含有圆形夹杂的双相介质半空间对 SH 波的散射与地震动

摘要

采用复变函数和 Green 函数方法，对双相介质界面附近含有圆形弹性夹杂的无限半空间在稳态入射 SH波作用下的地表运动问题进行研究。首先，利用“虚设点源”的方法构造所需 Green 函数，即在1／4空间自由表面上任意一点作用点源函数时位移基本解答；其次，利用界面“契合”技术和“镜像”的思想建立含有无穷未知力系的第一类 Fredholm 积分方程组，通过有效截断方法求解该方程组；最后，建立地表位移幅值表达式并给出其分布的具体算例分析。结果显示：入射角度、入射波数和圆形夹杂到自由表面的距离以及双相介质界面的距离均对地表位移幅值有一定程度的影响。%The analysis for problems of ground surface motion of an infinite half space including a circular elastic inclusion near bi-material interface under the action of steady incident SH waves was studied by using the methods of complex function and Green function.Firstly,Green function needed for the problem was constructed with the aid of the“imaging a point source load”method,it was an essential solution to displacement function for a quarter space under the action of a point source load at any point of its free surface.Secondly,a series of the first kind of Fredholm integral equations containing infinite unknown forces were established by using the technology of interfacial “conjunction”and the idea of “image”.Then the equations were solved with the aid of an effective truncation.Finally,some examples for the expressions of amplitude of ground surface displacement and its distribution were presented.Numerical examples demonstrated that the distribution of amplitude of ground surface displacement is influenced to a certain level by incident angle,incident wave numbers,distance between the circular inclusion and the free surface and distance between the circular inclusion and the bi-material interface and so on.