正交各向异性半圆形沉积谷对SH波的散射

Scattering of an orthotropic semi-cylindrical alluvial valley by SH waves

采用波函数展开法给出了具有圆柱型正交各向异性半圆形沉积谷地形对SH波散射的解答,研究了入射波特性和沉积谷的各向异性对地面运动的影响。稳态SH波入射时,在圆柱型正交各向异性沉积谷中波函数的径向函数满足非整数阶的Bessel方程。数值结果表明:沉积谷地表位移的幅值大小与入射波的频率、入射方向、沉积谷介质的径向与环向剪切模量比及半空间与沉积谷剪切波速比和密度比密切相关,当沉积谷介质比半空间介质软时,沉积谷地表位移幅值明显增大,与各向同性介质的沉积谷地相比,沉积谷介质的各向异性对地面运动的影响非常显著。

Solution to scattering of SH waves by a cylindrically orthotropic semi-cylindrical alluvial valley is given by using wave function expansion,and the effects of incident wave characteristics and orthotropy of alluvial valley on ground motion are investigated. The radial wave function in a cylindrically orthotropic alluvial valley satisfies the non-integer order Bessel equation under the incidence of steady-state SH waves. Numerical results show that the ground displacement amplitude of alluvial valley is closely related to incident waves frequency,incident waves direction,radial and circumferential shear modulus ratio of alluvial valley,and shear velocity and density ratio between half-space and alluvial valley. When alluvial valley is softer than half-space,the ground displacement amplitude of alluvial valley increases significantly. Meanwhile,the influence is more obvious on orthotropy of alluvial valley compared with isotropic one.