【作者】 王国庆；

【导师】 刘殿魁；

【作者基本信息】 哈尔滨工程大学 ， 结构工程， 2002， 硕士

【摘要】 建立了求解半无限空间中界面附近相邻多个圆形孔洞对SH波散射与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，在复平面上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多个圆形孔洞对SH波散射的波函数。利用这一波函数，则可将该问题转化成为一个对无限空间中相邻多个圆形孔洞对SH波散射的求解问题。该问题的解答，可以应用移动坐标的方法逐个满足各个圆孔上的边界条件，因此，最终又可归结为对一组无穷代数方程组的求解，可利用截断有限项的方法对其进行计算。通过具体算例，讨论了与界面等距离的相邻二个圆孔对SH波的散射，给出了数值结果，并讨论了波数与圆孔至边界距离和二圆孔中心距离变化对动应力集中和地面运动的影响。更多还原

【Abstract】 In this paper, an analytic method is developed for the problem of scattering of steady SH-wave and dynamic analysis of multiple circular cavities in half space. The scattered wave function which satisfies the condition of stress free at the horizontal surface by multiple circular cavities impacted by incident steady SH-wave is constructed based upon the symmetry of scattering of SH-wave and the method of multi-polar coordinate system. Using this scattered wave function and moving coordinate system, the problem can be summarized to scattering of SH-wave by multiple circular cavities in infinite space and the boundary conditions can be satisfied. And finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations. Numerical examples, two cavities case, are provided to show the effect of wave number, distance between the centers of the cavities and the ground surface and distance between the centers of the cavities upon the dynamic stress concentration around the cavities edge and ground motion impacted by incident steady SH-wave.更多还原