This article explores the applicability of numerical homogenization techniques for analyzing transport properties in real foam samples mostly open-cell, to understand long-wavelength acoustics of rigid-frame air-saturated porous media, on the basis of microstructural parameters. Experimental characterization of porosity and permeability of real foam samples are used to provide the scaling of a polyhedral unit-cell. The Stokes, Laplace, and diffusioncontrolled reaction equations are numerically solved in such media by a finite element method in three-dimensions; an estimation of the materials' transport parameters is derived from these solution fields. The frequency-dependent visco-inertial and thermal response functions governing the long-wavelength acoustic wave propagation in rigid-frame porous materials are then determined from generic approximate but robust models and compared to standing wave tube measurements. With no adjustable constant, the predicted quantities were found to be in acceptable agreement with multi-scale experimental data, and further analyzed in light of scanning electron micrograph observations and critical path considerations.

An experimental method to estimate the acoustical parameters of perforated facings used for noise control applications is proposed. These perforating facings (also called screens) can be woven or non-woven fabrics or even micro-perforated plates (MPP). Following the work by Atalla and Sgard [J. Sound Vib. 303, 195-208 (2007)], the perforated facings are modeled as porous media composed with identical cylindrical perforations of circular cross-section. The acoustical parameters characterized with the proposed method are the radius of the perforations and the perforation rate (also named the open-porosity). These parameters are obtained from analytical expressions and a single measurement of the normal acoustic surface impedance of the perforated facing backed by an air cavity in a standing wave tube. The value of the static air flow resistivity can also be recovered with no additional assumption or measurement. In the case of a facing that contains perforations of an arbitrary shape, the radius parameter should be understood as a characteristic length of the visco-inertial dissipative effects. Results for two characterization examples (a low porosity screen and a high porosity one) are presented and discussed. Values of the estimated static air flow resistivity are compared with the results from direct measurements. Values of the predicted sound absorption coefficients are compared to the measured ones.

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.

Based on a modified equivalent fluid model, the present work proposes a composite model which analytically includes the shape of the inclusions, whether they are porous or not. This model enables to describe the acoustic behavior of a large range of media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible permeability interactions between the substrate material and the inclusions are accounted for.