Approximate Transient Solutions for the Coupled Equations of Thermoelasticity

Abstract

The propagation of mechanical and thermal disturbances studied according to the coupled thermoelastic theory. In the formulation of the coupled theory of thermoelasticity, the heat-conduction equation contains the time derivative of the dilatation as a source term. In the procedure introduced here, that term is replaced by one representing the time derivative of the dilatation at the wavefront only. In this way, the equations governing the mechanical and thermal effects are formally uncoupled, and thus are easier to solve; at the same time, it is shown that most of the coupling effect is retained. To check the approximation procedure, two one-dimensional problems are considered. The solutions for these problems show excellent agreement with known exact solutions. The approximation is then applied to the three-dimensional problem of the suddenly applied force in the infinite medium. Curves for the displacement and temperature distributions are provided for this case. The temperature distribution shows a discontinuity that moves with the wavefront of the dilatational wave.