In this paper, the propagation properties of anti-plane elastic waves in a piezoelectric semiconductor (PS) layered periodic composites are theoretically investigated. The periodic layered composites consist of periodically repeated two micro-scale geometrical thickness PS slabs with different elasticity, piezoelectricity and charge carriers. Following consideration of the coupling mechanical anti-plane displacement, electric potential and perturbation of charge carriers, the influences of interface effects resulted from homo- and hetero-junctions on the dispersion relations of anti-plane elastic waves are systematically discussed. It is found that homo- and hetero-junctions can be approximately treated as rigid imperfect interfaces, which can enhance the width of band-gaps of anti-plane elastic waves, especially for high-frequency short-wavelength anti-plane elastic waves. The establishment of mathematical models and the revelation of physical mechanisms are all fundamental to the analysis and optimization of micro-scale energy harvesters based on the propagation of anti-plane elastic waves.

本文从理论上研究了反平面弹性波在压电半导体 (PS) 层状周期复合材料中的传播特性。周期性层状复合材料由周期性重复的两个微尺度几何厚度 PS 板组成，具有不同的弹性、压电性和电荷载流子。考虑耦合机械反平面位移、电势和电荷载流子扰动，系统讨论了同质结和异质结引起的界面效应对反平面弹性波色散关系的影响。发现同质结和异质结可以近似视为刚性缺陷界面，这可以增加反平面弹性波的带隙宽度，特别适用于高频短波反平面弹性波。数学模型的建立和物理机制的揭示都是基于反平面弹性波传播的微型能量采集器的分析和优化的基础。