Wave propagation in materials with double porosity

Abstract

This paper is dedicated to propagation of waves with assigned length in a model describing the evolutionary behavior of materials with double porosity. Basic equations are considered for an isotropic and homogeneous material which occupies the entire three dimensional space. Wave solutions with assigned wavelength are sought. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system. There also exist other three longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes due to presence of pore system. The dispersion relation is explicitly established like a quartic equation and it is shown that it could allow negative real roots, thus explaining the existence of standing waves. A numerical analysis indicates that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elasticity theory. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established.