Abstract
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.
Highlights
In the context of acoustic wave propagation, porous structures are commonly employed for sound absorption [1,2,3]
Results of the optimization procedure are shown for different acoustic targets, in order to highlight the benefits of anisotropic and graded effective properties with respect to the isotropic and non-graded ones
We first display the results in the case of a single frequency, when the porous layer operates in its sub–wavelength regime, that is, when the wavelength of the incident wave was larger than the thickness of the porous material (λ = c0 / f > L)
Summary
In the context of acoustic wave propagation, porous structures are commonly employed for sound absorption [1,2,3]. As soon as the micro-structure is known, as for example in porous materials made of periodic arrangements of unit cells, the parameters of the Johnson–Champoux–Allard–Lafarge (JCAL) model can be efficiently computed by a two-scale asymptotic method These parameters are the open porosity, high-frequency limit of tortuosity, characteristic thermal and viscous lengths, and static thermal and viscous permeabilities. We use a database of 100 anisotropic unit cells, which links the JCAL parameters to the geometric ones, for every unit cell Starting from this set of homogenized anisotropic unit cells, variations of the geometry are introduced along the depth of the equivalent fluid layer, so as to achieve prescribed targets for the frequency and angular absorption.
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