纳米尺度下半空间内浅埋圆形弹性夹杂对SH波的散射

Scattering of a Nanoscale Circular Elastic Inclusion on SH Wave in a Semi-Space

摘要: 本文利用复变函数法、多极坐标法、虚源法和Graf加法公式研究了在纳米尺度下含有圆形夹杂的弹性半空间对SH波的散射问题。首先根据边界条件求出了介质内的入射、反射、散射、折射波函数，然后利用波函数求出在复数坐标系下相对应的应力场，最后，给出了界面圆形夹杂的动应力集中的算例和结果。具体讨论了圆孔夹杂边界处的环向动应力随无量纲波数、入射角变化时的变化情况，以及分析了表面参数S对动应力集中的影响，比较了在宏观和微观下的动应力集中。结果表明：在纳米尺度下，表面参数越小，引起的圆形夹杂边界处的应力集中程度越强；无量纲波数越大，引起的圆形夹杂边界处的应力集中程度越强。

Abstract: Using complex function method, multi-polar coordinate method, image-source method, and Graf’s addition formula, the scattering of SH wave by a nano-circular inclusion in elastic half space was studied. Firstly, according to the boundary conditions, the reflected, scattered and refracted wave functions in medium were calculated. Then the wave functions of the corresponding stress field in complex coordinate system were derived. Finally, the calculation examples and results of the dynamic stress concentration around the interface of the circular inclusion were presented in the paper. The variation of circumferential dynamic stress around the boundary of circular inclusion with dimensionless wave number and the change of incidence angle were discussed in detail. The researcher also analyzed the influence of surface parameters on dynamic stress concentration and compared the dynamic stress concentration under macroscopic and microscopic conditions. The results show that the stress concentration at the boundary of the circular inclusion is stronger with the smaller the surface parameter and the higher the dimensionless wave number.