An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification

Graded and Anisotropic Porous Materials for Broadband and Angular Maximal Acoustic Absorption

The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption.

Acoustic wave propagation in effective graded fully anisotropic fluid layers

This work deals with the sound wave propagation modeling in anisotropic and heterogeneous media. The considered scattering problem involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary along the layer depth. The specular transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism for the acoustic fields. This is solved using three different numerical techniques, namely, the transfer matrix method, Peano series, and transfer Green's function. These three methods are compared to demonstrate the convergence of the numerical solutions. Moreover, the implemented numerical procedures allow the authors to retrieve the internal acoustic fields and show their dependency along with the fluid anisotropic properties. Results are presented to illustrate the changes in absorption that can be achieved by tuning the fluid anisotropy as well as the variation of these properties across the depth of the layer. The results presented are in very good agreement across the different methods. Given that many porous materials can be modeled as equivalent fluids, the results presented show the potential offered by such numerical techniques, and can further give more insight into inhomogeneous anisotropic porous materials.

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials

Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

A mixture approach to the acoustic properties of a macroscopically inhomogeneous porous aluminum in the equivalent fluid approximation

The acoustic properties of an air-saturated macroscopically inhomogeneous aluminum foam in the equivalent fluid approximation are studied. A reference sample built by forcing a highly compressible melamine foam with conical shape inside a constant diameter rigid tube is studied first. In this process, a radial compression varying with depth is applied. With the help of an assumption on the compressed pore geometry, properties of the reference sample can be modelled everywhere in the thickness and it is possible to use the classical transfer matrix method as theoretical reference. In the mixture approach, the material is viewed as a mixture of two known materials placed in a patchwork configuration and with proportions of each varying with depth. The properties are derived from the use of a mixing law. For the reference sample, the classical transfer matrix method is used to validate the experimental results. These results are used to validate the mixture approach. The mixture approach is then used to characterize a porous aluminium for which only the properties of the external faces are known. A porosity profile is needed and is obtained from the simulated annealing optimization process.