Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition

¹ Facultad de Ingeniería, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile. mduran@ing.puc.cl; egodoy@ing.puc.cl
² CMAP, École polytechnique, 91128 Palaiseau, France. nedelec@cmap.polytechnique.fr

Received: 10 June 2008
Revised: 18 June 2009

Abstract

This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math. 107 (2007) 295–314; IMA J. Appl. Math. 71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important advantage because the obtention of explicit expressions for the surface waves. We show, in addition to the usual Rayleigh wave, another surface wave appearing in some special cases. Numerical results are given to illustrate that. This is an extended and detailed version of the previous article by Durán et al. [C. R. Acad. Sci. Paris, Ser. IIB 334 (2006) 725–731].