Equations of anisotropic elastodynamics as a symmetric hyperbolic system: Deriving the time-dependent fundamental solution

Yakhno V. G., Yaslan H. C.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.235, no.16, pp.4802-4815, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 235 Issue: 16
  • Publication Date: 2011
  • Doi Number: 10.1016/j.cam.2010.10.048
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4802-4815
  • Keywords: Anisotropic elasticity, Dynamic system, Fundamental solution, Wave simulation, GREENS-FUNCTIONS, WAVE-PROPAGATION, DYNAMIC-SYSTEM, ELASTIC-WAVES, HALF-SPACE, SOLIDS, MEDIA, SURFACE
  • Dokuz Eylül University Affiliated: Yes

Abstract

The dynamic system of anisotropic elasticity from three second order partial differential equations is written in the form of the time-dependent first order symmetric hyperbolic system with respect to displacement velocity and stress components. A new method of deriving the time-dependent fundamental solution of the obtained system is suggested in this paper. This method consists of the following. The Fourier transform image of the fundamental solution with respect to a space variable is presented as a power series expansion relative to the Fourier parameters. Then explicit formulae for the coefficients of these power series are derived successively. Using these formulae the computer calculation of fundamental solution components (displacement velocity and stress components arising from pulse point forces) has been made for general anisotropic media (orthorhombic and monoclinic) and the simulation of elastic waves has been obtained. These computational examples confirm the robustness of the suggested method. (C) 2010 Elsevier B.V. All rights reserved.