  We consider a linear system of differential equations describing a joint
motion of elastic porous body and fluid occupying porous space. The rigorous
justification, under various conditions imposed on physical parameters, is
fulfilled for homogenization procedures as the dimensionless size of the pores
tends to zero, while the porous body is geometrically periodic and a
characteristic time of processes is small enough. Such kind of models may
describe, for example, hydraulic fracturing or acoustic or seismic waves
propagation. As the results, we derive different types of homogenized equations
involving non-isotropic Stokes system for fluid velocity coupled with acoustic
equations for the solid component or different types of acoustic equations,
depending on ratios between physical parameters. The proofs are based on
Nguetseng's two-scale convergence method of homogenization in periodic
structures.
