The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media.

Recently Chazot et al. [J. Sound Vib. 332, 1918-1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

Acoustical and mechanical characterization of poroelastic materials using a Bayesian approach.

A characterization method of poroelastic materials saturated by air is described. This inverse method enables the evaluation of all the parameters with a simple measurement in a standing wave tube. Moreover, a Bayesian approach is used to return probabilistic data such as the maximum a posteriori and the confidence interval of each parameter. To get these data, it is necessary to define prior probability distributions on the parameters characterizing the studied material. This last point is very important to regularize the inverse problem of identification. In a first step, the direct problem formulation is presented. Then, the inverse characterization is developed and applied to simulated and experimental data.

Transmission loss of double panels filled with porogranular materials.

Sound transmission through hollow structures found its interest in several industrial domains such as building acoustics, automotive industry, and aeronautics. However, in practice, hollow structures are often filled with porous materials to improve acoustic properties without adding an excessive mass. Recently a lot of interest arises for granular materials of low density that can be an alternative to standard absorbing materials. This paper aims to predict vibro-acoustic behavior of double panels filled with porogranular materials by using the patch-mobility method recently published. Biot's theory is a basic tool for the description of porous material but is quite difficult to use in practice, mostly because of the solid phase characterization. The original simplified Biot's model (fluid-fluid model) for porogranular material permitting a considerable reduction in data necessary for calculation has been recently published. The aim of the present paper is to propose a model to predict sound transmission through a double panel filled with a porogranular material. The method is an extension of a previous paper to take into account the porogranular material through fluid-fluid Biot's model. After a global overview of the method, the case of a double panel filled with expanded polystyrene beads is studied and a comparison with measurements is realized.