Propagation of longitudinal viscoelastic stress waves in a fluid saturated Voigt porous medium

Abstract

This paper is concerned with giving a simple mathematical model on the propagation of longitudinal stress waves in a Voigt viscoelastic porous media. This model is congruent with the Frankel-Biot theory and describes the differences between vibrations of solid and liquid parts of porous medium. Furthermore, this model shows that there is a critical value of frequency that depends on the relaxation coefficient, and by this critical frequency value, stress waves are divided into two low and high frequency ranges. It is also demonstrated that behavior of stress waves differs between these two different ranges. It is normally expected that increasing attenuation yields to decreased phase velocity, but contrary to our expectation, in the propagation of slow waves in the low frequency range, increasing attenuation leads to increased phase velocity. In the high frequency range this holds true regarding the propagation of both fast and slow waves. Keywords: Longitudinal stress waves, Voigt viscoelastic, Porous media, Low frequency wave, High frequency wave, Biot theory