Asymmetric motion of a transversely isotropic thermoelastic half-space under time-harmonic buried source

Abstract

With the aid of complete representations in terms of two scalar potential functions, the governing equations of coupled thermoelasticity are uncoupled into a sixth- and second-order partial differential equations in cylindrical coordinate system, which are solved by virtue of Fourier series expansion and Hankel integral transforms. Utilizing the transformed stresses-, displacements- and temperature-potential functions relationships, these functions are derived and represented in terms of improper line integrals. The general solutions are changed for point and circular patch load and heat flux Green’s functions in order to derive the related displacement and temperature Green’s functions. Some numerical evaluations of Greens functions are represented to portray the dependency of response on thermo-mechanical coupling as well as the anisotropy of the medium.