平面SV波入射下半圆凸起地形地表运动解析解

SURFACE MOTION OF A SEMI-CYLINDRICAL HILL FOR INCIDENT PLANE SV WAVES:ANALYTICAL SOLUTION

采用波函数展开法,并借助辅助函数思想,给出了平面SV波入射下半圆凸起地形地表运动的一个解析解,并对解答的收敛性和截断计算精度进行了检验;最后通过若干算例分析了入射频率和入射角度以及凸起地形宽度对地表运动的影响.数值结果表明,凸起地形对入射SV波具有显著的放大作用,该放大作用可达自由场的4倍以上.当入射频率较低时,位移峰值多位于半空间地表;而当入射频率较高时,位移峰值多位于凸起地形表面.

An analytical solution for surface motion of a semi-cylindrical hill for incident plane SV waves was derived by using the wave function expansion method and the auxiliary function technique, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and angle as well as hill width on the surface motion of the hill was discussed by numerical examples. It was shown that, a hill greatly amplifies incident plane SV waves, and the maximal amplification may reach 4 times of that for free-field response; and for incident waves of low frequency, the maximal displacement amplitudes emerge mostly at the half-space, however, for incident waves of high frequency, the maximal displacement amplitudes appear mostly at the hill.