采用复变函数法和格林函数法研究了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，从而获得椭圆夹杂对SH波的散射位移场，并通过“虚设点源”的方法进而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。
Abstract
The diffraction of time harmonic SH-wave by an elliptic inclusion near vertical interface in a bi-material half-space is considered by using complex function and Green's function methods. Firstly, conformal mapping method is used to map the outer boundary of elliptic inclusion into a unit circle in order to construct the expression of scattering wave. With the rid of image method, the Green's function in 1/4 space is constructed. Secondly, the interface "conjunction" technique is utilized to obtain a series of Fredholm integral equations of first kind containing unknown forces at the interface. The integral equations are reduced to a system of algebraic equations and solved numerically by using the effective truncation. Finally, numerical results demonstrate that verticlal interface, incident angle, incident wave number, medium parameters under consideration are indeed capable of effecting the DSCF of the inclusion.
关键词
SH波 /
垂直界面 /
椭圆夹杂 /
保角映射 /
动应力集中系数（DSCF）
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Key words
SH-wave /
vertical interface /
elliptic inclusion /
conformal mapping /
dynamic stress concentration factor (DSCF)
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