SH波冲击下浅埋任意形孔洞的动力分析

Dynamic response on a shallowly buried cavity of arbitrary shape impacted by vertical SH-wave

求解了稳态SH波垂直弹性半空间水平表面入射时,浅埋任意形孔洞的动力响应。采用复变函数和多极坐标方法构造了一个能够自动满足水平表面上应力自由边界条件的散射波函数。应用这一波函数,将半空间中的问题转化为求解一个全空间中任意形孔洞的散射问题,最终将问题归结为对一组无穷代数方程组的求解。作为对抗爆问题的研究,给出了浅埋椭圆孔和方孔附近的动应力集中系数的数值结果,并对算例进行了讨论。

The scattering of plane SH-wave, whose incidence direction is vertical to the horizontal plane, by a shallowly buried cavity of arbitrary shape in a homogeneous elastic half-space is analyzed. A scattered wave function, which satisfies the condition of stress free on the ground surface, is constructed. The methods of complex function and multi-polar coordinate system are used here. Using this scattered wave function, the problem can be summarized to scattering of SH-wave by a cavity of arbitrary shape in the infinite space, and finally the problem comes to be solving a series of algebraic equations. Numerical results of dynamic stress concentration are provided when the cavity is ellipse or square. The influences of wave numbers or cavity shape upon the dynamic stress concentration factors around the cavity are discussed.