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

Mario Durán; Eduardo Godoy; Jean-Claude Nédélec

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 4, page 671-692
  • ISSN: 0764-583X

Abstract

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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].

How to cite

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Durán, Mario, Godoy, Eduardo, and Nédélec, Jean-Claude. "Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition." ESAIM: Mathematical Modelling and Numerical Analysis 44.4 (2010): 671-692. <http://eudml.org/doc/250769>.

@article{Durán2010,
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]. },
author = {Durán, Mario, Godoy, Eduardo, Nédélec, Jean-Claude},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Green's function; half-plane; time-harmonic elasticity; impedance boundary condition; surface waves},
language = {eng},
month = {6},
number = {4},
pages = {671-692},
publisher = {EDP Sciences},
title = {Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition},
url = {http://eudml.org/doc/250769},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Durán, Mario
AU - Godoy, Eduardo
AU - Nédélec, Jean-Claude
TI - Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/6//
PB - EDP Sciences
VL - 44
IS - 4
SP - 671
EP - 692
AB - 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].
LA - eng
KW - Green's function; half-plane; time-harmonic elasticity; impedance boundary condition; surface waves
UR - http://eudml.org/doc/250769
ER -

References

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