Analytical Solution of Coupled Thermoelastic Axisymmetric Transient Waves in a Transversely Isotropic Half-Space

A half-space containing transversely isotropic thermoelastic material with a depth-wise axis of material symmetry is considered to be under the effects of axisymmetric transient surface thermal and forced excitations. With the use of a new scalar potential function, the coupled equations of motion and energy equation are uncoupled, and the governing equation for the potential function, is solved with the use of Hankel and Laplace integral transforms. As a result, the displacements and temperature are represented in the form of improper double integrals. The solutions are also investigated in detail for surface traction and thermal pulses varying with time as Heaviside step function. It is also shown that the derived solutions degenerate to the results given in the literature for isotropic materials. Some numerical evaluations for displacement and temperature functions for two different transversely isotropic materials with different degree of anisotropy are presented to portray the dependency of response on the thermal properties as well as the degree of anisotropy of the medium.