Learning acoustic responses from experiments: A multiscale-informed transfer learning approach.

A methodology to learn acoustical responses based on limited experimental datasets is presented. From a methodological standpoint, the approach involves a multiscale-informed encoder used to cast the learning task in a finite-dimensional setting. A neural network model mapping parameters of interest to the latent variables is then constructed and calibrated using transfer learning and knowledge gained from the multiscale surrogate. The relevance of the approach is assessed by considering the prediction of the sound absorption coefficient for randomly-packed rigid spherical beads of equal diameter. A two-microphone method is used in this context to measure the absorption coefficient on a set of configurations with various monodisperse particle diameters and sample thicknesses, and a hybrid numerical approach relying on the Johnson-Champoux-Allard-Pride-Lafarge model is deployed as the multiscale-based predictor. It is shown that the strategy allows for the relationship between the micro-/structural parameters and the experimental acoustic response to be well approximated, even if a small physical dataset (comprised of ten samples) is used for training. The methodology, therefore, enables the identification and validation of acoustical models under constraints related to data limitation and parametric dependence. It also paves the way for an efficient exploration of the parameter space for acoustical materials design.

Two-component versus three-component metasolids.

Analytic analysis and parametric investigation are employed to study and compare metamaterial properties of two types of composite metasolids. Metasolids are composed of either an elastic inclusion or a rigid core coated by an elastic material, embedded in a stiff matrix. For these types of materials, results related to cylindrical as well as spherical inclusions are presented. Such mono-inclusion two-component and bi-inclusion three-component metasolids have been previously known to exhibit negative mass density near local-resonance frequencies. Through a unified formulation, it is analytically shown how and why adding a rigid mass inside the elastic inclusion to make a bi-inclusion three-component material can dramatically change the homogenized property of the resultant inclusion and increase the tunability of the composite, particularly in terms of local-resonance frequencies and the associated metamaterial-effect frequency bandwidth. In this way, concerning distinctly sound and vibration insulation, a low-frequency metamaterial effect with larger bandwidth can be designed via an inverse problem using a simplified mass-spring model.

Effect of the three-dimensional microstructure on the sound absorption of foams: A parametric study.

The purpose of this work is to systematically study the effect of the throat and the pore sizes on the sound absorbing properties of open-cell foams. The three-dimensional idealized unit cell used in this work enables to mimic the acoustical macro-behavior of a large class of cellular solid foams. This study is carried out for a normal incidence and also for a diffuse field excitation, with a relatively large range of sample thicknesses. The transport and sound absorbing properties are numerically studied as a function of the throat size, the pore size, and the sample thickness. The resulting diagrams show the ranges of the specific throat sizes and pore sizes where the sound absorption grading is maximized due to the pore morphology as a function of the sample thickness, and how it correlates with the corresponding transport parameters. These charts demonstrate, together with typical examples, how the morphological characteristics of foam could be modified in order to increase the visco-thermal dissipation effects.

Effective fiber diameter for modeling the acoustic properties of polydisperse fiber networks.

The purpose of this research is to determine whether the acoustic properties of polydisperse fibrous medium (PDFM) and bidisperse fibrous medium (BDFM) can be modeled by monodisperse fiber media (MDFM) with an effective fiber diameter. Multi-scale numerical simulations on representative elementary volumes of these media are performed to retrieve the transport and geometrical properties governing their acoustic properties. Results show no significant difference between predictions obtained by PDFM or BDFM, and their corresponding effective MDFM.

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties.

The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc "fiber anisotropies" and "volume weighted average radii," used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the permeability and frequency-dependent sound absorption coefficient are successfully compared with permeability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.

Linear elastic properties derivation from microstructures representative of transport parameters.

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

A direct link between microstructure and acoustical macro-behavior of real double porosity foams.

The acoustical macro-behavior of mineral open-cell foam samples is modeled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres allowed to interpenetrate during the foaming process. Identification and sizing of the 3D-PUC is made from x-ray computed microtomography and manufacturing process information. In addition, the 3D-PUC used allows to account for two scales of porosity: The interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso-scales are calculated from first principles, and a hybrid micro-macro method is used to determine the frequency-dependent visco-thermal dissipation properties. Olny and Boutin found that the double porosity theory provides the visco-thermal coupling between the meso- and micro-scales [J. Acoust. Soc. Am. 114, 73-89 (2003)]. Finally, the results are successfully compared with experiments for two different mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behavior all along the multi-scale modeling process, without any adjusted parameter.

Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams.

Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed.

Bottom-up approach for microstructure optimization of sound absorbing materials.

Results from a numerical study examining micro-/macrorelations linking local geometry parameters to sound absorption properties are presented. For a hexagonal structure of solid fibers, the porosity phi, the thermal characteristic length Lambda('), the static viscous permeability k(0), the tortuosity alpha(infinity), the viscous characteristic length Lambda, and the sound absorption coefficient are computed. Numerical solutions of the steady Stokes and electrical equations are employed to provide k(0), alpha(infinity), and Lambda. Hybrid estimates based on direct numerical evaluation of phi, Lambda('), k(0), alpha(infinity), Lambda, and the analytical model derived by Johnson, Allard, and Champoux are used to relate varying (i) throat size, (ii) pore size, and (iii) fibers' cross-section shapes to the sound absorption spectrum. The result of this paper tends to demonstrate the important effect of throat size in the sound absorption level, cell size in the sound absorption frequency selectivity, and fibers' cross-section shape in the porous material weight reduction. In a hexagonal porous structure with solid fibers, the sound absorption level will tend to be maximized with a 48+/-10 microm throat size corresponding to an intermediate resistivity, a 13+/-8 microm fiber radius associated with relatively small interfiber distances, and convex triangular cross-section shape fibers allowing weight reduction.

On the dynamic viscous permeability tensor symmetry.

Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.