Abstract This article presents a study of the dispersion characteristics of wave propagation in layered piezoelectric structures under plane strain and open-loop conditions. The exact dispersion relation is first determined based on an electro-elastodynamic analysis. The dispersion equation is complicated and can be solved only by numerical methods. Since the piezoelectric layer is very thin and can be modeled as an electro-elastic film, a simplified model of the piezoelectric layer reduces this complex problem to a non-trivial solution of a series of quadratic equations of wave numbers. The model is simple, yet captures the main phenomena of wave propagation. This model determines the dispersion curves of PZT4-Aluminum layered structures and identifies the two lowest modes of waves: the generalized longitudinal mode and the generalized Rayleigh mode. The model is validated by comparing with exact solutions, indicating that the results are accurate when the thickness of the layer is smaller or comparable to the typical wavelength. The effect of the piezoelectricity is examined, showing a significant influence on the generalized longitudinal wave but a very limited effect on the generalized Rayleigh wave. Typical examples are provided to illustrate the wave modes and the effects of layer thickness in the simplified model and the effects of the material combinations.

中文翻译：

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层状压电结构中波传播的色散特性：精确和简化的模型

摘要 本文研究了平面应变和开环条件下层状压电结构中波传播的色散特性。精确的色散关系首先是基于电弹动力学分析确定的。色散方程很复杂，只能通过数值方法求解。由于压电层非常薄并且可以建模为电弹性膜，压电层的简化模型将这个复杂问题简化为一系列波数二次方程的非平凡解。该模型很简单，但捕获了波传播的主要现象。该模型确定了 PZT4-Aluminum 层状结构的色散曲线，并确定了两种最低波模式：广义纵模和广义瑞利模。该模型通过与精确解的比较得到验证，表明当层的厚度小于或与典型波长相当时，结果是准确的。检查了压电效应，显示对广义纵波的显着影响，但对广义瑞利波的影响非常有限。提供了典型的例子来说明简化模型中的波模式和层厚度的影响以及材料组合的影响。显示对广义纵波的显着影响，但对广义瑞利波的影响非常有限。提供了典型的例子来说明简化模型中的波模式和层厚度的影响以及材料组合的影响。显示对广义纵波的显着影响，但对广义瑞利波的影响非常有限。提供了典型的例子来说明简化模型中的波模式和层厚度的影响以及材料组合的影响。