Numerical Analysis of Generalized Thermoelastic Problems by the Method of Characteristics

At present two theories for the generalized thermoelastic problems are presented. The first theory proposed by Lord and Shulman (L-S theory) admits only one relaxation time: a relaxation time τ that modifies the classical Fourier law. The second one due to Green and Lindsay (G-L theory) involves two relaxation times in a thermoelastic process: a relaxation time τ0 modifies the classical energy equation and another relaxation time τ1 changes the Duhamel-Neumann's constitutive relations. This paper is concerned with the thermal and mechanical waves in an infinite plate subjected to impulsive heating on the surface of the plate. The formulation of the problems is based on the G-L theory and the solution are obtained by the method of characteristics. The numerical results are compared with the existing results obtained by the L-S theory. The influence of relaxation times of G-L theory on the thermal and mechanical waves are examined numerically, and the results are shown in figures.