Dynamic Green's Functions of an Axisymmetric Thermoelastic Half-Space by a Method of Potentials

Abstract

With the aid of a new complete scalar potential function, an analytical formulation for thermoelastic Green's functions of an axisymmetric linear elastic isotropic half-space is presented within the theory of Biot's coupled thermoelasticity. By using the potential function, the governing equations of coupled thermoelasticity are uncoupled into a sixth-order partial differential equation in a cylindrical coordinate system. Then, by using Hankel integral transforms to suppress the radial variable, a sixth-order ordinary differential equation is received. By solving this equation and considering boundary conditions, displacements, stresses, and temperature are derived in the Hankel integral transformed domain. By applying the theorem of inverse Hankel transforms, the solution is obtained generally for arbitrary surface time-harmonic traction and heat distribution. Subsequently, point-load Green's functions for the displacements, temperature, and stresses are given in the form of some improper line integrals. For more investigations, the solutions are also determined analytically for uniform patch-load and patch-heat distributed on the surface. For validation, it is shown that the derived solutions could be degenerated to elastodynamic and quasi-static thermoelastic cases reported in the literature. Numerical evaluations of improper integrals, which have some branch points and pole, are carried out using a suitable quadrature scheme by