3-dimensional moving load problems for elastic and coated elastic half-spaces

Abstract

This study deals with 3-dimensional analysis of a point load moving at a constant speed along the surface of elastic and coated elastic half-spaces. Formulation of the problems is based on the framework of an asymptotic hyperbolic-elliptic model for the wave field developed to extract the contribution of surface waves. The validity of the model is restricted to the range of speeds close to the surface Rayleigh wave speed for both problems. It is also assumed that for the coated half-space the thickness of the coating is small compared to a typical wavelength of the surface wave. First, the uncoated elastic half-space problem is considered and both sub and super-Rayleigh cases are studied. The surface solutions for both cases are obtained through the fundamental solution of the differential operators. Then these solutions are restored over the interior of the half-space by the means of Poisson's formula. Thus the steady-state near-field solutions are derived in terms of the elementary functions. Finally numerical computations based on the derived approximate formulae are presented. In the coated half-space problem the surface solutions are given in integral forms obtained through the use of integral transforms for sub and super-Rayleigh cases. Then the integral solutions of the perturbed wave equation describing wave propagation along the surface are derived with their far-field asymptotic expansion using the uniform stationary phase method. Finally, numerical comparisons of exact and asymptotic results are presented for both cases.