Another form of 3D Green’s function for an elastic solid with exponential inhomogeneity

Abstract

The 3D Green’s function for an elastic solid with exponential inhomogeneity has already been obtained by Martin et al. (Proc R Soc Lond A 458:1931–1947, 2002). But, their Green’s function is separated into grading and non-grading parts, and the grading part is in terms of infinite and double finite integrals. In order to obtain a more convenient form for numerical evaluation and for clear insight into physical meanings, the present paper reconsiders the Green’s function for an inhomogeneous elastic solid. Applying the Cauchy complex integral theorem to complex-valued Hankel inversion integrals, Green’s function is reduced to real-valued finite integrals, whose integrands are characterized by exponential decay, and has no singularity. It is thus more convenient for the numerical evaluation.