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Recently, finite element models based on Biot's displacement (u,U) formulation for poroelastic materials have been extensively used to predict the acoustical and structural behavior of multilayer structures. These models while accurate lead to large frequency dependent matrices for three-dimensional problems necessitating important setup time, computer storage and solution time. In this paper, a novel exact mixed displacement pressure (u,p) formulation is presented. The formulation derives directly from Biot's poroelasticity equations. It has the form of a classical coupled fluid-structure problem involving the dynamic equations of the skeleton in vacuo and the equivalent fluid in the rigid skeleton limit. The governing (u,p) equations and their weak integral form are given together with the coupling conditions with acoustic media. The numerical implementation of the presented approach in a finite element code is discussed. Examples are presented to show the accuracy and effectiveness of the presented formulation.

The present paper proposes to investigate the links between the microstructure of polyurethane foams and their sound absorbing efficiency, and more specifically the effect of membranes closing the cells. This study is based on the complete characterization of 15 polyurethane foam with various cell sizes and reticulation rates (i.e., open pore content): (i) characterization of the microstructure properties (cell size C s , strut thickness t, reticulation rate R w …) from SEM pictures, (ii) characterization of nonacoustic parameters (porosity U, airflow resistivity r, tortuosity a 1 …) from direct and indirect methods. Existing analytical links between microstructure properties and nonacoustic parameters are first applied to fully reticulated materials. Then, they are improved empirically to account for the presence of the closed pore content. The proposed expressions associated to the Johnson-Champoux-Allard porous model allow a good estimation of the sound absorbing behavior of all polyurethane foams, fully reticulated or not. This paper also demonstrates the important effect of the presence of cell membranes: increase of the airflow resistivity, tortuosity, and the ratio between the thermal and viscous characteristic lengths while decreasing these two characteristic lengths. Thus, the sound absorption efficiency at low frequencies is improved but can be worsened in some higher frequency bands.

Recently Atalla et al. [J. Acoust. Soc. Am. 104, 1444–1452 (1998)] and Debergue et al. [J. Acoust. Soc. Am. 106, 2383–2390 (1999)] presented a weak integral formulation and the general boundary conditions for a mixed pressure-displacement version of the Biot’s poroelasticity equations. Finite element discretization was applied to the formulation to solve 3D vibro-acoustic problems involving elastic, acoustic, and poroelastic domains. In this letter, an enhancement of the weak integral formulation is proposed to facilitate its finite element implementation. It is shown that this formulation simplifies the assembly process of the poroelastic medium, the imposition of its boundary conditions, and its coupling with elastic and acoustic media.