Application of the Reciprocity Theorem to Analyze Ultrasound Generated by High-Intensity Surface Heating of Elastic Bodies

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 th...

Full description

Saved in:
Bibliographic Details
Published in:Journal of thermal stresses 2007-07, Vol.30 (8), p.841-853
Main Author: Achenbach, Jan D.
Format: Article
Language:English
Subjects:
Boundary heating
Elastic solid
Lamb waves
Reciprocity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0149-5739
1521-074X
DOI:10.1080/01495730701462782