Computing Green's function of elasticity in a half-plane with impedance boundary condition
Loading...
Date
2006
Journal Title
Journal ISSN
Volume Title
Publisher
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Abstract
This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Duran et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate (G) over cap as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in R-2 (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. (c) 2006 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Description
Keywords
computational solid mechanics, spectral Green's function, seismology