On the 3D Rayleigh wave field on an elastic half-space subject to tangential surface loads

Abstract

This study is concerned with analysis of the Rayleigh wave field in a 3D isotropic elastic half-space subject to in-plane surface loading. The approach relies on the slow time perturbation of the general representation for the Rayleigh wave eigensolutions in terms of harmonic functions. The resulting hyperbolic-elliptic formulation allows decomposition of the original vector problem of 3D elasticity into a sequence of scalar Dirichlet and Neumann problems for the Laplace equation. The boundary conditions for these are specified through a 2D hyperbolic equation. An example of an impulse tangential load illustrates the efficiency of the derived asymptotic formulation, with the results expressed in terms of elementary functions