An alternative Biot's formulation for dissipative porous media with skeleton deformation

Abstract

This paper presents an alternative formulation of Biot's theory to account for the elastic frame effects in a porous medium in which the acoustical properties of the fluid phase are predicted with an equivalent fluid model. This approach was originally developed for a double porosity medium. In this paper, the alternative formulation is applied to predict the transmission loss and absorption coefficient in the case of a single layer fibrous material, a multi-layer system, vibrating perforated plates, and porous composite materials. In the proposed formulation the coupling coefficients in Biot's poroelasticity equations are expressed in terms of the dynamic volumic mass and dynamic bulk modulus. By doing so, the elastic properties of the material frame are considered independently from the properties of the fluid. This formulation is implemented in the form of a transfer matrix algorithm which is validated against experimental data on sound absorption and sound transmission which are obtained for a range of various sound excitations and material arrangements. It is shown that this approach is able to predict accurately the acoustical properties of vibrating perforated plates and porous composites. The proposed approach is sufficiently general to be implemented in a finite element method.