Three dimensional transient Green's functions in a thermoelastic transversely isotropic half‐space

AbstractA transversely isotropic thermoelastic half‐space in both mechanical and thermal points of view is considered as the domain of the initial boundary value problem involved in this paper. The governing partial differential equations of thermoelasticity in a cylindrical coordinate system are uncoupled with the aid of a complete set of displacement‐potential and temperature‐potential functions, which with the help of Fourier series decomposition and Hankel‐Laplace integral transforms, are reduced to ordinary differential equations in terms of depth. Then, the general solutions due to an arbitrary patch‐load and surface heat flux are investigated for the case of a point load varying with time as Heaviside step function and a point heat flux varying with time as Dirac delta function in order to compute the related Green's functions. The governing equations for the potential functions are in such a way that different longitudinal and transverse waves are recognized and the transport properties can be discovered from the governing equations. Some numerical illustrations are also presented to depict the dependency of response on the thermal properties as well as the anisotropy of the medium.