含半圆形凸起的直角域对平面SH波的地震动

按Green函数和积分方程方法,分析了含半圆形凸起的直角域对平面SH波的稳态响应,讨论了由凸起散射所造成的地震动。对含半圆形凸起的直角域做分区,分为直角域和半圆域,按镜像方法构造直角域的Green函数,按Graf加法公式和波函数展开法构造半圆域的Green函数。对直角域和半圆域做契合,在契合界面施加一组分布力,使直角域和半圆域中的位移场和应力场满足契合界面上的连续性条件,得到分布力的定解积分方程组。数值求解,得到契合界面上的应力分布和地表位移幅值,结果表明入射波的波数和角度以及凸起与直角域垂直边界的距离对凸起散射的影响。

Ground motion of right-angle domain with a semi-circular cylindrical hill subjected to plane SH waves

Steady state responses in a right-angle domain with a semi-circular cylindrical hill to plane SH waves are analyzed, and the ground motion caused by hill scattering is discussed by using the Green function method and the integral equation method. The right-angle domain with a semi-circular hill is divided into two domains: Domain Ⅰ is right-angle space and Domain Ⅱ is semi-circular space. Green functions for the two domains are established, respectively: the image method is employed in Domain Ⅰ, and the Graf addition formula and wave function expansion method are employed in Domain Ⅱ. The conjunction condition is introduced between Domain Ⅰ and Domain Ⅱ. Distributed forces along conjunctive interface are adopted to formulate displacement and stress fields in the two domains which are continuous on the interface, and an integral equation for unknown forces is presented. Distribution of stress on the conjunctive interface and displacement amplitude on the horizontal surface are numerically solved to present the effects of incident wave number, angle and distance between hill and vertical bound of the right-angle domain on SH wave scattering of hill.