【摘要】 按照波函数展开法和镜像方法,对直角域中半圆形凸起和圆形孔洞对SH波的散射进行了分析,得到其稳态解。对含孔洞和凸起的直角域做分区,等效为一个含孔洞与凹陷的直角域和一个圆域的契合,其在分界面上满足位移和应力的连续性条件,即契合条件,分别构造两个区域内的位移波函数,按照孔洞边界柱面上的应力自由和契合条件定解波函数展开式的系数。按Fourier级数展开法,得到定解条件的线性代数方程组,截断求解,进而得到问题的解析解。数值算例给出圆形孔洞边沿动应力和地表位移幅值的分布情况,得到直角域自由边界、凸起、孔洞对散射和地震动的影响。更多还原

【Abstract】 By using wave function expansion method and image method, scattering of a salient and a circular cavity with SH wave in an elastic quarter space is analyzed to obtain the steady state solution. The elastic quarter space which contains a salient and a circular cavity is divided into two media, while medium I is a quarter spaces which contain a circular cavity and a semi-circular canyon,medium II is a circular domain. Conjunction condition is introduced to force displacements and stresses of two media continued on the divided bound. Specific expressions of constructed displacement wave in medium I and medium II are determined by employing stress free condition on cavity bound and conjunction condition by using wave function expansion method and Fourier series expansion method. Simultaneously, the analytical solution is presented by solving truncated linear algebraic equations of definite boundary conditions. Numerical results are calculated to describe distribution of dynamic stress around the circular cavity and amplitude of displacement along the horizontal surface, then, effects of salient, cavity and stress free bounds of the quarter space to scattering and seismic ground motion are quantified.更多还原