Thermoelastodynamic disturbances in a half-space under the action of a buried thermal/mechanical line source

The transient dynamic coupled!thermoelasticity problem of a half!space under the action of a buried thermal:mechanical source is analyzed here[ This situation aims primarily at modeling underground explosions and impulsively applied heat loadings near a boundary[ Also\ the present basic analysis may yield the necessary _eld quantities required to apply the Boundary Element Method in more complicated thermoelastodynamic problems involving half!plane domains[ A material response for the half!space pre! dicted by Biot|s thermoelasticity theory is assumed in an e}ort to give a formulation of the problem as general as possible "within the con_nes of a linear theory#[ The loading consists of a concentrated thermal source and a concentrated force "mechanical source# having arbitrary direction with respect to the half! plane surface[ Both thermal and mechanical line sources are situated at the same location in a _xed distance from the surface[ Plane!strain conditions are assumed to prevail[ Our problem can be viewed as a generalization of the classical Nakano Lapwood Garvin problem and its recent versions due to Payton "0857# and Tsai and Ma "0880#[ The initial:boundary value problem is attacked with one! and two!sided Laplace transforms to suppress\ respectively\ the time variable and the horizontal space variable[ A 8 8 system of linear equations arises in the double transformed domain and its exact solution is obtained by employing a program of symbolic manipulations[ From this solution the two!sided Laplace transform inversion is then obtained exactly through contour integration[ The one!sided Laplace transform inversion for the vertical displacement at the surface is obtained here asymptotically for long times and numerically for short times