任意圆弧形凸起地形对平面SH波的散射

本文采用波函数展开方法提出弹性半空间表面一任意圆弧形凸起边界对平面ＳＨ波二维散射的封闭级数解答，利用引入的辅助函数和推广的外域型Ｇｒａｆ加法公式将解答归结为一代无穷代数方程组的求解，解答的数值结果可由无穷方程的截断计算得出，文中从级数项数增加时计算结果的收敛以及边界条件的收敛满足两方面检验了截断计算的精度，并指出了位移解答的收敛速度与主要参数之间的关系，同时，对凸起角点的应力奇异性及其对解答精度的

SCATTERING OF PLANE SH WAVES BY A CYLINDRICAL HILL OF CIRCULAR-ARC CROSS-SECTION

A closed- form solution of two-dimensional scattering of plane SH waves by a cylindrical hill of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the auxiliary functions and the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and the accuracy is demonstrated by convergence of the numerical results and by the extent to which the numerical results fit the exact boundary conditions with the increasing of the truncation order. The singularity in the shear stress near the rim of the hill is evaluated and its effect on the accuracy of the numerical results is explained.The figures and their data for the numerical results of two typical cases are then given for comparison with various approximate methods and the effects of the height-to-width ratio of the hill on surface ground motion are finally illustrated.