State space approach to generalized thermo-viscoelasticity with two relaxation times

The model of the equation of generalized thermo-viscoelasticity with two relaxation times is established. The state space formulation for thermo-viscoelasticity with two relaxation times is introduced. The formulation is valid for problems with or without heat sources. The resulting formulations together with the Laplace transform technique are applied to a variety of problems. The solutions to a thermal shock problem and to a problem of a layer media both without heat sources are obtained. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace-transforms. Numerical results are given and illustrated graphically for the problems considered. Comparisons are made with the results predicted by the coupled theory. (C) 2001 Elsevier Science Ltd. All rights reserved.