Cratering occurs inevitably on the surface of materials at all scales due to comprehensive factors. The presence of craters may have a significant influence on the mechanical performance of the surface of an elastic body. In this paper, we study the SH wave propagation in an elastic semi-infinite medium whose surface has a semi-elliptical crater. We explore the scattering of the SH wave by the crater when surface elasticity is incorporated in the model of deformation to account for possible small-scale effects of the crater. We obtain a series solution for the scattered wave function by employing the Mathieu functions in the corresponding elliptical coordinate system. We discuss in some numerical examples the dynamic stress concentration around the crater relative to the wave frequency and few geometric parameters.

中文翻译：

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具有表面弹性的半椭圆坑对SH波在弹性半空间中的散射


由于综合因素的影响，各种尺度的材料表面都不可避免地会出现缩孔。凹坑的存在可能对弹性体表面的机械性能产生显着影响。本文研究了表面具有半椭圆坑的弹性半无限介质中SH波的传播。我们探讨了当表面弹性被纳入变形模型时，陨石坑对 SH 波的散射，以解释陨石坑可能产生的小规模效应。我们利用相应椭圆坐标系中的马蒂厄函数得到了散射波函数的级数解。我们在一些数值例子中讨论了火山口周围相对于波频率和一些几何参数的动态应力集中。