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.

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.

The sound transmission performance of finite multilayer systems containing poroelastic materials is of utmost importance for noise control in automobiles, aircrafts, buildings, and several other engineering applications. Currently, the need for tools predicting the acoustical and structural behaviors of such structures is considerably increasing. In this paper, such a tool is presented. It is applied to the sound transmission loss through multilayer structures made from a combination of elastic, air, and poroelastic materials. The presented approach is based on a three-dimensional finite element model. It uses classical elastic and fluid elements to model the elastic and fluid media. For the poroelastic material, it uses a two-field displacement formulation derived from the Biot theory. Furthermore, it couples with a boundary element approach to account, when important, for fluid–structure coupling and to calculate the transmission loss through the multilayer structure. Numerical predictions of the transmission loss through a poroelastic material sandwiched between two finite elastic plates are presented for various configurations. It is shown that the unbonded/bonded configuration gives better transmission loss. Also, comparisons with laterally infinite double panels and with an equivalent fluid approach for the porous material are presented. It is shown that these two simplified models lead to erroneous predictions at low frequencies and for certain design configurations, respectively.

Analytical solutions are derived to extract from dynamic density the macroscopic parameters governing viscous dissipation of sound waves in open-cell porous media. While dynamic density is obtained from acoustical techniques, the analytical solutions are derived from the model describing this dynamic density. Here, semiphenomenological models by Johnson et al. and by Wilson are investigated. Assuming dynamic density, open porosity, and static airflow resistivity known, analytical solutions derived from the Johnson et al. model yield geometrical tortuosity and viscous characteristic dimension. For the Wilson model, only dynamic density needs to be known. In this case, analytical solutions yield-for the first time-Wilson's density parameter and vorticity-mode relaxation time. To alleviate constraints on the Johnson et al. model, an extrapolation approach is proposed to avoid prior knowledge of static resistivity. This approach may also be used to determine this latter parameter. The characterization methods are tested on three materials covering a wide range of static airflow resistivities (2300-150 100 Ns/m4), frame rigidities (soft and rigid), and pore geometries (cells and fibers). It is shown that the analytical solutions can be used to assess the validity of the descriptive models for a given material.

This paper presents a straightforward application of an indirect method based on a threemicrophone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements. Doutres et al.3