双相介质半空间内椭圆夹杂对透射SH波的散射

摘要

In this paper we studied the scattering of the transmission SH-wave form by elliptic elastic inclusions in a bi-material half-space using mainly the Green function,the complex function,the conformal mapping and the polar coordinate.Firstly,by introducing the complex variables and using the conformal mapping,we mapped the elliptic boundary into a unit circle.Next,by dividing the doublephase medium along the vertical boundaries into two quarter-spaces and adding a force system on the subdivision surface to make the SH wave satisfy the displacement and stress continuity conditions in the vertical boundary,we constructed a quarter-space Green function of displacement field.Then,we established an additional force system of integro differential equations in the vertical interface using the "conjunction" technique,and solved the unknown additional force system using the effective truncation.Finally,we presented and discussed the distribution of the dynamic stress concentration factor around the elliptic inclusion under the conditions of different parameters.The results show that the SH-wave incident angle and frequency,and the media both have influences on the distribution of the dynamic stress concentration factor.%为探究双相介质弹性半空间内椭圆弹性夹杂对透射SH波的散射问题,主要采用Green函数法、复变函数法、保角映射法和极坐标移动技术.首先,引入复变量并在复平面上运用保角映射的方法将椭圆边界映射为单位圆边界;然后,将双相介质沿垂直边界剖开分成两个四分之一空间,在剖分面上作用附加力系使SH波在垂直边界上满足位移和应力连续的条件,并构造四分之一空间内点源荷载作用下的Green函数位移场;进而,利用“契合”的思想在垂直边界上建立定解积分方程组,并利用SH波衰减的性质进行有限项截断来求解未知附加力系.最后,通过具体算例得出在不同参数情况下椭圆夹杂周边动应力集中因子分布情况.结果得知,SH波的入射角度和频率以及介质的性质对夹杂周边动应力集中分布有一定影响.