This paper proposes an alternative displacement formulation of Biot's linear model for poroelastic materials. Its advantage is a simplification of the formalism without making any additional assumptions. The main difference between the method proposed in this paper and the original one is the choice of the generalized coordinates. In the present approach, the generalized coordinates are chosen in order to simplify the expression of the strain energy, which is expressed as the sum of two decoupled terms. Hence, new equations of motion are obtained whose elastic forces are decoupled. The simplification of the formalism is extended to Biot and Willis thought experiments, and simpler expressions of the parameters of the three Biot waves are also provided. A rigorous derivation of equivalent and limp models is then proposed. It is finally shown that, for the particular case of sound-absorbing materials, additional simplifications of the formalism can be obtained.

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This paper studies the acoustical properties of hard-backed porous layers with periodically embedded air filled Helmholtz resonators. It is demonstrated that some enhancements in the acoustic absorption coefficient can be achieved in the viscous and inertial regimes at wavelengths much larger than the layer thickness. This enhancement is attributed to the excitation of two specific modes: Helmholtz resonance in the viscous regime and a trapped mode in the inertial regime. The enhancement in the absorption that is attributed to the Helmholtz resonance can be further improved when a small amount of porous material is removed from the resonator necks. In this way the frequency range in which these porous materials exhibit high values of the absorption coefficient can be extended by using Helmholtz resonators with a range of carefully tuned neck lengths.

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Backed Porous layer with inclusions 1 AbstractThe absorption properties of a metaporous material made of nonresonant simple shape three-dimensional inclusions (cube, cylinder, sphere, cone and torus) embedded in a rigidly backed rigid frame porous material is studied. A nearly total absorption can be obtained for a frequency lower than the quarter-wavelength resonance frequency due to the excitation of a trapped mode. To be correctly excited, this mode requires a filling fraction larger in the three-dimensions than in the two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At low frequencies, a cube is found to be the best purely convex inclusion shape to embed in a cubic unit cell, while the embedment of a sphere or a cone cannot lead to an optimal absorption for some porous materials. At fixed position of purely convex shape inclusion barycentre, the absorption coefficient only depends on and filling fraction and does not depend on the shape below the Bragg frequency arising from the interaction between the inclusion and its image with respect to the rigid backing. The influence of the angle of incidence is also shown. The results, in particular the excitation of the trapped mode, are validated experimentally in case of cubic inclusions.

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.

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 twon umerical) based on normal modes are proposed secondly.These methods takebenefitfrom 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 ad irect and an iterative scheme. The direct method allows ar eduction by 2o ft he number of degrees without making anya pproximation. The iterative method provides an approximation corresponding to acontrolled tolerance. The finite element formulation is validated by comparison with an analytical model in twom ono-dimensional configurations corresponding to as ingle and am ultilayered problem. The efficiencyo ft he twon umerical resolution methods is also illustrated in term of computation time in comparison with classical formulations, such as the mixed displacement-pressure formulation.

The measurement of acoustic material characteristics using a standard impedance tube method is generally limited to the plane wave regime below the tube cut-on frequency. This implies that the size of the tube and, consequently, the size of the material specimen must remain smaller than a half of the wavelength. This paper presents a method that enables the extension of the frequency range beyond the plane wave regime by at least a factor of 3, so that the size of the material specimen can be much larger than the wavelength. The proposed method is based on measuring of the sound pressure at different axial locations and applying the spatial Fourier transform. A normal mode decomposition approach is used together with an optimization algorithm to minimize the discrepancy between the measured and predicted sound pressure spectra. This allows the frequency and angle dependent reflection and absorption coefficients of the material specimen to be calculated in an extended frequency range. The method has been tested successfully on samples of melamine foam and wood fiber. The measured data are in close agreement with the predictions by the equivalent fluid model for the acoustical properties of porous media.