推导传感器自振频率变化对质量变化的灵敏度与传感器各部分结构几何尺寸设计参数依赖关系的计算格式,并讨论了结构尺寸、截面形状以及谐振模态对传感器检测灵敏度的影响。     

Damage analysis and fracture criteria for piezoelectric ceramics

Both the mechanical and the electrical damages are introduced to study fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are proposed by using the damage theory combined with the well-known piezoelectric fracture experiments of Park and Sun [Fracture criteria of piezoelectric ceramics, J. Am. Ceram. Soc. 78 (1995) 1475-1480]. One is based on a critical state of the mechanical damage and the other on a critical value of a proper linear combination of both the mechanical and the electrical damage variables. It is found that the fracture load predicted, which takes the mechanical damage into account only (mode 1), has greater deviation than predicted result by considering a proper linear combination of the mechanical and the electrical damages (mode 2). And the fracture criterion corresponding to mode 2 presented is shown to be superior to mode 1. It is also demonstrated that the mechanical damage has greater effect on fracture than the electrical damage.     

A model for electroelastic plates under biasing fields with applications in buckling analysis

This paper presents a theoretical model for coupled extension and flexure with shear deformations of an electroelastic plate under biasing fields. The governing equations of this model, defined in the middle plane of the plates, are derived from the full three-dimensional theory of electroelasticity for small fields superposed upon finite biasing fields, under the assumption that the stress component normal to the plate vanishes identically. As examples to illustrate the applications of this model, the authors include their analysis of buckling of three plates, one single-layered plate and two double-layered plates (i.e., bimorphs) of distinct poling configurations. This analysis indicates that the electromechanical coupling strengthens the plates against buckling.     

Numerical analysis for a crack in piezoelectric material under impact

In this paper, a numerical analysis of impact interfacial fracture for a piezoelectric bimaterial is provided. Starting from the basic equilibrium equation, a dynamic electro-mechanical FEM formulation is briefly presented. Then, the path-independent separated dynamic J integral is extended to piezoelectric bimaterials. Based on the relationship of the path-independent dynamic J integral and the stress and electric displacement intensity factors, the component separation method is used to calculate the stress and electric displacement intensity factors for piezoelectric bimaterials in this finite-element analysis. The response curves of the dynamic J integral, the stress and electric displacement intensity factors are obtained for both homogeneous material (PZT-4 and CdSe) and CdSe/PZT-4 bimaterial. The influences of the piezoelectricity and the electro-mechanical coupling factor on these responses are discussed. The effects of an applied electric field are also discussed.     

An analytical model for electrode–ceramic interaction in multilayer piezoelectric actuators

The present paper develops an analytical model for multi-electrodes in multi-layered piezoelectric actuators, in which the electrodes are vertical to and terminated at the edges of the medium and electroelastic field concentrations ahead of the electrodes in the multilayer piezoelectric actuators are examined. By considering a representative unit in realistic multilayers, the problem is formulated in terms of electric potential between the electrode tips and results in a system of singular integral equations in which the electric potential is taken as unknown function. Effects are investigated of electrode spacing and piezoelectric coupling on the singular electroelastic fields at the electrode tips, and closed-form expressions are given for the electromechanical field near the electrode tips. Exact solution for un-coupled dielectrics is provided, where no piezoelectric coupling is present. The English text was polished by Yunming Chen.     

A modeling and vibration analysis of a piezoelectric micro-pump diaphragm

The vibration analysis of a micro-pump diaphragm is presented. A piezoelectric micro-pump is studied. For this purpose, a dynamic model of the micro-pump is derived. The micro-pump diaphragm is modeled as circular double membranes, a piezoelectric one as actuator and a silicon one for representing the membrane for pumping action. The damping effect of the fluid is introduced into the equations. Vibration analysis is established by explicitly solving the dynamic model. The natural frequencies and mode shapes are calculated. The orthogonality conditions of the system are discussed. To verify the results, the finite-element micro-pump model is developed in ANSYS software package. The results show that the two methods are well comparable.     

A finite element study of the deformations, forces, stress formations, and energy losses in sliding cylindrical contacts

This work presents the results of a finite element analysis (FEA) used to simulate two-dimensional (2D) sliding between two interfering elasto-plastic cylinders. The material for the cylinders is modeled as elastic-perfectly plastic and follows the von Mises yield criterion. The FEA provides trends in the deformations, reaction forces, stresses, and net energy losses as a function of the interference and sliding distance between the cylinders. Results are presented for both frictionless and frictional sliding and comparisons are drawn. The effects of plasticity and friction on energy loss during sliding are isolated. This work also presents empirical equations thatt relate the net energy loss due to sliding under an elasto-plastic deformation as a function of the sliding distance. Contour plots of the von Mises stresses are presented to show the formation and distribution of stresses with increasing plastic deformation as sliding progresses. This work shows that for the plastic loading cases the ratio of the horizontal force to the vertical reaction force is non-zero at the point where the cylinders are perfectly aligned about the vertical axis. In addition, a “load ratio” of the horizontal tugging force to the vertical reaction force is defined. Although this is analogous to the common definition of the coefficient of friction between sliding surfaces, it just contains the effect of energy loss in plasticity. The values of the contact half-width are obtained for different vertical interferences as sliding progresses.     

A three-layer structure model for the effect of a soft middle layer on Love waves propagating in layered piezoelectric systems

A three-layer structure model is proposed for investigating the effect of a soft elastic middle layer on the propagation behavior of Love waves in piezoelectric layered systems, with "soft" implying that the bulk-shear-wave velocity of the middle layer is smaller than that of the upper sensitive layer. Dispersion equations are obtained for unelectroded and traction-free upper surfaces which, in the limit, can be reduced to those for classical Love waves. Systematic parametric studies are subsequently carried out to quantify the effects of the soft middle layer upon Love wave propagation, including its thickness, mass density, dielectric constant and elastic coefficient. It is demonstrated that whilst the thickness and elastic coefficient of the middle layer affect significantly Love wave propagation, its mass density and dielectric constant have negligible influence. On condition that both the thickness and elastic coefficient of the middle layer are vanishingly small so that it degenerates into an imperfectly bonded interface, the three-layer model is also employed to investigate the influence of imperfect interfaces on Love waves propagating in piezoelectric layer/elastic substrate systems. Upon comparing with the predictions obtained by employing the traditional shear-lag model, the present three-layer structure model is found to be more accurate as it avoids the unrealistic displacement discontinuity across imperfectly bonded interfaces assumed by the shearlag model, especially for long waves when the piezoelectric layer is relatively thin.     

Electro-mechanical analysis of an interfacial crack between a piezoelectric and two orthotropic layers

Summary  The problem of an interfacially cracked three-layered structure constructed of a piezoelectric and two orthotropic materials is analyzed using the theory of linear piezoelectricity and fracture mechanics. Anti-plane shear loading is considered, and the integral transform technique is used to determine the stress intensity factor. Numerical examples show the electro-mechanical effects of various material combinations and layer thicknesses on the stress intensity factor. Interesting results are obtained in comparison with earlier solutions for interfacially cracked piezoelectric structures. Received 29 December 2000; accepted for publication 3 May 2001     

Crack analysis in semi-infinite transversely isotropic piezoelectric solid. I. Green’s functions

Three-dimensional fundamental solutions corresponding to a unit point force and point electric charge are obtained for a semi-infinite transversely isotropic piezoelectric solid. The free boundary is parallel to the plane of isotropy. They can be used as the Green’s function for solving the problem of a flat circular crack near the free surface which will be dealt with in Part II of this work.     

Electroelastic analysis of a penny-shaped crack in a piezoelectric ceramic under mode I loading

Following the theory of linear piezoelectricity, we consider the electroelastic problem for a piezoelectric ceramic with a penny-shaped crack under mode I loading. The problem is formulated by means of Hankel transform and the solution is solved exactly. The stress intensity factor, energy release rate and energy density factor for the exact and impermeable crack models are expressed in closed form and compared for a P-7 piezoelectric ceramic. Based on current findings, we suggest that the energy release rate and energy density factor criteria for the exact crack model are superior to fracture criteria for the impermeable crack model.