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 $(2300–150100\mathrm{Ns}∕{\mathrm{m}}^4)$ , 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.

In this letter, the low and high frequency limits of the effective density characterizing a limp frame porous medium are investigated. These theoretical limits are compared to the ones found for a classical rigid frame porous medium, and to experimental measurements. While the high frequency asymptotic behaviors of both limp and rigid effective densities are usually only slightly different, their low frequency behaviors are significantly different. Compared to experimental measurements performed on a limp frame fibrous layer, only the limp frame effective density yields good correlations over the whole frequency range.

This study examines the acoustic properties of materials with complex micro-geometry containing partially open or dead-end (DE) porosity. One of these kinds of materials can be obtained from dissolving salt grains embedded in a solid metal matrix with the help of water. The solid matrix is obtained after the metal, in liquid form, has invaded the granular material formed by the salt particles at negative pressure and high temperature, and after cooling and solidification of the metal. Comparisons between theoretical and experimental results show that the classical Johnson-Champoux-Allard model does not quite accurately predict the acoustic behavior. These results suggest that the assumptions of the Biot theory may not all be fulfilled and that cavity resonators and dead ends can be present in the material. The first part of the study proposes a simple model to account for this geometry. Based upon this model, two acoustic transfer matrices are developed: one for non-symmetric and one for symmetric dead-end porous elements. It is thought that this model can be used to study the acoustic absorption and sound transmission properties of the type of material previously described. In the second part, a series of simplified samples are proposed and tested with a three-microphone impedance tube to validate the exposed model. Finally, the third part compares the predictions of the exposed model to the impedance tube results on a real aluminum foam sample containing dead-end pores. These first results are encouraging and show that this simple model also provides a good prediction for these materials with more complicated microstructure.

A simple equivalent fluid model is proposed to describe the acoustic behavior of post-consumer and post-industrial recycled fibers otherwise known as Shoddies. The model requires knowledge of the bulk density only, a parameter that is easily measured. Characterization testing was completed on nine Shoddy fiber constructions processed by one of three different methods: thermal bonding, resin bonding, and mechanical bonding. The parameters measured directly were bulk density, open porosity, tortuosity, static airflow resistivity, and normal incidence sound absorption. The materials’ viscous and thermal characteristic lengths and static thermal permeability are determined using indirect acoustical techniques. Empirical relationships linking the material parameters to the bulk density are then substituted into several popular equivalent fluid models. The most accurate ‘simplified’ model is selected by comparing each model’s ability to accurately predict the materials’ acoustic behavior using normal incidence sound absorption to assess performance. The present work is of interest to sound engineers in predicting the acoustic performance of Shoddy-based absorbers.

The purpose of this research is to determine whether the acoustic properties of polydisperse fibrous medium (PDFM) and bidisperse fibrous medium (BDFM) can be modeled by monodisperse fiber media (MDFM) with an effective fiber diameter. Multi-scale numerical simulations on representative elementary volumes of these media are performed to retrieve the transport and geometrical properties governing their acoustic properties. Results show no significant difference between predictions obtained by PDFM or BDFM, and their corresponding effective MDFM.