重力对具有表面层的半空间中Rayleigh波的影响

摘要

The propagation of Rayleigh wave in a half space supporting a layer under the influence of gravity field was investigated. It was assumed that both the layer and the half-space are homogeneous, isotropic and elastic solids. The dispersion equation of Rayleigh wave under the influence of gravity field was deduced based on the Biot's theory of initial stress and the dynamical equations, and the degenerated dispersion equation is in agreement with the corresponding equation when the gravity field is neglected. Then, the dispersion curves were obtained by means of numerical methods,and the influences of the Possion's ratio and the thickness of the layer were analysed. The results indicate that the Possion'sratio and the thickness of the layer have obvious effect on the dispersion curves.%重力对具有表面层的半空间中Rayleish波具有重要的影响,假设表面层和半空间均为均匀各向同性介质,首先利用考虑重力作用的运动方程得出了重力影响下具有表面层的半空间中Rayleigh波的弥散方程.该方程经退化后得出了不受重力作用时的弥散方程,且与忽略重力时得到的方程完全一致.然后利用数值方法得到了重力影响下的Rayleigh波弥散曲线,分析了泊松比和表面层的厚度的影响,结果表明泊松比和表面层的厚度对弥散曲线具有明显影响.