On the analysis of wave motions in a multi-layered solid
Abstract
A rigorous treatment of the singular visco-elastodynamic solutions for a semi-infinite multi-layered solid is presented. It is shown explicitly via an asymptotic analysis of the propagator matrices that the singular components of the dynamic Green’s functions, which are critical to the theoretical foundation of boundary integral equation methods, correspond fully to the static point-load solutions for an appropriate bi-material full-space. With the aid of the analytical expressions for the bi-material response, a computational formulation for the multi-layered Green’s functions is also developed where the integral representation of the solution is decomposed into a closed-form singular part and a residual component which is amenable to numerical contour integration. With the foregoing treatment, the multi-layered fundamental solutions can be accurately and efficiently evaluated for a wide range of material and geometric configurations, including the special cases of elastic strata and the source points at the interface between two layers. As an illustration, the performance of the method in simulating the exact solution for an elastic half-space with a linear wave velocity profile is demonstrated.