Coupled thermoviscoelastodynamic Green's functions for bi-material half-space

By virtue of the representations of displacements, stresses, and temperature fields in terms of two scalar potential functions and the use of correspondence principle, an analytical derivation of fundamental Green's functions for bi-material half-space composed of a transversely isotropic thermo-elastic layer and an isotropic thermo-visco-elastic half-space affected by finite surface or interfacial sources is presented. With the aid of the potential function relationships, the coupled equations of motion and energy equation in both the half-space and the layer are uncoupled and solved with the aid of Fourier series and Hankel integral transforms. Responses of the medium are derived in the form of improper line integrals related to Hankel inversion transforms. To show the effects of anisotropy and viscoelasticity on the propagation of coupled thermoviscoelastic waves, the derived integrals for displacements, stresses, and temperature Green's functions are evaluated by a numerical scheme. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim