Acoustic characterization of graded porous materials under the rigid frame approximation

Abstract

Graded porous materials are of growing interest because of their ability to improve the impedance matching between air and material itself. Theoretical models have been developed to predict the acoustical properties of these media. Traditionally, graded materials have been manufactured by stacking a discrete number of homogeneous porous layers with different pore microstructure. More recently, a novel foaming process for the manufacturing of porous materials with continuous pore stratification has been developed. This paper reports on the application of the numerical procedure proposed by De Ryck to invert the parameters of the pore size distribution from the impedance tube measurements for materials with continuously stratified pore microstructure. Specifically, this reconstruction procedure has been successfully applied to retrieve the flow resistivity and tortuosity profiles of graded porous materials manufactured with the method proposed by Mahasaranon et al. In this work, the porosity and standard deviation in pore size are assumed constant and measured using methods, which are applied routinely for homogeneous materials characterization. The numerical method is based on the wave splitting together with the transmission Green's functions approach, yielding an analytical expression of the objective function in the least-square sense. The objective function is constructed to minimize the discrepancy between the predicted and measured reflection coefficient spectra.