Standing torsional waves in a fully saturated, porous, circular cylinder

For dynamic measurement of the elastic moduli of a porous material saturated with viscous fluid using the resonance-bar technique, one also observes attenuation. In this article we have carried out the solution of the boundary-value problem associated with standing torsional oscillations of a finite, poroelastic, circular cylinder cast in the framework of volume-averaged theory of poroelasticity. Analysing this solution by eigenvalue perturbation approach we are able to develop expressions for torsional resonance and temporal attenuation frequencies in which the dependence upon the material properties are transparent. It shows how the attenuation is controlled by the permeability and the fluid properties, and how the resonance frequency drops over its value for the dry solid-frame due to the drag effect of fluid mass. Based upon this work we have a firm basis to determine solid-frame shear modulus, permeability, and tortuosity factor from torsional oscillation experiments.