Bruno Brouard

Effects of compression on the sound absorption of fibrous materials

Abstract During the compression of a fibrous mat, it is well known that the absorption properties are decreasing. In order to predict this change, some heuristic formulae are proposed which take into account the modifications of the physical parameters (porosity, resistivity, tortuosity and shape factors) which enter the standard “equivalent fluid” model. Numerical predictions are then discussed and compared to experimental data obtained on a fibrous material (uncompressed and then compressed) used in the automotive industry.

Frame decoupling at low frequency in thin porous layers saturated by air

According to the Biot theory and other models of propagation, two compressional waves can propagate in a porous medium saturated by air. At low frequencies each wave creates displacements of the same order of magnitude in the fluid and the frame. It is shown that for the case of thin materials bonded onto a rigid impervious backing, at low frequencies the acoustic field can nevertheless be described by only one wave which propagates in the air. This simple description is related to a mixing of both compressional waves which leaves the frame motionless.

Characteristic dimensions and prediction at high frequencies of the surface impedance of porous layers

The surface acoustic impedance of a glass wool and a reticulated foam is measured in a free field up to 20 000 Hz. The characteristic dimensions Λ and Λ’ can be calculated for the glass wool, and the surface impedance can be predicted with no adjustable parameters. The motion of the frame is not taken into account. The agreement between measurement and prediction is good. For the foam, the characteristic dimensions cannot be calculated, because the geometry of the frame is not simple. A correct choice of Λ and Λ’ allows a precise prediction of the surface impedance for a large range of frequencies and different thicknesses.

Enhanced Biot's Finite Element Displacement Formulation for Porous Materials and Original Resolution Methods Based on Normal Modes

The use of finite element modeling for porous sound absorbing materials is often limited by the numerical cost of the resolution scheme. To overcome this limitation, an alternative finite element formulation for poroelastic materials modelled with the Biot-Allard theory is first presented. This formulation is based on the solid and total displacement fields of the porous medium. Three resolution methods (one semi-analytical and two numerical) based on normal modes are proposed secondly. These methods take benefit from the decoupling properties of normal modes. The semi-analytical method is associated with problems in which the shear wave can be neglected. The numerical methods are a direct and an iterative scheme. The direct method allows a reduction by 2 of the number of degrees without making any approximation. The iterative method provides an approximation corresponding to a controlled tolerance. The finite element formulation is validated by comparison with an analytical model in two mono-dimensional configurations corresponding to a single and a multilayered problem. The efficiency of the two numerical resolution methods is also illustrated in term of computation time in comparison with classical formulations, such as the mixed displacement-pressure formulation.

Measurement and prediction of the reflection coefficient of porous layers at oblique incidence and for inhomogeneous waves

Near‐field acoustical holography (NAH) is used in the present work to measure the reflection coefficient of porous layers from normal to grazing incidence and for inhomogeneous waves. Measurements are compared with predictions obtained from a recent model. A lateral propagating mode inside the porous layer is evident.

Reciprocity and antireciprocity in sound transmission through layered materials including elastic and porous media

Abstract Sound transmission through elastic solids and porous media having an elastic frame involves longitudinal and transverse waves. A modelling of sound propagation through layers of these media by transfer matrices, which is equivalent to a representation by analogous multi-port circuits was performed previously. The different ports of the circuits are related to the normal and the tangential strains and velocities on the two faces of the layers. The use of impedance matrices instead of transfer matrices shows that the coupling between the normal and the tangential conjugate variables is antireciprocal, and is reciprocal for conjugate variables having the same nature. Moreover, it can be proven that the transmission loss through strafied materials in contact with the same fluid on the and the rear face is the same in opposite directions of propagation.

A stable method to model the acoustic response of multilayered structures

A general approach to determine the acoustic reflection and transmission coefficients of multilayered panels is proposed in this paper. Contrary to the Transfer Matrix Method (TMM), this method does not become unstable for high frequencies or large layer thicknesses. This method is shown to be as general as the TMM and mathematically equivalent. Its principle is to consider a so called Information Vector which contains all the information necessary to deduce the State Vector through a Translation Matrix. The Information Vector is of reduced length compared to that of the State Vector and can be propagated in any layer without involving exponentially growing terms. In addition, this method enables the coupling between any type of physical media as far as proper boundary relations can be written. Moreover, the method does not lead to an enlargement of the systems’ size in the case of interfaces between media of different physical type. Finally, this method can be easily implemented in numerical codes. The method is validated on three cases classically encountered in acoustic problems. However, it is general enough to model any type of multilayered problems in any field of applied physics.A general approach to determine the acoustic reflection and transmission coefficients of multilayered panels is proposed in this paper. Contrary to the Transfer Matrix Method (TMM), this method does not become unstable for high frequencies or large layer thicknesses. This method is shown to be as general as the TMM and mathematically equivalent. Its principle is to consider a so called Information Vector which contains all the information necessary to deduce the State Vector through a Translation Matrix. The Information Vector is of reduced length compared to that of the State Vector and can be propagated in any layer without involving exponentially growing terms. In addition, this method enables the coupling between any type of physical media as far as proper boundary relations can be written. Moreover, the method does not lead to an enlargement of the systems’ size in the case of interfaces between media of different physical type. Finally, this method can be easily implemented in numerical codes. The m...

Surface waves above honeycombs

The phase velocity of surface waves above honeycomb structures has been evaluated with the near-field holography method developed by Tamura [J. Acoust. Soc. Am. 88, 2259 (1990)]. A simple empirical expression is suggested to predict this velocity, by analogy with the case of comblike structures and layers with square cross-sectional shaped holes.

Enhancing rigid frame porous layer absorption with three-dimensional periodic irregularities

This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.

Excitation of soft porous frame resonances and evaluation of rigidity coefficients

Recent works have been performed concerning the guided elastic waves in soft porous elastic frames and the related normal displacement of the surface generated by a mechanical excitation. In this work, the mechanical excitation is replaced by a monopole acoustic field in air above the porous structure. Two cases are considered: a frame bonded on a rigid impervious layer and a free frame. The normal and the radial velocity induced by the monopole field at the surface of the frame is predicted with the Biot theory and the Sommerfeld representation of the monopole field. Measurements are performed with a laser vibrometer on a urethane foam. It is shown that the characterization of the excited modes can lead to an evaluation of the rigidity coefficients of the frames at acoustical frequencies.