Three-dimensional thermoelastic wave motions in a half-space under the action of a buried source

Abstract

Abstract A three-dimensional (3D) transient dynamic problem within Biot’s coupled thermoelastic theory is studied in this paper. It involves a half-space acted upon by a thermal and mechanical buried point source. It is assumed that the half-space behaves like a coupled thermoelastic solid, whereas the loading consists of a concentrated heat flux (thermal source) and a concentrated force (mechanical source) of arbitrary direction with respect to the half-space surface. Both thermal and mechanical sources are situated at the same point in the interior of the half-space. The problem aims at modeling both underground explosions and impulsively applied heat loadings near a boundary. In addition, the present solution provides the necessary Green’s function which can be employed in the boundary element method for numerical treatment of more complicated transient thermoelastodynamic problems involving half-space geometries (e.g. domains with openings or contact problems). The situation studied here is the 3D analogue of a recent plane-strain problem considered by Georgiadis et al. (1999a) . It can also be viewed as a generalization of the classical buried-force elastodynamic problem of Pekeris (1955) in the sense that more complicated material behavior and loading are considered. The associated initial/boundary value problem is treated via unilateral and double bilateral Laplace transforms, which suppress, respectively, the time variable and two of the space variables. A 12×12 system of linear equations arises in the multiple transform domain and its exact solution is obtained by employing mathematica TM. From this solution, results for the vertical displacement at the surface due to a buried thermal source are obtained through numerical wave number integrations and numerical unilateral Laplace-transform inversions.