Thermo-elastic interactions in an infinite elastic solid due to distributed time-dependent heat sources in generalized thermo-elasticity III

Abstract

The generalized theory of thermo-elasticity of Type III recently developed by Green and Naghdi is employed to study thermo-elastic interactions in a homogeneous isotropic unbounded solid having distributed instantaneous and continuous heat sources. The solutions are derived by using Laplace transform on time and then Fourier transform on space. It is found that the interactions consist of a wave travelling with the speed of dilatational wave and a diffusive part. The temperature and the deformation field are both continuous at the dilatational wave front while the stress field exhibits finite discontinuity at this location in case of instantaneous distributed heat sources. For continuous distributed heat sources, the thermal, deformation, and stress fields are however all continuous at the dilatational wave front. All the fields suffer exponential attenuation at the dilatational wave front and the attenuation is influenced by the thermo-elastic coupling and the thermal diffusivity of the medium. The results of the present analysis are compared to those derived by using other generalized thermo-elasticity theories such as L-S theory and G-L theory. The analysis reveals that G-N theory III eliminates some of the finite discontinuities and δ-function singularity in the deformation, temperature and stress fields derived by using other generalized thermo-elasticity theories in earlier investigations. Finally, numerical results applicable to a copper-like material are presented in order to illustrate the analytical result.