半无限空间中圆形孔洞周围SH波的散射

建立了求解在含有圆形孔洞的弹性半空间中SH波散射与圆形孔洞附近动应力集中问题的解析方法。利用SH波散射的对称性和多极坐标的方法，构造了一个可以预先满足半空间自由表面上应力自由边界条件的圆形孔洞对SH波散射的波函数。利用这一波函数，则可将该问题转化成对一个圆形孔洞散射的求解问题。该问题的解答最终又可归结为对一组无究代数方程组的求解问题，并可利用截断有限项的方法对其进行计算，最后给出了有关圆形也洞附近动应力集中问题的算例和数值结果，并讨论了波数与圆孔至自由边界距离变化对动应力集中的影响。

Scatte ring of SH-wave around a circular cavity in haflf space

An analytic method is developed for the problem of scattering of SH-wave and dynamic stress concentration around a circular cavity near the interface of elastic half space. The scattered wave function which can satisfy the condition of stress free on the horizontal surface around a circular cavity in half space is constructed based upon the symmetry of scattering of SH-wave and the method of multi-polar coordinate systems. Using this scattered wave function, the problem can be summarized into scattering of SH-wave around a circular cavity in full space. And finally, the problem can be reduced to solution of a series of algebraic equations and solved numerically truncating the finite terms of the infinite algebraic equations. Numerical examples are provided to show the effect of wave number and distance between the center of the cavity and the horizontal interface upon the dynamic stress concentration around the circular cavity.