Waves in a Porous Viscoelastic Material Saturated with a Fluid

Abstract

The problem for a fluid-saturated porous viscoelastic material is a direct analogy of the problem for a saturated elastic material solved earlier. The material is theoretically described using Biot’s classical linear model. The system of coupled integro-differential equations for the displacements of the skeleton and fluid is derived using the Volterra principle and Rabotnov’s operator method. The propagation of linear elastic waves in a half-space subject to a short harmonic pulse of given frequency is studied. The problem is solved using the Laplace transform method. The analytical solution in the frequency domain is obtained taking into account the viscoelastic properties of the skeleton. The inverse transformation procedure is described in detail