Dispersion of Elastic Waves Propagating in a Fluid-Saturated Porous Medium with Cavities

The propagation of plane longitudinal waves in a fluid-saturated porous medium with cavities is considered in linear elastic approximation. It has been shown that as distinct from the classical porous medium (Biot's medium) where two longitudinal dispersionless waves can propagate (a fast wave and a slow wave), in the porous-cavity media three dispersive longitudinal waves propagate and one of them is solely induced due to cavities in the material. The study of waves is carried out by obtaining and analyzing the dispersion equation, phase velocity and group velocity. The frequency spectrum density is considered, which enables to identify the degree of dispersion expressiveness. At certain values of the system parameters some regions of strong and weak dispersion, regions of normal and anomalous dispersion have been identified.