Wave motion equation and the dynamic Green’s function for a transverse isotropic multilayered half-space

Abstract

A new formulation is presented here for harmonic wave motion in a transverse isotropic multilayered half-space. By means of a Fourier-Bessel transform, the complex partial differential equations of wave motion can be uncoupled into a pair of second order ordinary differential equations: one for SV-P vectorial waves (matrix size 2×2) and the other for SH scalar waves (matrix size 1×1). They have the same form as that for isotropic media. Thus, the same solution procedure as that for isotropic media is equally applicable to transverse isotropic media, which considerably simplifies the solution. Furthermore, by introducing a mixed variable formulation of the wave motion solution, the matrix form of Green’s function for various boundary conditions of stratified soil is analytically derived. Numerical examples of Green’s function and the dynamic foundation impedance demonstrate the accuracy and the efficiency of the proposed approach. The computation is unconditionally stable.