General method to retrieve all effective acoustic properties of fully-anisotropic fluid materials in three dimensional space

TL;DR

This paper introduces a straightforward analytical method to accurately retrieve all effective acoustic parameters of fully-anisotropic fluid materials in three dimensions, facilitating their characterization and design.

Contribution

It presents a novel, closed-form inverse approach to determine the full density tensor and bulk modulus from six incident plane waves, applicable to complex anisotropic fluids.

Findings

Method accurately retrieves all seven parameters.

Robustness demonstrated on anisotropic fluid examples.

Applicable to materials with viscothermal losses.

Abstract

Anisotropic fluid materials are of growing interest with the development of metamaterials and transformation acoustics. In the general three-dimensional case, such materials are characterized by a bulk modulus and a full symmetric matrix of density. Here, a method is presented to retrieve the bulk modulus and all six components of the density matrix from a selected set of six incident plane waves impinging on a layer of the material. From the six components of the density tensor, the three principal directions and the three principal densities of the material are recovered. The approach relies on the analytical expression of the reflection and transmission coefficients derived from a state vector analysis. It results in simple, closed-form, and easily-implementable inverse relations for the material parameters. As an illustration, the case of sound propagation through an orthorhombic lattice of overlapping air-filled ellipsoids is considered, the effective complex and frequency-dependent bulk modulus and density matrix of which are derived from homogenization cell problems and account for viscothermal losses. The retrieval method is then applied to the homogenized layer and results bear testament to its robustness to extract accurately all seven material parameters. This makes possible the characterization and design of anisotropic fluid materials in three dimensions.