A new method to obtain 3-D Green's functions for anisotropic solids

C. Y. Wang*, Jan Drewes Achenbach

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

Three-dimensional time-domain elastodynamic basic singular solutions for anisotropic solids have been obtained in relatively simple form by the use of the Radon transform. The procedure is introduced by an application to the simple case of the 3-D scalar wave equation. For general anisotropic solids the Radon transform reduces the set of 3-D hyperbolic partial differential equations to a set of 1-D hyperbolic pde's. The 1-D equations are solved by an eigenvalue decomposition, and the 3-D solution is subsequently expressed as an inversion integral, in the form of an integral over a unit sphere. For general anisotropic materials the integral can be evaluated numerically in a relatively simple manner. Radiated fields are presented for transversely isotropic materials such as ice and graphite epoxy fiber-reinforced composites.

Original languageEnglish (US)
Pages (from-to)273-289
Number of pages17
JournalWave Motion
Volume18
Issue number3
DOIs
StatePublished - Jan 1 1993

ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics

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