Equilibrium and dynamics of porous and cracked media

Abstract

Abstract We established equilibrium and motion equations for media with internal structure, characterized by integral geometry parameters. These equations are linear differential equations of the infinite order. Besides usual elastic waves, there are many waves with sufficiently lower velocities without bottom limit. Corresponding dispersion equations have both real and imaginary roots. Complex roots represent parametric resonances (catastrophes). This model of structured continuum describes intermediate states between statics and dynamics. It means that the equilibrium equations are valid for large scales, while the dynamic equations are valid in small ones.