Inhomogeneous wave propagation in porothermoelastic medium with dual-phase-lag heat conduction

We are examining a mathematical model incorporating a heat conduction dual-phase-lags (DPL) model. One may use this model to examine how thermoelastic waves behave in a porous thermoelastic material. A modified version of the Christoffel equations is extracted from the model to investigate the propagation of harmonic plane waves. We next solve these equations to get the complex velocities of waves in the medium. Four waves appear in the medium, and the equations explain their existence and propagation. We find the correlations between the displacements of solid and fluid particles and the wave-induced temperature in the medium. The study considers the case of inhomogeneous wave propagation, defined by a complex slowness vector specification with a finite non-dimensional parameter indicating the inhomogeneity degree. Each of the four attenuated waves propagating inhomogeneously through the porous aggregate has its phase velocities and attenuation coefficients determined. We calculate the velocities and attenuation of the compressional and shear waves using a numerical model of liquid-saturated sandstone. Their fluctuations with thermal and poroelastic parameters are depicted visually.