Dynamic Model of a Periodic Medium with Double Porosity

Abstract

The paper presents a unified mathematical approach for describing the dynamic stressstrain state of mechanical structures from heterogeneous materials possessing a double coupled system of pore channels filled with fluid. New dynamic equations describing the oscillations of poroelastic systems based on the developed model of a continuous medium with additional degrees of freedom in the form of various pressures of the components constituting the liquid phase of the material are obtained. The equations and the method of obtaining them have a greater degree of generalization than those encountered in the literature. Theoretical results can be used to study the propagation of vibrations in fractured geological rocks saturated with liquid, to develop technical systems of new structural materials with a porous structure, for the analysis of micro streams of fluid in the hierarchical system of microporous bone tissue.