Propagation of the torsional surface waves in a medium consisting of a functionally graded (FG) substrate bonded to a thin piezoelectric over-layer has been analytically formulated in the mathematical framework of surface/interface elasticity theory. In the cases where the wavelength and/or the thickness of the over-layer are comparable to the surface/interface characteristic length, then the surface/interface effects are not negligible. It is assumed that the over-layer is made of hexagonal 622 crystals with a single axis of rotational symmetry coinciding with the axis of polarization. The half-space is made of an FG transversely isotropic material in which the elasticity tensor and the mass density vary linearly with depth. Accounting for the surface/interface effects, the pertinent dispersion relation is derived analytically and verified for five different limiting cases of the proposed problem. The effect of the inhomogeneity parameters of the FG half-space and the surface/interface parameters on the dispersion relation is studied numerically, and the results are compared with those obtained from the classical theory.

中文翻译：

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在表面/界面理论中具有压电覆盖层的横向各向同性 FG 衬底中的扭转表面波传播

在表面/界面弹性理论的数学框架中分析公式化了扭转表面波在由粘合到薄压电覆盖层的功能梯度 (FG) 衬底组成的介质中的传播。在波长和/或覆盖层的厚度与表面/界面特征长度相当的情况下，表面/界面效应是不可忽略的。假定覆盖层由六边形 622 晶体制成，其单轴旋转对称与偏振轴重合。半空间由 FG 横向各向同性材料制成，其中弹性张量和质量密度随深度线性变化。考虑到表面/界面效应，相关色散关系是针对所提出问题的五种不同限制情况进行分析和验证的。数值研究了FG半空间的不均匀性参数和表面/界面参数对色散关系的影响，并将结果与​​经典理论的结果进行了比较。