Experimental characterization of the effective acoustic properties of anisotropic porous materials via free-field measurements

Porous media are commonly described as effective isotropic fluid materials, such that their acoustic properties can be adequately determined from their bulk modulus and dynamic density. Most acoustic absorbents, however, possess a marked anisotropy, which influences their acoustical behavior and the parameters necessary to deduce it. Specifically, the influence of anisotropy translates into a full symmetric density tensor (in place of a scalar). This study presents a method for retrieving the bulk modulus and all six components of the density tensor of a layer of porous material from reflection coefficients measured in free field with an array of microphones. The procedure consists in expressing the sound field measured in the vicinity of the layer as a superposition of plane waves, from which the surface impedance and the reflection coefficient are reconstructed. The reflection properties, as well as the pressure at the rigid backing interface, are estimated for various source positions (i.e., various angles of incidence) and an inverse problem is formulated to infer the effective fluid parameters. The validity of the method is examined experimentally on a manufactured porous material, and the resulting fluid parameters compared with experimental results obtained from reflection and transmission coefficients measured in an impedance tube.