A 1D time-domain method for in-plane wave motions in a layered half-space

A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.