Dispersion properties of porous media | Mekhanika | kompozitsionnykh | materialov i konstruktsii

Dispersion properties of porous media



In the article we investigate the dynamic properties of a porous medium, and establish a feature associated with the effect of “locking” i.e. with the effect of impermeability (filtration) for certain wavelengths in a porous medium. Investigation of the singularities of the propagation of longitudinal harmonic waves is carried out on the basis of the equations of motion obtained for a porous medium and the analysis of the dispersion equation. Dissipation of wave energy in the medium is not considered. The study of the propagation of acoustic waves in a porous medium allows to develop an understanding of the processes that arise in inhomogeneous medias with defect fields. The porosity model is constructed as a particular case of the general model of Mindlin’s media with considering the fields of free deformations associated with defect fields, ie, with structural features of the material. In this paper, we present a variant of the applied theory of porous medias constructed as a special case of the theory of medias with conserved dislocations. It is given the variational mathematical formulation of the theory of porous medias which includes the determining equations, the equilibrium equations, and boundary conditions. For a generalized model of a porous medium, expressions for the densities of the potential and kinetic energy are written. The kinetic energy has a nonclassical form and is determined by an extended list of generalized variables of the model. It is shown that with a certain combination of characteristics of a porous medium, a “locking” effect occurs, in which the porous medium is a filter for a certain range of waves. It is established that to model this effect, it is necessary to involve a model of the medium which takes into account the evolution of defects- pores during deformation.