An in-depth investigation on plane harmonic waves under two-temperature thermoelasticity with two relaxation parameters

Abstract

The present work is concerned with an in-depth analysis of plane harmonic waves in a thermoelastic medium under two-temperature thermoelasticity with two relaxation parameters. After the mathematical formulation of the present problem, we obtain the dispersion relation solution of harmonic plane waves propagating in the medium. The transverse wave is observed to be not affected by the thermal field and the longitudinal wave is coupled with the thermal field. Hence, special attention is paid on two different modes of longitudinal plane wave. One is predominantly elastic and the other is predominantly thermal in nature. The asymptotic expressions for the phase velocity, specific loss and many other important wave characteristics are derived in the cases of very high- and low-frequency regions for both the elastic and thermal mode longitudinal waves. Numerical results of these wave components are obtained for the intermediate values of frequency and the results are illustrated graphically in order to verify the analytical results. On the basis of analytical and numerical results a thorough analysis of the effects of the thermal relaxation parameters on various wave characteristics is presented. A detailed comparison of the results in the context of the present model with the corresponding results of three other models is also provided and several findings regarding the prediction of the present model as compared to other models are highlighted. The present investigation brought out the effects of the second relaxation parameter and the two-temperature parameter on the propagation of a plane harmonic wave through the medium.