Application of the reciprocity theorem to analyze ultrasound generated by high-intensity surface heating of elastic bodies

Jan D. Achenbach*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The global reciprocity theorem for thermo-anisotropic elastodynamics, which relates body forces, surface tractions, displacements, temperatures and strains of two solutions of the field equations, states A and B, by integrals over a volume V and its bounding surface S, is derived and discussed in this article. The difference between various anisotropies enters via the stress-temperature tensor, which is different for different cases of anisotropy. The reciprocity theorem is used to analyze the dynamic response to high-intensity heating of a small surface region. The particular example of line-focused laser-beam irradiation of one side of a homogeneous elastic plate is worked out in some detail. For the time-harmonic case, the amplitude of the lowest anti-symmetric mode is obtained in a simple and elegant manner by application of the reciprocity theorem, where the desired mode is state A and state B is taken as a free anti-symmetric mode. The amplitude of any anti-symmetric or symmetric mode can be obtained in an analogous manner, and an appropriate selection of modes can be used with Fourier superposition to obtain the transient response.

Original languageEnglish (US)
Pages (from-to)841-853
Number of pages13
JournalJournal of Thermal Stresses
Volume30
Issue number8
DOIs
StatePublished - Aug 2007

Keywords

  • Boundary heating
  • Elastic solid
  • Lamb waves
  • Reciprocity

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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