Application of Reciprocity Relations to Laser-Based Ultrasonics

Abstract

An application of the global reciprocity theorem for thermo-anisotropic elastodynamics of inhomogeneous solids is discussed. The theorem 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. 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 of a half-space that is transversely isotropic and whose elastic moduli and mass density depend on the depth coordinate.