The dependence of the modulus of elasticity on reference temperature in the theory of generalized thermoelastic diffusion with one relaxation time

In this paper,the model of the equations of generalized thermoelastic diffiusion for a homogeneous isotropic elastic halfspace under the dependence of the modulus of elasticityon the reference temperature is established. the modulus of elasticity is taken as a linearfunction of the reference temperature. the formulation is applied to the generalized thermoelasticity theory under the lord-shulman and the classical dynamical coupled theories.also the normal mode analysis is used to obtain the exact expressions for the displacement components temperature distribution and thermal stress.finally the variations of theconsidered variables are represented graphically and comparison is made with the resultspredicted by two theories and with the case where the modulus of elasticity is independentof temperature.