Recovery of Biot's transition frequency of air-saturated poroelastic media using vibroacoustic spectroscopy

Abstract

The transition frequency marks the passage from low-frequency viscosity dominated flow to high-frequency inertia dominated one in porous media. It was one of the principal characteristics predicted by Biot's theory. The transition frequency has been a theoretical concept for which only theoretical expressions have been developed in recent years. A vibroacoustic spectroscopy experimental method to recover the characteristic frequency (fC) and for gaining insight into the frequency response of fluid-saturated porous materials has been developed. Long thin air-saturated porous rods solicited mechanically are employed for the experiment. Changes in the fluid flow profile with excitation frequency results in relative motion between the skeleton and the saturating-fluid. This enhances the frictional viscous forces, which, in turn, increases damping of the skeletal motion. These transitions are signaled by observable cues in the acquired laser-vibrometry spectrum of the rods' longitudinal vibration mode patterns. The resonance peaks exhibit sudden attenuation (increase in damping) and are interrupted at the transition frequencies evoking a change of propagation medium. These patterns are compared with those of two plains, single phase material (viscoelastic) rods whose modes stand out as regularly spaced moderately damped peaks.