This article presents a numerical optimization procedure of continuous gradient porous layer properties to achieve perfect absorption under normal incidence. This design tool is applied on a graded porous medium composed of a periodic arrangement of ordered unit cells allowing one to link the effective acoustic properties to its geometry. The best microgeometry continuous gradient providing the optimal acoustic reflection and/or transmission is designed via a nonlinear conjugate gradient algorithm. The acoustic performances of the so-designed continuous graded material are discussed with respect to the optimized homogeneous, i.e., nongraded and monotonically graded material. The numerical results show a shifting of the perfect absorption peak to lower frequencies or a widening of the perfect absorption frequency range for graded materials when compared to uniform ones. The results are validated experimentally on 3D-printed samples, therefore, confirming the relevance of such a gradient along with the efficiency of the control of the entire design process.

This Letter reports a folded metaporous surface optimized to achieve sub-wavelength and broadband perfect absorption. Its unit cell is composed of four different helicoidal cavities filled by porous media, which are structured and quasi-isotropic micro-lattices with a variable lattice constant. The effective thickness and intrinsic losses of each helicoidal cavity can be adjusted independently by varying their macro- and micro-structures, namely, the number of revolution of the folded structure and the lattice constant of the micro-lattice. An analytical model predicting the physical properties of this metaporous surface is developed. The macro- and micro-structures are then jointly optimized for sub-wavelength broadband perfect absorption. Finally, the system is 3D printed and experimentally tested. The experimental results are found to be in good agreement with the theory and show an almost perfect absorption over a frequency range out of reach for the homogeneous constitutive porous medium and the only helicoidal cavities.

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.

Porous materials and metamaterials play a key role in sound absorbing and insulation solutions in acoustics. With the growing interest in additive manufacturing techniques, recent work has focused on the printing of porous and resonant structures for acoustic purposes. Usual metaporous surfaces/interfaces are generally built by periodically inserting resonant elements in an existing porous layer. This complex manufacturing process can be significantly simplified by using additive manufacturing techniques, which also eases the design and optimization of the metaporous surface. In this work, the acoustic properties of the metaporous surface are controlled by simple geometric parameters defining both the anisotropic porous layer and the shapes of the resonators. Hence, we focus on optimizing split-ring resonators embedded in a micro-treillis porous layer, which are built in a single part using additive manufacturing techniques. A finite-element method together with Bloch wave decomposition provides a numerical model used to predict the reflection and absorption coefficients under normal incidence. The geometric parameters of the anisotropic metaporous surface are then optimized by non-linear minimization techniques to maximize acoustic absorption. An optimal metaporous surface is 3D printed by fused-deposition modeling, and its acoustic properties are measured in an impedance tube. The measurements are in good agreement with the predicted optimal broadband absorption coefficient. This work demonstrates the benefits of additive manufacturing for designing metaporous acoustic surfaces.