Piezoeffect in polar materials using moment theory

A method for describing the piezoelectric effect in a polar material is proposed based on the use of a composite particle model with seven degrees of freedom and a nonzero dipole moment. Based on micropolar theory, a system of equations is obtained which differs from the classical theory of piezoelectricity in the presence of additional terms. It is shown that under certain assumptions, the proposed system of equations becomes the classical system but the piezoelectric moduli depend strongly on the spontaneous polarization vector. It is shown that for anisotropic media with different symmetries, the structure of the third-rank piezoelectric tensors obtained using the proposed micropolar theory coincides with the structure of the tensors obtained using classical theory. For the media considered, dispersion relations are given and it is shown that in the proposed theory, unlike classical theory, the piezoelectric moduli are proportional to the spontaneous polarization.     

Complete band gaps in two-dimensional piezoelectric phononic crystals with {1–3} connectivity family

In this paper, we present results of full band structures for two-dimensional piezoelectric phononic crystals with {1–3} connectivity family. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes: a transverse polarization mode and a mixed (longitudinal-transverse) polarization mode. And the band structures of the two modes for both the case of piezoelectric rods embedded in a polymer matrix and the case of polymer rods embedded in a piezoelectric matrix are calculated for two different cross-sections of the rods, i.e., circular and square, considering the practical fabrication of phononic crystals. We reveal the existence of several very large complete band gaps in a material of practical interest such as PZT rods reinforced polythene composite. The effects of shapes and filling fraction of the rods on band gaps are discussed in detail. The existence of these gaps in relation to the physical parameters of the constituent materials involved is studied. Understanding the band structures of piezoelectric phononic crystals can give some information for improvements in the design of acoustic transducers.     

Electroacoustic waves in piezoelectric crystals: Certain limiting cases

The Christoffel equations for electroacoustic waves in unbounded piezoelectric crystals are solved in the limits of weak and strong electromechanical coupling and for the case where the unstiffened elastic constants satisfy the conditions of elastic isotropy. Lyubimov's proof that piezoelectric stiffening of the elastic constants increases acoustic velocities is extended to cover degenerate modes. It is shown that when the elastic contribution to the stiffened elastic constants is zero, only one acoustic branch survives with a finite velocity. When the unstiffened elastic constants satisfy the conditions of elastic isotropy one of the acoustic branches is unaffected by the piezoelectric stiffening and, moreover, Lyubimov's theorem holds nonperturbatively.     

Effects of covering layer thickness on Love waves in functionally graded piezoelectric substrates

An analytical approach is used to investigate the effects of covering layer thickness on the propagation behavior of Love waves in functionally graded piezoelectric materials (FGPMs) covered with a dielectric layer. The piezoelectric substrate is polarized in the direction perpendicular to the wave propagation plane, and its material parameters change continuously along the thickness direction. The dispersion equations for the existence of Love waves with respect to phase velocity are obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of the covering dielectric layer thickness on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out. Numerical results show that for a given FGPM, the covering dielectric layer thickness affects significantly the fundamental mode of Love waves but has only negligible effects on the high-order modes. The changes in phase velocity, group velocity, and electromechanical coupling factor due to the change of gradient coefficient of FGPMs could be approached approximately by changing the thickness of the covering dielectric layer, which imply a potential factor for designing new-type surface wave devices with FGPMs.     

On the physical interpretation of material parameters in phase field models for ferroelectrics

This publication intends to clarify the relations between the free energy expansion and the choice of the order parameter in phase field models for ferroelectrics. The free energy is expanded to include the piezoelectric coupling terms, reflecting the symmetry properties of the material below the Curie temperature. The order parameter can then be interpreted as the material polarization less than the dielectric and piezoelectric contributions. Furthermore, a 1d reduction of the problem is used to identify the physical meaning of the remaining model parameters. The theoretical results are verified by numerical simulations of 180^? and 90^? domain walls. Both the static case, where the emphasis lies on the specific energy and the interface width, and the dynamic case, where interfaces are subjected to an electric driving field, are considered in the simulations.     

初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

The effective electroelastic property of piezoelectric media with parallel dielectric cracks

Existing studies on the coupled electroelastic behaviour of cracked piezoelectric media have been based mostly on the electrically impermeable and permeable crack models. The current paper presents a study of the effective electroelastic property of piezoelectric media weakened by parallel cracks using a dielectric crack model with the electric boundary condition along the crack surfaces being governed by the opening displacement. The theoretical formulation is obtained using the dilute model of distributed cracks and the solution of a single dielectric crack problem. It is observed that the effective electroelastic property of cracked piezoelectric media is nonlinear and sensitive to loading conditions. Different modes of crack deformation are predicted and discussed. Attention is paid to the transition between electrically permeable and impermeable crack models.     

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal(SH)wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder.The interface of the two media is assumed mechanically imperfect.For obtaining the dispersion relation,the mathematical formulation has been developed and solved by an analytical treatment.The effects of various parameters,i.e.,the thickness ratio,the imperfect interface,the initial stress,the reinforcement,and the piezoelectric and dielectric constants,on the dispersion curve are observed prominently.The dispersion curves for different modes have been also plotted.The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.     

PMN-PT层/弹性基底结构中声表面波特性分析

研究了PMN-PT 压电层/弹性(金刚石) 基底结构中表面波的传播特性,压电层表面是机械自由的,电学边界条件分为电学开路和电学短路,压电层与基底之间采用理想连接. 得到了满足控制方程和边界条件的电弹场以及弹性波在结构中传播时的频散方程,通过数值算例分析了压电材料PMN-PT 的极化方向对弹性波频散曲线和机电耦合系数的影响,以及不同极化方向时弹性位移和电势随结构深度方向的变化,结果可为PMN-PT 压电材料在高频声表面波器件中的应用提供有价值的理论参考.      

Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure

The propagation of a Bleustein-Gulyaev (B-G) type wave in a structure consisting of multiple layers and a half-space of porous piezoelectric materials is theoretically studied. The solutions of the problem in terms of the mechanical displacements and electric potential functions are obtained for each layer and the half-space. The dispersion equation is obtained for electrically open and shorted boundary conditions by use of the transfer matrix method. A peculiar kind of B-G waves is investigated, which can propagate only in the layer over the half-space. The relationship between the piezoelectric constants and the dielectric constants is found for the existence of a peculiar kind of propagation modes. The numerical results in terms of the phase velocity and the electromechanical coupling factor with different thicknesses of the layer stack are presented.     

Vibration of beams with piezoelectric inclusions

A mathematical model for the vibration of beams with piezoelectric inclusions is presented. The piezoelectric inclusion in a non-piezoelectric matrix (host beam) is analyzed as two inhomogeneous inclusion problems, elastic and dielectric, by using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form, which is expressed as functions of the elastic strain energy and dielectric energy of the piezoelectric inclusion. The Euler–Bernoulli beam theory and Rayleigh–Ritz approximation technique are used in the present analysis. In addition, a parametric study is conducted to investigate the influence of the energies due to piezoelectric coupling on the natural frequency of the beam.     

Dielectric Breakdown Model for an Electrically Semi-Permeable Penny-Shaped Crack in Three-Dimensional Piezoelectric Media

The dielectric breakdown(DB) model for a penny-shaped crack under a semipermeable boundary condition in a three-dimensional piezoelectric medium is studied.An approximate analytical solution is derived by using the boundary integral equation with extended displacement discontinuity,and the corresponding boundary element method with double iterative approaches is developed to analyze the semi-permeable crack.The effect of electric boundary conditions on crack faces is discussed on the basis of DB model.By comparing the DB model with the polarization saturation(PS) model for different piezoelectric materials,some interesting phenomena related to the electric yielding zone and local J-integral are observed.     

Effects of interface contacts on the magneto electro-elastic coupling for fiber reinforced composites

Imperfect bonding between constituents is studied where displacements, electric and magnetic static potentials are considered to have a jump proportional to the normal component of the mechanical traction, electric displacement and magnetic flux. This condition may model various interface damages or the thin glue layer between two adjacent phases. They are termed as the mechanically compliant, dielectrically weakly capacitance and magnetically weakly inductance at the interface. It is shown that while the more imperfect the interface is, the overall properties become weaker, such as longitudinal shear stiffness, out-of-plane piezoelectric coupling, and magnetoelectric coupling. Out-of-plane piezomagnetic coupling, transverse dielectric permittivity and transverse dielectric permeability exhibit no influence by imperfect bonding. The imperfect interface proposed is mimicked by the springs, capacitors and inductances for the mechanical, electric and magnetic interaction between the phases and are highly sensitive to the interphase properties. The results are compared mainly with the self consistent model reported in the literature and good agreements are shown.     

Linear stability of triple-diffusive convection in micropolar ferromagnetic fluid saturating porous medium

The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters (i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter) are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M ₁. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.     

A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.     

铁电陶瓷PZT53复杂力电耦合行为的实验研究

通过实验研究了平行和垂直于极化方向的正应力对铁电陶瓷锆钛酸铅(PZT53)的电滞回线(E3-P3)和电致应变曲线(E-ε)的影响. 实验发现平行于极化方向的压应力对PZT53陶瓷的电滞回线、电致应变曲线形状以及矫顽场大小都有明显的影响,但是垂直于极化方向的拉、压应力只对PZT53陶瓷的电致应变曲线形状有明显的影响,但对电滞回线形状和矫顽场大小都没有显著影响. 采用畴翻转的模型详细解释了观察到的实验现象,所得结果为建立铁电陶瓷的多轴力、电耦合本构模型,提供了物理基础.     

State dependent linear moduli in ferroelectrics

A novel experimental method is used to measure the evolution of the linear elastic, dielectric and piezoelectric moduli of a soft ferroelectric ceramic during loading. The applied loading states are combinations of uniaxial compressive stress and electric field. Short pulses of electric field and stress are used to increment the remanent strain and polarization state of the material, while the rates of change of electric displacement and strain during unloading are used to assess the moduli. The remanent quantities are treated as state variables, with a view to expressing the moduli as functions of the material state. The piezoelectric moduli are found to vary approximately linearly with polarization, regardless of the remanent strain state, whilst the dielectric moduli and elastic compliances show more complex behaviour. A simple model of the state dependence of the moduli, based on varying the volume fractions of six crystal variants in the tetragonal system, is used to interpret the results.     

ANALYSIS OF THE PIEZOTRONIC EFFECT OF A PIEZOELETRIC SEMICONDUCTOR FIBER UNDER MUTIPLE LOCAL TEMPERATURE LOADINGS 1)

温度改变产生的极化电势可对压电半导体结构内的物理量进行有效调控, 这在穿戴电子器件及与温度相关的半导体电子器件中有重要工程应用价值. 本文针对在多个局部均匀温度变化作用下的压电半导体杆结构, 采用一维热压电半导体多场耦合方程, 基于线性化的漂移-扩散(drift-diffusion)电流模型导出了问题的解析解. 以两个局部温度载荷情况为例, 数值分析了局部温度改变对压电半导体内位移、电势、电位移、极化强度、载流子分布等物理场的影响. 对于温度改变较大的情况, 在COMSOL软件的PDE模块中, 采用非线性电流模型, 进行数值模拟. 研究结果表明: 由于两个局部区域的温度改变, 在半导体杆内形成了局部势垒和势阱, 不同的温度改变量和作用区域会产生不同高度/深度的势垒/势阱, 为基于压电半导体的热压电电子学器件结构设计提供了理论指导.     

多个局部温度载荷下压电半导体纤维杆的压电电子学行为分析

温度改变产生的极化电势可对压电半导体结构内的物理量进行有效调控,这在穿戴电子器件及与温度相关的半导体电子器件中有重要工程应用价值.本文针对在多个局部均匀温度变化作用下的压电半导体杆结构,采用一维热压电半导体多场耦合方程,基于线性化的漂移-扩散(drift-diffusion)电流模型导出了问题的解析解.以两个局部温度载荷情况为例,数值分析了局部温度改变对压电半导体内位移、电势、电位移、极化强度、载流子分布等物理场的影响.对于温度改变较大的情况,在COMSOL软件的PDE模块中,采用非线性电流模型,进行数值模拟.研究结果表明:由于两个局部区域的温度改变,在半导体杆内形成了局部势垒和势阱,不同的温度改变量和作用区域会产生不同高度/深度的势垒/势阱,为基于压电半导体的热压电电子学器件结构设计提供了理论指导.     

Transient piezothemoelasticity of a hexagonal plate of class 6 mm

Summary Piezoelastic materials entail piezoelectric polarization that is directly proportional to the applied strain. Therefore, piezoelastic materials have recently attracted considerable attention because of their potential use in intelligent structural systems. In this paper, we treat a transient problem of piezothermoelasticity in a hexagonal plate of class 6 mm subjected to transient temperature change. We analyze the transient problem by use of the potential function method, which can separate the coupling between the thermoelastic and electric fields. Numerical calculations for the transient problem are carried out for a cadmium selenide solid, and the results are presented graphically in comparison with those for a steady problem.