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

Non-Hermitian metagrating for perfect absorption of elastic waves

Beyond the fashion of Hermitian physics, non-Hermiticity has inspired, most recently, a surge of nontrivial principles and significant applications in both open quantum and classical systems characterized by gain or loss. However, research on elastic wave manipulation is still predominantly focused on conservative Hermitian systems, overlooking the energy interaction with the environment. The unavoidable energy loss, originating from the inherent material properties, is normally ignored. Additionally, most existing materials for elastic wave absorption suffer from complex configurations, sophisticated designs, and large volumes. Achieving highly efficient absorption properties in advanced artificial materials with ultrathin size and easy fabrication is still a challenge. This work proposes a design strategy based on non-Hermitian modulation to address such a challenge. The proposed non-Hermitian metagrating (NHMG), featured with the subwavelength unit cell, achieves the perfect absorption of elastic waves under specific low-loss conditions. The loss-induced non-Hermitian effects for perfect absorption are theoretically elucidated and a design framework is established in the NHMG with irregular and arbitrary shapes. The robust performance of omnidirectional and perfect absorption capabilities with respect to the boundary shape, rotation angle, and wave source location is numerically and experimentally verified. Consequently, a cloaking device based on the NHMG is further designed to avoid arbitrary-shaped targets being detected. Our study enriches the ways to elastic wave manipulation in non-Hermitian materials and provides an ultra-compact solution for wave absorption in engineering applications.

Mass-spring model for acoustic metamaterials consisting of a compact linear periodic array of dead-end resonators

This paper presents a mass-spring model to predict the normal incidence acoustic response of a metamaterial composed of a compact linear periodic array of dead-end resonators. The dead-end resonators considered are ring-shaped Helmholtz resonators. The model is based on a mass-spring analogy and considers the thermoviscous losses in the metamaterial following an effective fluid approach. A matrix equation of acoustic motion is derived for the finite case of N-periodic arrays. Under external excitation, its direct solution predicts the sound absorption coefficient and transmission loss. Under the homogeneous case, the solution of its associated eigenvalue problem predicts the acoustic eigenfrequencies and mode shapes. The dispersion relation is also solved to predict the beginning of the first stopband, and a low frequency approximation allows development of a formula to estimate the first eigenfrequency. The results show that the system with N degrees of freedom has three stopbands over the frequency range studied, with zero sound absorption and transmission. The model also helps to understand how the acoustic dissipation, at a given resonant frequency, is affected by the position of the acoustic velocity nodes (eigenmodes) in the geometry of the metamaterial. Prototypes are designed, manufactured, and tested in an impedance tube to validate the model.

Ultrathin acoustic metamaterial as super absorber for broadband low-frequency underwater sound

In this work, an ultrathin acoustic metamaterial formed by space-coiled water channels with a rubber coating is proposed for underwater sound absorption. The proposed metamaterial achieves perfect sound absorption ([Formula: see text] > 0.99) at 181 Hz, which has a deep subwavelength thickness ([Formula: see text]). The theoretical prediction is consistent with the numerical simulation, which demonstrate the broadband low-frequency sound absorption performance of the proposed super absorber. The introduction of rubber coating leads to a significant decrease of the effective sound speed in the water channel, resulting in the phenomenon of slow-sound propagation. From the perspective of numerical simulations and acoustic impedance analysis, it is proved that the rubber coating on the channel boundary causes slow-sound propagation with inherent dissipation, which is the key to meet the impedance matching condition and achieve perfect low-frequency sound absorption. Parametric studies are also carried out to investigate the effect of specific structural and material parameters on sound absorption. By tailoring key geometric parameters, an ultra-broadband underwater sound absorber is constructed, with a perfect absorption range of 365-900 Hz and a deep subwavelength thickness of 33 mm. This work paves a new way for designing underwater acoustic metamaterials and controlling underwater acoustic waves.

Compact resonant systems for perfect and broadband sound absorption in wide waveguides in transmission problems

This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 × 15 cm² rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz.

Influence of thermal deformations on sound absorption of three-dimensional printed metamaterials

Acoustic metamaterials (AMMs) are designed with complex geometrical shapes to obtain unconventional sound-absorbing performances. As additive manufacturing is particularly suited to print complex structures in a more straightforward and controllable way, AMMs often exploit three-dimensional (3-D) printing techniques. However, when exposed to different temperature conditions, such structures can be affected by geometrical deformations, especially when they are polymer-based. This can cause a mismatch between the experimental data and the expected theoretical performance; therefore, it is important to take thermal effects into account. The present paper investigates the influence of thermal deformations on the sound absorption of three geometries: a coplanar spiral tube, a system with double coiled resonators, and a neck-embedded resonator. Measurements were performed on each 3-D printed specimen in the impedance tube after the samples had been placed in a climate chamber to modify the temperature settings (T = 10-50 °C). Numerical models, validated on the measurements, were employed to quantify the geometrical deformation of AMM structures through a multiphysics approach, highlighting the effects of thermal stress on the acoustic behavior. The main outcomes prove that the frequency shifts of sound absorption peaks depend on temperature configurations and follow exponential regressions, in accordance with previous literature on polymeric materials.

Underwater metamaterial absorber with impedance-matched composite

By using a structured tungsten-polyurethane composite that is impedance matched to water while simultaneously having a much slower longitudinal sound speed, we have theoretically designed and experimentally realized an underwater acoustic absorber exhibiting high absorption from 4 to 20 kHz, measured in a 5.6 m by 3.6 m water pool with the time-domain approach. The broadband functionality is achieved by optimally engineering the distribution of the Fabry-Perot resonances, based on an integration scheme, to attain impedance matching over a broad frequency range. The average thickness of the integrated absorber, 8.9 mm, is in the deep subwavelength regime (~λ/42 at 4 kHz) and close to the causal minimum thickness of 8.2 mm that is evaluated from the simulated absorption spectrum. The structured composite represents a new type of acoustic metamaterials that has high acoustic energy density and promises broad underwater applications.

Enhancing of broadband sound absorption through soft matter

This paper proposed a metamaterial design method that uses soft matter for constructing a unique soft acoustic boundary to effectively improve broadband sound absorption performance. Specifically, attaching a flexible polyvinyl chloride (PVC) gel layer with an elastic modulus as low as a few kilopascals and a thickness of a few millimeters to the inner wall of a cavity-type sound-absorbing metamaterial structure significantly improved the absorption performance of the composite structure in low-frequency broadband ranges. The sound absorption enhancement mechanism differed from those proposed in previous research. On the one hand, the soft PVC gel layer acted as a soft acoustic boundary, substantially reducing the sound speed and reflection and producing considerable elastic strain energy at the interface between two different media to improve the sound absorption performance. On the other hand, this PVC gel layer displayed extremely low stiffness and high damping, producing an abundance of plasmon-like resonance modes in low-frequency broadband ranges, achieving a resonance absorption effect. Since this sound absorption enhancement method did not require an increase in the external dimensions or a change in the structural parameters of the original absorber and achieved robust enhancement in a wide frequency band, it displayed potential application value in various engineering fields.

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.

Broadband thin sound absorber based on hybrid labyrinthine metastructures with optimally designed parameters

Broadband acoustic absorbers with thin thickness are highly desired in practical situations such as architectural acoustics, yet it is still challenging to achieve high absorption by using structure with limited thickness. Here we report the theoretical optimal design, numerical simulation and experimental demonstration of a planar acoustic absorber capable of producing broadband sound absorption with deep-subwavelength thickness. The mechanism is that, we use a hybrid design of individual unit cell comprising multiple resonators with a coiled configuration for expanding the working bandwidth and downscaling the resulting device, and, on the other hand, the geometries of the constituent resonance elements are optimally designed by using genetic algorithm. Based on an analytical formula we derive for an efficient prediction of the absorption efficiency, the optimization process is accelerated and gives rise to an optimally maximized amount of absorbed energy with limited device thickness. As a result, the proposed absorber features planar profile, broad bandwidth, wide absorbing angle (the absorber works well when the incident angle of sound wave reaches 60°) and thin thickness (< 1/25 wavelength). In addition, the proposed scheme does not rely on extra sound-absorptive materials or the type of constituent solid material, which significantly simplifies the sample fabrication and improves the application potential of resulting device. The measured data agree well with the theoretical predictions, showing high sound absorption in the prescribed frequency range. We envision our design to further improve the performance of acoustic absorbers and find applications in practical situations in need of elimination of broadband acoustic waves within limited spaces.

3D-printed sound absorbing metafluid inspired by cereal straws

Used as building biomaterials for centuries, cereal straws are known for their remarkable acoustic performances in sound absorption. Yet, their use as fibrous media disregards their internal structure made of nodes partitioning stems. Here, we show that such nodes can impart negative acoustic bulk modulus to straw balls when straws are cut on either side of a node. Such metafluid inspired by cereal straws combines visco-thermal diffusion with strong wave dispersion arising from quarter-wavelength resonances within straws. Large spectral bandgaps and slow sound regimes are theoretically predicted and experimental data from impedance tube measurements on an idealised 3D-printed sample layer are in good agreement with the theoretical model. Perfect absorption is achieved at wavelengths 13 times larger than the thickness of the metafluid layer, and slow sound entails an increased density of states causing a cascade of high absorption peaks. Such features could lead cereal straws to serve as cheap acoustic bio-metamaterials.

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.

Subwavelength Interferometric Control of Absorption in Three-port Acoustic Network

Utilizing the effect of losses, we show that symmetric 3-port devices exhibit coherent perfect absorption of waves and we provide the corresponding conditions on the reflection and transmission coefficients. Infinite combinations of asymmetric inputs with different amplitudes and phase at each port as well as a completely symmetric input, are found to be perfectly absorbed. To illustrate the above we study an acoustic 3-port network operating in a subwavelength frequency both theoretically and experimentally. In addition we show how the output from a 3-port network is altered, when conditions of perfect absorption are met but the input waves phase and amplitude vary. In that regard, we propose optimized structures which feature both perfect absorption and perfect transmission at the same frequency by tuning the amplitudes and phases of the input waves.

Subwavelength and quasi-perfect underwater sound absorber for multiple and broad frequency bands

A structure for an underwater sound absorber with subwavelength thickness and a quasi-perfect absorption property at multiple frequency bands is reported. This absorber consists of a viscoelastic coating layer embedded with periodically distributed plate scatterers (PSs). The embedded PSs cannot only slow sound waves in the coating, leading to a down-shifted resonance frequency where the absorption is maximized, but also introduce multiple local bending modes and local longitudinal modes in the coating. Via proper selection of the parameters of the PSs and the PS array, multiple local resonance modes of different types in a coating unit can be excited, resulting in quasi-perfect absorption of incident sound at multiple frequencies whose wavelengths are much longer than the thickness of the coating layer. For example, absorption (89%) of underwater sound at 462.9 Hz is achieved by such a layer with a thickness of 6 cm, which is 1.9% of the wavelength of the incident sound. Broadband quasi-perfect absorption can also be realized by coupling of those multiple local resonant modes. This quasi-perfect absorption property can also be observed for sound waves with different incident angles, because a large number of local intrinsic modes could still be excited.

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.