# Acoustical estimation of macroscopic properties of poroelastic materials

#### Abstract

The acoustical properties of isotropic, elastic porous materials are now conventionally specified by a set of nine, frequency-independent macroscopic parameters: e.g., flow resistivity, tortuosity, viscous and thermal characteristic lengths, etc. When these properties are known, it is possible to predict the sound absorption performance of the material, for example, in arbitrary geometries. However, measuring all of the nine material properties by using individual experimental setups for each material property requires a significant investment in measurement equipment and effort. Conversely, it has become popular to infer the macroscopic parameters of porous materials by finding the set of parameters that results in an optimal match of sound absorption performance measurements and prediction. The software packages FOAM-X and COMET/TRIM, for example, offer inverse characterization features of this type. However, here it is shown that it may not be possible to represent large and small diameter samples of the same material as measured in standing wave tubes by using a single set of parameters. In practice, measurements in standing wave tubes can be significantly affected by sample edge effects, particularly gaps around the sample resulting from minor damage of the sample during cutting. It will be shown that the damage to the edge of a sample may cause a discrepancy between small and large tube results in the frequency range in which they would be expected to overlap. As a result, small and large tube results cannot be reproduced by using a single set of material properties in combination with a homogeneous finite element model. However, by allowing the sample edge to have different properties than the main body of the sample, i.e., by making the model inhomogeneous, it is possible to fit both large and small tube results simultaneously with a single set of parameters. This behavior may have implications regarding the estimation of poroelastic material properties by inverse method, e.g., by using the software packages FOAM-X or COMET/TRIM, since it is usually assumed that the material properties are homogeneous and that the acoustical data input to the parameter estimation procedure is unaffected by finite size sample effects: i.e., edge effects. ^ Even though the inverse characterization process is widely used to extract the poroelastic material properties, the research related to stability and optimization of the inverse characterization process has not receive a much attention. For example, all nine poroelastic material properties have individual effects on the acoustic performance of a porous material. However, it is hard to estimate what each material property contributes to the acoustical performance of porous material and what effect each of these material properties will have on the inverse characterization process. To gain a more concrete understanding of the inverse characterization process, singular value decomposition has been performed based on a linearized sensitivity matrix. Singular value decomposition is a widely used technique in various fields to identify principal components. How to check and improve the stability of the inverse process by using principal component analysis will also be discussed.^

#### Degree

Ph.D.

#### Advisors

J. Stuart Bolton, Purdue University.

#### Subject Area

Engineering, Mechanical

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