Wave propagation in porous thermoelasticity with two delay times

Plane time-harmonic waves with assigned wavelength are supposed to propagate in an infinite linear thermoelastic space: The thermodynamic response is framed into the time differential dual-phase-lag model, while the Cowin–Nunziato theory is used to depict the effect of porosity for the elastic part. We are able to show that it is possible to identify two shear waves, undamped in time and not affected by porosity and/or temperature, as well as four longitudinal waves (a quasi-elastic wave, a quasi-pore wave, a quasi-thermal mode, and a quasi-phase-lag thermal wave); the corresponding dispersion relation is presented like a seventh-degree algebraic equation. The numerical simulations and the graphs presented show the effects of the various elasto-porous-thermal couplings on the characteristics of the four longitudinal waves. The work has to be intended as evolution and, at the same time, as a point of synthesis with respect to similar previous studies which took into account, exclusively, or the double delay time or the presence of voids.