State-space approach to generalized thermoelasticity plane waves with two relaxation times under dependence of the modulus of elasticity on reference temperature

We construct a model of the two-dimensional equations of generalized thermoelasticity with two relaxation times in an isotropic elastic medium with the modulus of elasticity being dependent on the reference temperature. The method of the matrix exponential, which constitutes the basis of the state-space approach of modern theory, is applied to the nondimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate, varying exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison is made with the results predicted by the coupled theory and with the case where the modulus of elasticity is independent of temperature. PACS No.: 46.25.Hf