表面效应对偏场下介电高弹体表面波传播的影响

采用表面薄层模型考察偏场下介电高弹体的表面效应,针对不同边界情形,建立一阶等效边界条件.基于有限变形电弹性体的线性增量理论,利用Stroh公式和Ting方法,给出等效边界条件的严格推导过程.进一步利用Stroh公式,获得了偏场下具有表面效应的介电高弹体中表面波的频散方程.以可压缩Neo-Hookean介电高弹体为例,分析了表面效应对预变形和电学偏场作用下的介电高弹体表面波传播特性的影响.结果表明,通过施加适当的偏场,可以调控和优化纳米声表器件的性能.     

Fundamental elastic field in an infinite plane of two-dimensional piezoelectric quasicrystal subjected to multi-physics loads

By utilizing the extended Stroh formalism, the Green's function of infinite plane is obtained for the problem of two-dimensional decagonal quasicrystals with the piezoelectric effect subjected to multi-physics loads. By numerical computations, the piezoelectric effect of the two-dimensional decagonal quasicrystals is revealed; the changes of the stress and displacement fields with multi-physics loads are discussed. The variation laws of material constants in stress and displacement fields are investigated. The results show that the effect of the phason field on the generalized displacement is larger than that on the generalized stress; and the effects of material parameters are different in diverse field.     

含界面电极压电介质的Green函数

研究了由两个不同压电材料和一半无限长电极组成的复合材料系统的广义二维问题·　基于Stroh公式,提供了当一个线力、线电荷和一个线电偶极子施加在电极端附近时,精确的Green函数解·　进一步地,获得了相应的场强度系数·　这些结果可作为边界元的基本解,以分析更加复杂的压电复合材料断裂问题·     

Tension of a compound piezoceramic plate with a hole intersecting the phase interface

We study the two-dimensional electroelastic problem for an unbounded compound plate with an arbitrary hole located in both components of the plate. The corresponding boundary-value problem is reduced to a system of singular integral equations of second kind, which for the case of an elliptic hole can be solved numerically by the method of quadratures. We give the data of computations that characterize the concentration of the electroelastic fields near the hole subject to action at infinity by fields of mechanical stresses and electric tension. It is noted that in the case of the inverse piezoelectric effect the influence of inhomogeneities of the plate on the stress concentrations is sharply expressed. Six figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 67–75.     

两压电介质之间的界面夹杂问题

应用Stroh理论,研究了两压电介质之间的刚性介电线夹杂问题。首先该问题被化为Hilbert问题,然后分别给出了压电介质内的复势函数解、夹杂内的电场解和夹杂尖端场的解析表达式。结果表明,在夹杂尖端附近,所有的场变量均呈现奇异性和振荡性,且其强度取决于介质的材料常数和无限场远处的应变。此外,结果还表明,当从夹杂内部趋近夹杂尖端时,夹杂内的电场也呈现奇异性和振荡性。     

Anisotropic transient wave motions in a conducting fluid under uniform magnetic and current fields

An initial value investigation into the development of two-dimensional anisotropic surface waves generated by a harmonically oscillating pressure distribution acting on the undisturbed free surface of an inviscid, incompressible homogeneous and electrically conducting fluid is made in this paper in considerable detail. The problem is solved by the use of generalized function treatment in conjunction with asymptotic methods. An asymptotic solution of the problem related to some physically realistic pressure distributions is presented. It is shown that an ultimate steady state is set up in the limit. Two limiting cases such as (i) very deep fluid and (ii) very shallow fluid, which are of particular interest have been examined with some emphasis. Finally, the effects of the imposed magnetic and current fields as well as the surface tension on the wave motions has been examined in some detail. Additionally, it is shown that the present method of solution provides an interesting example of the applicability of the generalized function method in problems of magnetohydrodynamics     

压电体光滑接触界面有局部分离时的滑移脉冲波传播

应用关于压电材料的Stroh方法以及Fourier分析和奇异积分方程技术,研究了压电体光滑接触界面有局部分离时的滑移脉冲波传播问题,分析了其存在的判据．压电体由单向压应力作用而光滑接触并处于一定强度的电场中．待求问题最终转化为含Cauchy核的奇异积分方程组,并给出其解析解．数值计算结果表明:光滑接触界面上有局部分离的滑移脉冲波普遍存在,且界面法向面力和法向电位移在局部分离区两端有奇异性;对某些特殊的材料组合,外载荷不影响滑移脉冲波的存在性．     

Riemann theta functions periodic wave solutions and rational characteristics for the nonlinear equations

In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct multiperiodic Riemann theta functions periodic wave solutions for nonlinear equations such as the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and (2+1)-dimensional breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional so that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze in detail, asymptotic behavior of the multiperiodic waves and the relations between the periodic wave solutions and soliton solutions are rigorously established. This generalized Hirota-Riemann method can also be demonstrated on a class variety of nonlinear difference equations such as Toeplitz lattice equation.     

Stokeswaves with vorticity

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep body of water under the force of gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a fixed semi-infinite cylinder with a parameter, the operator describing the problem is nonlinear and non-Fredholm. A global connected set of nontrivial solutions is obtained via singular theory of bifurcation. The proof combines a generalized degree theory, global bifurcation theory, and Whyburn’s lemma in topology with the Schauder theory for elliptic problems and the maximum principle.     

Two-dimensional analysis of a crack in quasicrystal materials

The two-dimensional problem of a crack in three-dimensional quasicrystals subject to far field loadings is studied. The analysis is based on the generalized Lekhnitskii's formalism. The analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The fracture quantities of quasicrystals, i.e., field intensity factors, energy release rates and so on, is a prerequisite. Numerical results for a Griffith crack under phason loading Mode I and II conditions are poltted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

半平面压电体的Green函数及其应用

本文研究半平面压电体在线力、电荷和位错作用下的弹性场和电场，即Green函数．基于各向异性弹性力学中的Stroh方法和解析延拓理论，推导了Green函数的封闭形式的解．作为解的应用，分析了含半无限裂纹的无限大压电介质的机电耦合场，给出了应力和电位移强度因子的解析表达式．     

Investigation of coupled physical fields in a compound piezoceramic wedge

A composition consisting of two infinite wedges fastened together along their common side is considered. The outer surfaces of the wedges are fixed and coated with grounded electrodes, and an ideal mechanical and electrical contact is assumed along the interface of both wedges. At certain relations of the geometric and stiffness parameters of the wedge components, the coupled electroelastic fields have a power-type singularity (intensified by oscillations) at the wedge vertex as a result of action of mechanical or electrical loads on the compound wedge. Such an effect is not observed in the case of piezopassive compound wedges (under antiplane strain conditions). The present study is dedicated to the investigation of this phenomenon. Closed-form solutions of some electroelastic boundary-value problems are constructed for the case of action of point shearing forces or electric charges.Sumskii State University, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 777–784, November–December, 1999.     

压电介质内裂纹问题的精确解

在压电介质断裂力学分析中,人们常假定裂纹面上的电位移法向分量为零,可是实验表明,这一假设将导致错误的结果。本文基于精确的电边界条件,并应用Stroh公式的方法,导出了含裂纹压电介质在无限远处均匀外载作用下二维问题的精确解。结果表明:(ⅰ)应力强度因子与各向同性材料相同,而电位移强度因子取决于材料常数和机械载荷,但与电载荷无关;(ⅱ)能量释放率大于纯弹性各向异性材料内的值,即总是正的,且与电载荷无关;(ⅲ)裂纹内所含空气的介电常数对介质内的场强无影响。     

含椭圆夹杂二维各向异性电磁弹性介质的耦合问题

研究了无限大二维各向异性电磁弹性固体的椭圆夹杂问题.基于广义Stroh方法、保角变换和扰动概念,得到了基体和夹杂内电场、磁场和弹性场的封闭解.本文结果可用于研究电磁弹性复合材料的有效性能.     

Dispersion Equations for Rayleigh Waves in a Piezoelectric Periodically Layered Structure

Dispersion equations are proposed for acoustoelectric Rayleigh waves in a periodically layered piezoelectric half space with various types of boundary conditions. The properties of the medium are specified by the determining relations for the 6mm crystallographic class. These equations are obtained using the mathematical formalism of periodic hamiltonian systems. This approach makes it possible to include the anisotropy and the piezoelectric interaction of the mechanical and electric fields and is valid for stratified media with arbitrary variations in the properties along the periodicity axis. Numerical results are presented for alternating layers of CdS and ZnO. The influence of the piezoelectric effect and type of boundary conditions on the dispersion spectra of surface waves is examined.     

An approach for optimization of robot-generated rigid-body interpolation using dynamic criteria

The present paper describes an approach for generating spatial trajectories in multibody systems including rigid–body rotations such that dynamic criteria such as forces, accelerations, velocities, etc. as well as limiting restrictions for the motion–generating mechanical device, e.g., a robot, can be considered. The task is to find a rigid–body interpolation that fulfills optimality criteria at the target trajectory as well as in the mechanical system. Application of general optimization methods fails due to the difficulty of finding feasible initial guesses that will converge. The present approach proposes to decouple the general problem into two stages, a first stage in which a pure trajectory optimization is carried out without regard of the mechanical system, and a second stage in which the carrying mechanical system is incorporated. The trajectory planning involves the use of splines of 5–th order as well as an SQP optimization for determining the spline support points as design variables. The approach is illustrated for the example of the generalized waiter problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular stress analysis near sharp corners in anisotropic notched plates subjected to bending loads

This paper presents an analytical approach to determine the singular stress fields near sharp corners in anisotropic notched plate subjected to bending. The first-order shear deformation plate theory (FSDPT) is used and the material anisotropy is modeled by the Stroh formalism. Based on the Mellin transform method, the stress singularity orders as well as the stress intensities are determined analytically. The results presented in this paper give us the singular behaviors for various plate angle α, material orientation angles ϕ and the anisotropic parameters ε. These new findings are helpful in reducing or even eliminating the singularities near the sharp corner.     

压电压磁复合材料中二维散射问题的解析研究

用极化方法分析了含一二维夹杂的无限压电压磁基体中的波动散射问题．以此为目的,首先构建了二维压电压磁“相对体”的极化方法．当一般性波动退减为简谐振动时,极化方法的核心函数退减为二维谐波Green函数．利用氡变换的解析方法,首次求得了二维谐波Green函数的积分表达式,该表达式在低频初始波与小尺度椭圆柱夹杂物的假设下可得到进一步的简化,并最终求得解析解．推导针对同时具有压电以及压磁效应的一般性各向异性材料进行,然后将所得的结果简化到仅针对压电复合材料的情况．以此简化解析解为基础,提供了两个算例,讨论了影响含一二维椭圆柱夹杂的PZT-5H压电陶瓷复合材料的散射截面的各种不同因素（包括夹杂的尺寸、形状效应,材料常数的影响,以及压电效应等）．     

On interface waves in misoriented pre-stressed incompressible elastic solids

Some relationships, fundamental to the resolution of interfacewave problems, are presented. These equations allow for thederivation of explicit secular equations for problems involvingwaves localized near the plane boundary of anisotropic elastichalf-spaces, such as Rayleigh, Scholte, or Stoneley waves. Theyare obtained rapidly, without recourse to the Stroh formalism.As an application, the problems of Stoneley wave propagationand of interface stability for misaligned predeformed incompressiblehalfspaces are treated. The upper and lower half-spaces aremade of the same material, subject to the same prestress, andare rigidly bonded along a common principal plane. The principalaxes in this plane do not, however, coincide, and the wave propagationis studied in the direction of the bisectrix of the angle betweena principal axis of the upper half-space and a principal axisof the lower half-space.     

Numerical analysis of the dispersion of acoustoelectric waves in a layer with a thickness axis of symmetry for its physical propertes

A numerical method is developed for studying normal electroelastic waves in a layer of piezoelectric materials with mm2 rhombic symmetry, and a second order thickness atris of symmetry. The main system of equations is reduced to eight hamiltonian-type equations in the thickness coordinate. For harmonic waves, the generalized spectral problem is solved numerically taking into account the even (odd) character of the solution with respect to the central plane of the layer. Some solutions of specific problems are analyzed. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 162–169, 1999.