Normalized inverse characterization of sound absorbing rigid porous media

Abstract

This paper presents a methodology for the inverse characterization of sound absorbing rigid porous media, based on standard measurements of the surface acoustic impedance of a porous sample. The model parameters need to be normalized to have a robust identification procedure which fits the model-predicted impedance curves with the measured ones. Such a normalization provides a substitute set of dimensionless (normalized) parameters unambiguously related to the original model parameters. Moreover, two scaling frequencies are introduced, however, they are not additional parameters and for different, yet reasonable, assumptions of their values, the identification procedure should eventually lead to the same solution. The proposed identification technique uses measured and computed impedance curves for a porous sample not only in the standard configuration, that is, set to the rigid termination piston in an impedance tube, but also with air gaps of known thicknesses between the sample and the piston. Therefore, all necessary analytical formulas for sound propagation in double-layered media are provided. The methodology is illustrated by one numerical test and by two examples based on the experimental measurements of the acoustic impedance and absorption of porous ceramic samples of different thicknesses and a sample of polyurethane foam.

Bayesian inference for the ultrasonic characterization of rigid porous materials using reflected waves by the first interface

“…Different inverse problems for parameter identifications have been attempted in the past regarding air-saturated porous media, mostly in the audio frequency regime [10,11,12,13,14]. The largest unaddressed issues of these studies are the modeling deficiency at these frequencies and the scarcity of uncertainty considerations.…”

How Do Acoustic Materials Work?

“…The relationship between the acoustic impedances does not only have to do with the modification of the amplitude of the incident wave: it is also related to the fraction of the incident energy that will be reflected or transmitted. Most of the acoustic properties of materials can be studied by the application of new laboratory and numerical methods as ultrasonic characterization [4], inverse characterization with basis on the acoustic impedance measurement [5], or ensemble averaged scattering [6].…”

Acoustical modeling and Bayesian inference for rigid porous media in the low-mid frequency regime

“…It suffices to invoke the general property that, because of the divergence-free nature of the fluid flow, the functions k 0 app (ω) and α 0 app (ω) necessarily are strictly decreasing functions of frequency: d dω k 0 app (ω) < 0 and d dω α 0 app (ω) < 0. Indeed, these are the inequalities (18) in Ref. [28], where the theory of asymptotic homogenization at two scales was used to derive the condition of incompressibility.…”

“…This model was later used in [17], where an inverse scattering problem was solved in the time domain to obtain both the static thermal permeability k 0 and the static viscous tortuosity α 0 simultaneously, using transmitted waves in the low-frequency range. Based on measurements of the surface impedance of a porous sample backed by different air gaps, the method developed by Zieliński [18] allowed the simultaneous retrieval of the 6 parameters of the Johnson-Champoux-Allard-Lafarge [4,19,7] JCAL model (φ, α ∞ , k 0 , Λ, Λ and k 0 ), using impedance tube experiments, in the frequency domain.…”