双相介质弹性半空间垂直界面附近椭圆形夹杂对SH波的散射

Scattering of SH-wave by an elliptic inclusion near vertical interface in a bi-material half-space

采用复变函数法和Green函数法研究了SH对双相介质弹性半空间垂直界面附近椭圆形夹杂的散射问题。首先,利用保角映射的方法将椭圆边界外域映射为单位圆外域,得到椭圆夹杂对SH波的散射位移场,并通过"虚设点源"的方法求出四分之一区域内的Green函数;其次,利用界面"契合"的思想,通过在界面上添加附加力系建立待解外力系的第一类Fredholm积分方程组,通过离散的方法并考虑波函数的衰减性将无穷代数方程组进行截断,求出剖分面上的未知外力系。最后,通过具体算例给出了不同参数条件下椭圆形夹杂周边的动应力集中情况。结果表明,垂直界面、入射角度、入射波数、介质参数等因素均对动应力集中系数有一定的影响。

The diffraction of harmonic SH-wave by an elliptic inclusion near vertical interface in a bi-material halfspace was considered by using the complex function and the method of Green＇s function. The conformal mapping method was used to map the outer boundary of elliptic inclusion into a unit circle in order to construct an expression for the dsisplacement field of scattering wave. With the ridding of image method,the Green＇s function in 1 /4 space was constructed. The interface ＂conjunction＂technique was utilized to obtain a series of first kind Fredholm integral equations containing unknown forces at the interface. The integral equations were reduced to a system of algebraic equations and solved numerically by using the effective truncation. The numerical results demonstrate that the verticlal interface,incident angle,incident wave number,medium parameters under consideration are indeed capable of effecting the DSCF around the inclusion.