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

Published online by Cambridge University Press:  23 February 2010

Mario Durán ,
Eduardo Godoy  and
Jean-Claude Nédélec
Mario Durán
Affiliation:
Facultad de Ingeniería, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile. mduran@ing.puc.cl; egodoy@ing.puc.cl
Eduardo Godoy
Affiliation:
Facultad de Ingeniería, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile. mduran@ing.puc.cl; egodoy@ing.puc.cl
Jean-Claude Nédélec
Affiliation:
CMAP, École polytechnique, 91128 Palaiseau, France. nedelec@cmap.polytechnique.fr
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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. IIB334 (2006) 725–731].

Keywords

Green's functionhalf-planetime-harmonic elasticityimpedance boundary conditionsurface waves
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 4 , July 2010 , pp. 671 - 692
Copyright
© EDP Sciences, SMAI, 2010

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