On the wave propagation in the time differential dual-phase-lag thermoelastic model

We study the propagation of plane time harmonic waves in the infinite space filled by a time differential dual-phase-lag thermoelastic material. There are six possible basic waves travelling with distinct speeds, out of which, two are shear waves, and the remaining four are dilatational waves. The shear waves are found to be uncoupled, undamped in time and travels independently with the speed that is unaffected by the thermal effects. All the other possible four dilatational waves are found to be coupled, damped in time and dispersive due to the presence of thermal properties of the material. In fact, there is a damped in time longitudinal quasi-elastic wave whose amplitude decreases exponentially to zero when the time is going to infinity. There is also a quasi-thermal mode, like the classical purely thermal disturbance, which is a standing wave decaying exponentially to zero when the time goes to infinity. Furthermore, there are two possible longitudinal quasi-thermal waves that are damped in time with different decreasing rates or there is one plane harmonic in time longitudinal thermal wave, depending on the values of the time delays. The surface wave problem is studied for a half space filled by a dual-phase-lag thermoelastic material. The surface of the half space is free of traction and it is free to exchange heat with the ambient medium. The dispersion relation is written in an explicit way and the secular equation is established. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.