The model of the equations of generalized thermoelasticity in a semi-conducting medium with two-temperature is established. The entire elastic medium is rotated with a uniform angular velocity. The formulation is applied under Lord-Schulman theory with one relaxation time. The normal mode analysis is used to obtain the expressions for the considered variables. Also some particular cases are discussed in the context of the problem. Numerical results for the considered variables are obtained and illustrated graphically. Comparisons are also made with the results predicted in the absence and presence of rotation as well as two-temperature parameter.

The theory of generalized two-temperature thermoelasticity is used to solve the boundary value problems between two elastic media with two different types of temprature under the influence of gravity.The classical dynamical coupled theory and Lord-Şhulman theory are used to obtain the general solution of the governing equations and investigate the effect of surface waves in an isotropic elastic medium subjected to gravity field. The harmonic vibrations method is used to obtain the displacement components, stress tensor and temperature distribution in the considerd physical domain with comparison with the two theories. The obtained analytic solution of the problem is applied for special cases for which the effect of two temperatures is studied. The conductive and dynamical temperatures as well as stress and strain components are shown graphically for a suitable material. Some comparisons are also introduced in the absence and in the presence of gravity, and two-temperature parameter. The differences in the obtained results between the two theories are considered.