A mixture approach to the acoustic properties of a macroscopically inhomogeneous porous aluminum in the equivalent fluid approximation.

The acoustic properties of an air-saturated macroscopically inhomogeneous aluminum foam in the equivalent fluid approximation are studied. A reference sample built by forcing a highly compressible melamine foam with conical shape inside a constant diameter rigid tube is studied first. In this process, a radial compression varying with depth is applied. With the help of an assumption on the compressed pore geometry, properties of the reference sample can be modelled everywhere in the thickness and it is possible to use the classical transfer matrix method as theoretical reference. In the mixture approach, the material is viewed as a mixture of two known materials placed in a patchwork configuration and with proportions of each varying with depth. The properties are derived from the use of a mixing law. For the reference sample, the classical transfer matrix method is used to validate the experimental results. These results are used to validate the mixture approach. The mixture approach is then used to characterize a porous aluminium for which only the properties of the external faces are known. A porosity profile is needed and is obtained from the simulated annealing optimization process.

Acoustical properties of air-saturated porous material with periodically distributed dead-end pores.

A theoretical and numerical study of the sound propagation in air-saturated porous media with straight main pores bearing lateral cavities (dead-ends) is presented. The lateral cavities are located at "nodes" periodically spaced along each main pore. The effect of periodicity in the distribution of the lateral cavities is studied, and the low frequency limit valid for the closely spaced dead-ends is considered separately. It is shown that the absorption coefficient and transmission loss are influenced by the viscous and thermal losses in the main pores as well as their perforation rate. The presence of long or short dead-ends significantly alters the acoustical properties of the material and can increase significantly the absorption at low frequencies (a few hundred hertz). These depend strongly on the geometry (diameter and length) of the dead-ends, on their number per node, and on the periodicity along the propagation axis. These effects are primarily due to low sound speed in the main pores and to thermal losses in the dead-end pores. The model predictions are compared with experimental results. Possible designs of materials of a few cm thicknesses displaying enhanced low frequency absorption at a few hundred hertz are proposed.

Acoustics of porous materials with partially opened porosity.

A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont, Leclaire, Sicot, Gong, and Panneton [J. Appl. Phys. 110, 094903 (2011)]. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect are proposed. In particular, a model involving the average effective length of the dead-end pores is presented. It is also shown that if the dead-end effect can be treated separately, the transfer matrix method is particularly well suited for the description of single or multilayer systems with dead-end porosity.

Quantifying the through-thickness asymmetry of sound absorbing porous materials.

A method to quantify the through-thickness asymmetry of a sound absorbing porous material is proposed and discussed. Its calculation only requires impedance tube measurements of the acoustical surface impedance performed on both sides of the tested material. The method may be used for quality control or to assess the level of asymmetry of the material in terms of its acoustic properties. As a first validation, a two-layered porous system seen as an equivalent asymmetrical single porous layer with a sudden change in its physical properties is studied. From this study, a criterion of asymmetry is suggested and experimentally tested.

Elastic characterization of closed cell foams from impedance tube absorption tests.

A method is presented to determine the bulk elastic properties of isotropic elastic closed-cell foams from impedance tube sound absorption tests. For such foams, a resonant sound absorption is generally observed, where acoustic energy is transformed into mechanical vibration, which in turn is dissipated into heat due to structural damping. This article shows how the bulk Young's modulus, Poisson's ratio, and damping loss factor can be deduced from the resonant absorption. Also, an optimal damping loss factor yielding 100% of absorption at the first resonance is defined from the developed theory. The method is introduced for a sliding edge condition which is an ideal condition. Then, the method is extended to a bonded edge condition which is more easily achievable and additionally enables the identification of the Poisson's ratio. The method is experimentally tested on expanding closed-cell foams to find their elastic properties in both cases. Using the found properties, sound absorption predictions using an equivalent solid model with and without surface absorption are compared to measurements. Good correlations are obtained when considering surface absorption.