Abstract

In the present article, a theoretical investigation has been carried out to analyze the propagation of shear horizontal surface waves (SH-waves) in a structure consisting of a functionally graded piezoelectric material (FGPM) layer lying over an FGPM half-space. The material properties of FGPM layer are assumed to have exponential function distribution along the thickness direction whereas those of FGPM half-space are presumed to have quadratic variation. The interface between the FGPM layer and the FGPM half-space has been considered to be imperfect. At the surface, two cases are considered, electrically open case and electrically short case. Moreover two types of imperfections at the interface are taken into account (one as mechanically compliant and dielectrically weakly conducting and other as mechanically compliant and dielectrically highly conducting). Variable separable method is used for the wave solution. In particular, the solutions for mechanical displacement and electric potential function for FGPM half-space has been obtained in the form of modified Bessel function. The dispersion relation for each case is obtained in determinant form using suitable boundary conditions. Numerical example is given and graphs are plotted. The numerical results show that the surface wave velocity is affected by the layer width, gradient coefficient of the two FGPM media, and the degree of mechanical and dielectrical imperfections at the interface between the covering layer and the substrate. This study finds its application in optimization of SAW devices.

摘要

在本文中，进行了一项理论研究，以分析剪切水平表面波 (SH 波) 在由位于 FGPM 半空间上的功能梯度压电材料 (FGPM) 层组成的结构中的传播。假设 FGPM 层的材料性质沿厚度方向呈指数函数分布，而 FGPM 半空间的材料性质假设呈二次变化。FGPM 层和 FGPM 半空间之间的界面被认为是不完美的。在表面上，考虑了两种情况，电开路情况和电短路情况。此外，还考虑了界面处的两种类型的缺陷（一种是机械顺应性和介电弱导电性，另一种是机械顺应性和介电性高导电性）。波动解采用变量可分法。特别是，FGPM半空间的机械位移和电势函数的解已经以修正的贝塞尔函数的形式得到。使用合适的边界条件以行列式形式获得每种情况的色散关系。给出了数值示例并绘制了图表。数值结果表明，表面波速度受层宽、两种 FGPM 介质的梯度系数以及覆盖层与基板之间界面处的机械和介电缺陷程度的影响。