Lord-Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermoelasticity

The model of the equations of generalized thermoelasticity based on Lord-Shulman theory in an isotropic elastic medium under the dependence of the modulus of elasticity on the reference temperature is established. The normal mode analysis is used to obtain the expressions for the temperature, the horizontal component of displacement, and thermal stress. The resulting formulation is applied to two different concrete problems. The first concerns the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The second deals with a thick plate subject to a time-dependent heat source on each face. Numerical results are illustrated graphically for each problem considered. Comparisons are made with the results obtained in the case of temperature independence of the modulus of elasticity.