Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions

Enhanced Low-Frequency Sound Absorption of a Porous Layer Mosaicked with Perforated Resonator

A composite structure composed of a porous-material layer mosaicked with a perforated resonator is proposed to improve the low-frequency sound absorption of the porous layer. This structure is investigated in the form of a porous-material matrix (PM) and a perforated resonator (PR), and the PR is a thin perforated plate filled with porous material in its back cavity. Theoretical and numerical models are established to predict the acoustic impedance and sound absorption coefficient of the proposed structure, and two samples made of polyurethane and melamine, respectively, are tested in an impedance tube. The predicted results are consistent with that of the measured. Compared with a single porous layer with the same thickness, the results show that the designed structure provides an additional sound absorption peak at low frequencies. The proposed structure is compact and has an effective absorption bandwidth of more than two octaves especially below the frequency corresponding to 1/4 wavelength. A comparison is also made between the sound absorption coefficients of the proposed structure and a classical micro-perforated plate (MPP), and the results reveal equivalent acoustic performance, suggesting that it can be used as an alternative to the MPP for low–mid frequency sound absorption. Moreover, the influences of the main parameters on the sound absorption coefficient of PPCS are also analyzed, such as the hole diameter, area ratio, flow resistance, and porous-material thickness in the PR. The mechanism of sound absorption is discussed through the surface acoustic impedance and the distributions of particle velocity and sound pressure at several specific frequencies. This work provides a new idea for the applications of the thin porous layer in low- and medium-frequency sound absorption.

Metamaterial-like aerogels for broadband vibration mitigation

We report a mechanical metamaterial-like behavior as a function of the micro/nanostructure of otherwise chemically identical aliphatic polyurea aerogels. Transmissibility varies dramatically with frequency in these aerogels. Broadband vibration mitigation is provided at low frequencies (500-1000 Hz) through self-assembly of locally resonant metastructures wherein polyurea microspheres are embedded in a polyurea web-like network. A micromechanical constitutive model based on a discrete element method is established to explain the vibration mitigation mechanism. Simulations confirm the metamaterial-like behavior with a negative dynamic material stiffness for the micro-metastructured aerogels in a much wider frequency range than the majority of previously reported locally resonant metamaterials.

Generative adversarial networks for the design of acoustic metamaterials

Metamaterials are attracting increasing interest in the field of acoustics due to their sound insulation effects. By periodically arranged structures, acoustic metamaterials can influence the way sound propagates in acoustic media. To date, the design of acoustic metamaterials relies primarily on the expertise of specialists since most effects are based on localized solutions and interference. This paper outlines a deep learning-based approach to extend current knowledge of metamaterial design in acoustics. We develop a design method by using conditional generative adversarial networks. The generative network proposes a cell candidate regarding a desired transmission behavior of the metamaterial. To validate our method, numerical simulations with the finite element method are performed. Our study reveals considerable insight into design strategies for sound insulation tasks. By providing design directives for acoustic metamaterials, cell candidates can be inspected and tailored to achieve desirable transmission characteristics.

Effect of the Pore Shape and Size of 3D-Printed Open-Porous ABS Materials on Sound Absorption Performance

Noise has a negative impact on our environment and human health. For this reason, it is necessary to eliminate excessive noise levels. This paper is focused on the study of the sound absorption properties of materials with open-porous structures, which were made of acrylonitrile butadiene styrene (ABS) material using additive technology. Four types of structures (Cartesian, Octagonal, Rhomboid, and Starlit) were evaluated in this work, and every structure was prepared in three different volume ratios of the porosity and three different thicknesses. The sound absorption properties of the investigated ABS specimens were examined utilizing the normal incidence sound absorption and noise reduction coefficients, which were experimentally determined by the transfer function method using a two-microphone acoustic impedance tube. This work deals with various factors that influence the sound absorption performance of four different types of investigated ABS material’s structures. It was found, in this study, that the sound absorption performance of the investigated ABS specimens is strongly affected by different factors, specifically by the structure geometry, material volume ratio, excitation frequency of an acoustic wave, material’s thickness, and air space size behind the tested sound-absorbing materials.

Teaching-learning-based optimization of a composite metastructure in the 0-10 kHz broadband sound absorption range

This paper proposes a strategy to broaden the sound absorption region of porous materials by embedding ribs. The theoretical solution and the numerical simulations of the optimization model show that the composite metastructure exhibits ultra-wide high absorption characteristics and an average sound absorption coefficient of 0.937 in the 0-10 kHz range upon its teaching-learning-based optimization. High sound pressures are present only among the embedded ribs. A significant slowing down of the sound takes place inside the metastructure. The impedance tube test confirms the design of the broadband sound absorption region in agreement with the teaching-learning-based optimization method.

Sound transmission loss of porous materials in ducts with embedded periodic scatterers

Porous materials that are commonly used for sound absorption have poor sound insulation capability. In this paper, rigid scatterers are installed periodically inside porous materials to improve their transmission loss (TL) with the Bragg diffraction. The Delany-Bazley impedance model is used to model the porous material and the transfer matrix method is adopted to calculate the TL of the mixed structure in a duct. Simulation results with a different number of scatterers and porous materials with different airflow resistivity show that the TL of porous materials can be increased significantly with periodically arranged scatterers. The decoupled analysis reveals that the TL of the mixed structure is larger than the sum of the TL of individual components in most frequency bands, except that around the first Bragg resonance frequency.

Damped resonance for broadband acoustic absorption in one-port and two-port systems

We demonstrate broadband perfect acoustic absorption by damped resonances through inclusion of lossy porous media. By minimally placing the lossy materials around the necks of single-resonance Helmholtz resonators, where acoustic energy is concentrated, we show an increase in absorption bandwidths (>100% of the resonance frequency). Using the damped resonance, we demonstrate three types of broadband acoustic absorbers in one-port and two-port systems: broadband absorbers (one-port), broadband sparse absorbers (two-port), and broadband duct absorbers (two-port). Our approach for broadband absorption allows to minimize the number of resonances for compact absorbers, while it is beneficial for practical applications owing to the minimum use of porous materials.

Enhancement of low frequency sound absorption by placing thin plates on surface or between layers of porous materials

Rigid thin plates can be used, either on the surface or between layers of materials, to improve the sound absorption properties of porous materials at low frequencies, especially for materials with low sound absorption. Measurement results obtained from a 100 mm impedance tube, for different combinations of porous materials and thin plates, are supplied. Possible physical explanations are discussed. The size of the plate, together with the original properties of the porous material, determines the useful frequency region of the method. The technique of surface-placed thin plates can be directly applied to existing structures without making any changes of the original system, and the results are comparable to those with more complicated modifications.

Coupled Resonators for Sound Trapping and Absorption

The leakage of sound waves in a resonance based rainbow trapping device prevents the sound wave being trapped in a specific location. In this study, we report a design of sound trapping device based on coupled Helmholtz resonators, loaded to an air waveguide, which can effectively tackle the wave leakage issue. We show that coupled resonators structure can generate dips in the transmission spectrum by an analytical model derived from Newton's second law and numerical analysis based on finite-element method. An effective medium theory is derived, which shows that coupled resonators cause a negative effective bulk modulus near the resonance frequency and induce flat bands that give rise to the confinement of the incoming wave inside the resonators. We compute the transmission spectra and band diagram from the effective medium theory, which are consistent with the simulation results. Trapping and high absorption of sound wave energy are demonstrated with our designed device.

A Review of Tunable Acoustic Metamaterials

Acoustic metamaterial science is an emerging field at the frontier of modern acoustics. It provides a prominent platform for acoustic wave control in subwavelength-sized metadevices or metasystems. However, most of the metamaterials can only work in a narrow frequency band once fabricated, which limits the practical application of acoustic metamaterials. This paper highlights some recent progress in tunable acoustic metamaterials based on various modulation techniques. Acoustic metamaterials have been designed to control the attenuation of acoustic waves, invisibility cloaking, and acoustic wavefront engineering, such as focusing via manipulating the acoustic impedance of metamaterials. The reviewed techniques are promising in extending the novel acoustics response into wider frequency bands, in that tunable acoustic metamaterials may be exploited for unusual applications compared to conventional acoustic devices.

A simplified model for thin acoustic screens

A generalization of the commonly used pressure jump modeling of thin porous layers is proposed. The starting point is a transfer matrix model of the layer derived using matrix exponentials. First order expansions of the propagating terms lead to a linear approximation of the associated phenomena and the resulting matrix is further simplified based on physical assumptions. As a consequence, the equivalent fluid parameters used in the model may be reduced to simpler expressions and the transfer matrix rendered sparser. The proposed model is validated for different backing conditions, from normal to grazing incidence and for a wide range of thin films. In the paper, the physical hypotheses are discussed, together with the origin of the field jumps.

Breaking the barriers: advances in acoustic functional materials

Acoustics is a classical field of study that has witnessed tremendous developments over the past 25 years. Driven by the novel acoustic effects underpinned by phononic crystals with periodic modulation of elastic building blocks in wavelength scale and acoustic metamaterials with localized resonant units in subwavelength scale, researchers in diverse disciplines of physics, mathematics, and engineering have pushed the boundary of possibilities beyond those long held as unbreakable limits. More recently, structure designs guided by the physics of graphene and topological electronic states of matter have further broadened the whole field of acoustic metamaterials by phenomena that reproduce the quantum effects classically. Use of active energy-gain components, directed by the parity–time reversal symmetry principle, has led to some previously unexpected wave characteristics. It is the intention of this review to trace historically these exciting developments, substantiated by brief accounts of the salient milestones. The latter can include, but are not limited to, zero/negative refraction, subwavelength imaging, sound cloaking, total sound absorption, metasurface and phase engineering, Dirac physics and topology-inspired acoustic engineering, non-Hermitian parity–time synthetic active metamaterials, and one-way propagation of sound waves. These developments may underpin the next generation of acoustic materials and devices, and offer new methods for sound manipulation, leading to exciting applications in noise reduction, imaging, sensing and navigation, as well as communications.

Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems

Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying crosssection waveguides, each of them being loaded by Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300 Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.

Metadiffusers: Deep-subwavelength sound diffusers

We present deep-subwavelength diffusing surfaces based on acoustic metamaterials, namely metadiffusers. These sound diffusers are rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Strong dispersion is produced in the slits and slow sound conditions are induced. Thus, the effective thickness of the panel is lengthened introducing its quarter wavelength resonance in the deep-subwavelength regime. By tuning the geometry of the metamaterial, the reflection coefficient of the panel can be tailored to obtain either a custom reflection phase, moderate or even perfect absorption. Using these concepts, we present ultra-thin diffusers where the geometry of the metadiffuser has been tuned to obtain surfaces with spatially dependent reflection coefficients having uniform magnitude Fourier transforms. Various designs are presented where, quadratic residue, primitive root and ternary sequence diffusers are mimicked by metadiffusers whose thickness are 1/46 to 1/20 times the design wavelength, i.e., between about a twentieth and a tenth of the thickness of traditional designs. Finally, a broadband metadiffuser panel of 3 cm thick was designed using optimization methods for frequencies ranging from 250 Hz to 2 kHz.

Tailoring broadband acoustic energy suppression characteristics of double porosity metamaterials with compression constraints and mass inclusions

A metamaterial that capitalizes on a double porosity architecture is introduced for controlling broadband acoustic energy suppression properties. When the metamaterial is subjected to static compressive stress, a global rotation of the internal metamaterial architecture is induced that softens the effective stiffness and results in a considerable means to tailor wave transmission and absorption properties. The influences of mass inclusions and compression constraints are examined by computational and experimental efforts. The results indicate that the mass inclusions and applied constraints can significantly impact the absorption and transmission properties of double porosity metamaterials, while the appropriate utilization of the underlying poroelastic media can further magnify these parametric influences. Based on the widespread implementation of compressed poroelastic media in applications, the results of this research uncover how internal metamaterial architecture and constraints may be exploited to enhance engineering noise control properties while using less poroelastic material mass.

Three-dimensional-printed membrane-type acoustic metamaterial for low frequency sound attenuation

Membrane-type acoustic metamaterials have received much attention for low-frequency sound manipulation, especially in the form of decorated membrane resonators. In this paper, such resonators are obtained using fused deposition modeling. Beyond the practical aspects provided by this manufacturing method, the low density of the flexible filament used increases their effectiveness. Indeed, the mass usually added to the membrane center can easily be divided into several disjoint elements. Using rotary inertia of the added structures, new peaks of efficiency in both absorption and normal transmission loss appear when compared to usual decorated membrane resonators.

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption

A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

Use of complex frequency plane to design broadband and sub-wavelength absorbers

The reflection of sound of frequency below 1 kHz, by a rigid-backed structure that contains sub-wavelength resonators is studied in this work. In particular, only single mode reflected waves are considered, an approximation which is accurate in this low frequency regime. A method of analysis of absorption that uses the structure of the reflection coefficient in the complex frequency plane is proposed. In the absence of losses, the reflection coefficient supports pairs of poles and zeros that are complex conjugate and which have imaginary parts linked to the energy leakage by radiation. When losses are introduced and balanced to the leakage, the critical coupling condition is satisfied and total absorption is obtained. Examples of a slot resonator and of multiple Helmholtz resonators are analyzed to obtain both narrow and broadband total absorption.

Use of slow sound to design perfect and broadband passive sound absorbing materials

Perfect (100%) absorption by thin structures consisting of a periodic arrangement of rectangular quarter-wavelength channels with side detuned quarter-wavelength resonators is demonstrated. The thickness of these structures is 13-17 times thinner than the acoustic wavelength. This low frequency absorption is due to a slow sound wave propagating in the main rectangular channel. A theoretical model is proposed to predict the complex wavenumber in this channel. It is shown that the speed of sound in the channel is much lower than in the air, almost independent of the frequency in the low frequency range, and it is dispersive inside the induced transparency band which is observed. The perfect absorption condition is found to be caused by a critical coupling between the rectangular channel (sub-wavelength resonators) and the incoming wave. It is shown that the width of a large absorption peak in the frequency spectrum can be broadened if several rectangular channels in the unit cell are detuned. The detuning is achieved by varying the length of the side resonators for each channel. The predicted absorption coefficients are validated experimentally. Two resonant cells were produced with stereolithography which enabled the authors to incorporate curved side resonators.

Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach

The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded is studied. A semi-analytical approach is presented, based on Biot's 1956 theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. This model is validated by comparing the derived absorption coefficients to finite element simulations. Numerical results are further exposed to investigate the influence of the properties of the inclusions (type, material properties, size) of this structure, while a modal analysis is performed to characterize the dynamic behaviors leading to high acoustic absorption. Particularly, in the case of thin viscoelastic membranes, an absorption coefficient larger than 0.8 is observed on a wide frequency band. This property is found to be due to the coupling between the first volume mode of the inclusion and the trapped mode induced by the periodic array and the rigid backing, for a wavelength in the air smaller than 11 times the material thickness.

Transfer matrix modeling and experimental validation of cellular porous material with resonant inclusions

Porous materials are widely used for improving sound absorption and sound transmission loss of vibrating structures. However, their efficiency is limited to medium and high frequencies of sound. A solution for improving their low frequency behavior while keeping an acceptable thickness is to embed resonant structures such as Helmholtz resonators (HRs). This work investigates the absorption and transmission acoustic performances of a cellular porous material with a two-dimensional periodic arrangement of HR inclusions. A low frequency model of a resonant periodic unit cell based on the parallel transfer matrix method is presented. The model is validated by comparison with impedance tube measurements and simulations based on both the finite element method and a homogenization based model. At the HR resonance frequency (i) the transmission loss is greatly improved and (ii) the sound absorption of the foam can be either decreased or improved depending on the HR tuning frequency and on the thickness and properties of the host foam. Finally, the diffuse field sound absorption and diffuse field sound transmission loss performance of a 2.6 m(2) resonant cellular material are measured. It is shown that the improvements observed at the Helmholtz resonant frequency on a single cell are confirmed at a larger scale.

Enhancing the absorption properties of acoustic porous plates by periodically embedding Helmholtz resonators

This paper studies the acoustical properties of hard-backed porous layers with periodically embedded air filled Helmholtz resonators. It is demonstrated that some enhancements in the acoustic absorption coefficient can be achieved in the viscous and inertial regimes at wavelengths much larger than the layer thickness. This enhancement is attributed to the excitation of two specific modes: Helmholtz resonance in the viscous regime and a trapped mode in the inertial regime. The enhancement in the absorption that is attributed to the Helmholtz resonance can be further improved when a small amount of porous material is removed from the resonator necks. In this way the frequency range in which these porous materials exhibit high values of the absorption coefficient can be extended by using Helmholtz resonators with a range of carefully tuned neck lengths.

Using simple shape three-dimensional rigid inclusions to enhance porous layer absorption

The absorption properties of a metaporous material made of non-resonant simple shape three-dimensional rigid inclusions (cube, cylinder, sphere, cone, and ring torus) embedded in a rigidly backed rigid-frame porous material are studied. A nearly total absorption can be obtained for a frequency lower than the quarter-wavelength resonance frequency due to the excitation of a trapped mode. To be correctly excited, this mode requires a filling fraction larger in three-dimensions than in two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At long wavelengths compared to the spatial period, a cube is found to be the best purely convex inclusion shape to embed in a cubic unit cell, while the embedment of a sphere or a cone cannot lead to an optimal absorption for some porous material properties and dimensions of the unit cell. At a fixed position of purely convex shape inclusion barycenter, the absorption coefficient only depends on the filling fraction and does not depend on the shape below the Bragg frequency arising from the interaction between the inclusion and its image with respect to the rigid backing. The influence of the incidence angle and of the material properties, namely, the flow resistivity is also shown. The results of the modeling are validated experimentally in the case of cubic and cylindrical inclusions.

An acoustic double fishnet using Helmholtz resonators

The acoustic transmission of a closely spaced pair of patterned and perforated rigid plates is explored in air. The structure resembles an acoustic double fishnet design, with each plate modified such that the gap between them acts as an array of Helmholtz resonators. This allows the center frequency of the stop band to be reduced by a factor greater than 2 from the value obtained for the conventional acoustic double fishnet design. Experimental results accord well with the predictions of a finite element model.