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

Autonomous design of noise-mitigating structures using deep reinforcement learning

This paper explores the application of deep reinforcement learning for autonomously designing noise-mitigating structures. Specifically, deep Q- and double deep Q-networks are employed to find material distributions that result in broadband noise mitigation for reflection and transmission problems. Unlike conventional deep learning approaches which require prior knowledge for data labeling, the double deep Q-network algorithm learns configurations that result in broadband noise mitigations without prior knowledge by utilizing pixel-based inputs. By employing unified hyperparameters and network architectures for transmission and reflection problems, the capability of the algorithms to generalize over different environments is demonstrated. In addition, a comparison with a genetic algorithm highlights the potential for generalized design in complex environments, despite the algorithms tending to predict local maxima. Furthermore, we examine the impact of hyperparameters and environment types on agent performance. The autonomous design approach offers generalized learning while avoiding restrictions to specific shapes or prior knowledge of the task.

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.

Design, Manufacturing, and Acoustical Analysis of a Helmholtz Resonator-Based Metamaterial Plate

Acoustic metamaterials are materials artificially engineered to control sound waves, which is not possible with conventional materials. We have proposed a design of an acoustic metamaterial plate with inbuilt Helmholtz resonators. The plate is made of Polylactic acid (PLA) which is fabricated using an additive manufacturing technique. It consists of Helmholtz resonator-shaped cavities of different sizes. In this paper, we have analyzed the acoustic properties of the Helmholtz resonators-based metamaterial plate experimentally as well as numerically. The experimental results are in good agreement with the numerical results. These types of 3D-printed metamaterial plates can find their application where high sound transmission loss is required to create a quieter ambience. There is an additional advantage of being lightweight because of the Helmholtz resonator-shaped cavities built inside the plate. Thus, these types of metamaterial plates can find their application in the design sector requiring lighter materials with high sound transmission loss.

Ultra-sparse metamaterials absorber for broadband low-frequency sound with free ventilation

An absorptive device for broadband low-frequency sound with ventilation is essential but challenging in acoustic engineering, which is subjected to the narrow-band limitation and difficulty of balancing high-efficiency absorption and excellent ventilation. Here, we have theoretically and experimentally demonstrated an ultra-sparse (with filling ratio of 53.7%) broadband metamaterial absorber which can efficiently absorb (absorptance  >90%) sound energy ranging from 307 to 341 Hz, while enabling air to flow freely. The broadband absorber is constructed by parallel coupling four ventilated metamaterials absorbers (VMAs) showing different operating frequencies. Each VMA is composed of three folded Fabry-Pérot resonators as paste components, which are patched subsequently to the walls of a waveguide and correspondingly act as dark, middle, and bright modes following the coupled mode theory. In the VMA, the dark mode is highly over-damped to absorb sound energy, while the bright mode is highly under-damped to be an effective acoustic soft boundary, and the middle mode in-between should be slightly over-damped to strengthen the absorptions. Further investigation demonstrates that broadband high-efficiency absorption is robust against oblique incident angles. The proposed VMA provides a clear scheme for efficiently absorbing low-frequency sound while allowing free air flow simultaneously, which may prompt versatile applications in noise control.

An extra-broadband compact sound-absorbing structure composing of double-layer resonator with multiple perforations

Based on multi-layer Helmholtz resonators with extended necks (HREN), a compact sound-absorbing structure is developed for extra-broadband sound absorption. The structure of HREN with a single perforation is beneficial for low-frequency absorption under a thin thickness. However, it faces the problem of effectively attenuating noise only within a narrow frequency bandwidth near the resonance frequency. To widen its effective absorption bandwidth, two potential solutions are proposed and evaluated: (1) increasing the perforation number, and (2) adding extra layers in series. Results reveal that more perforations produce a wider half-absorption bandwidth, and the added layers induce more absorption peaks. Thus, a multi-layer HREN unit with multiple perforations is a favorable candidate for broadband sound absorption. On the basis of these, we design a broadband acoustic structure constructed by 11 coupled parallelly arranged double-layer HREN units with multiple perforations. The structure possesses an average sound-absorption coefficient of 0.9 in a prescribed frequency ranging from 800 to 3000 Hz. The absorption effectiveness of the structure is validated via experiments. What is more, the dimension of the absorber is only 50 mm (long)×50 mm (width)×41 mm (depth), indicating its compact characteristic. Hence, the developed extra broadband and compact sound-absorbing structure possesses a promising potential in various engineering applications.

Numerical Simulation for the Sound Absorption Properties of Ceramic Resonators

This work reports the results of experimental measurements of the sound absorption coefficient of ceramic materials using the principle of acoustic resonators. Subsequently, the values obtained from the measurements were used to train a simulation model of the acoustic behavior of the analyzed material based on artificial neural networks. The possible applications of sound-absorbing materials made with ceramic can derive from aesthetic or architectural needs or from functional needs, as ceramic is a fireproof material resistant to high temperatures. The results returned by the simulation model based on the artificial neural networks algorithm are particularly significant. This result suggests the adoption of this technology to find the finest possible configuration that allows the best sound absorption performance of the material.

Investigation of Acoustic Properties on Wideband Sound-Absorber Composed of Hollow Perforated Spherical Structure with Extended Tubes and Porous Materials

Traditional porous media such as melamine foam absorb sound due to their three-dimensional porous struts. However, the acoustic properties at low frequencies are greatly related to its thickness. In this paper, a novel type of thin and lightweight sound absorber composed of melamine foam and hollow perforated spherical structure with extended tubes (HPSET) is introduced to enhance the sound absorption performance at low frequencies. A theoretical model for the normal absorption coefficient of the HPSET with melamine foam is established. Good agreements are observed between the simulated and the experimental results. Compared with the virgin melamine foam, the proposed absorber can greatly improve the low-frequency sound absorption and retain the mid- to high-frequency sound absorption, while the thickness of the proposed absorber is less than 1/28 of the wavelength.

Subwavelength broadband sound absorber based on a composite metasurface

Suppressing broadband low-frequency sound has great scientific and engineering significance. However, normal porous acoustic materials backed by a rigid wall cannot really play its deserved role on low-frequency sound absorption. Here, we demonstrate that an ultrathin sponge coating can achieve high-efficiency absorptions if backed by a metasurface with moderate surface impedance. Such a metasurface is constructed in a wide frequency range by integrating three types of coiled space resonators. By coupling an ultrathin sponge coating with the designed metasurface, a deep-subwavelength broadband absorber with high absorptivity (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${>}80\%$$\end{document}>80%) exceeding one octave from  185 Hz to  385 Hz (with wavelength \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}λ from 17.7 to 8.5 times of thickness of the absorber) has been demonstrated theoretically and experimentally. The construction mechanism is analyzed via coupled mode theory. The study provides a practical way in constructing broadband low-frequency sound absorber.

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.

Compact Acoustic Rainbow Trapping in a Bioinspired Spiral Array of Graded Locally Resonant Metamaterials

Acoustic rainbow trappers, based on frequency selective structures with graded geometries and/or properties, can filter mechanical waves spectrally and spatially to reduce noise and interference in receivers. These structures are especially useful as passive, always-on sensors in applications such as structural health monitoring. For devices that face space and weight constraints, such as microelectromechanical systems (MEMS) transducers and artificial cochleae, the rainbow trapping structures must be compact as well. To address this requirement, we investigated the frequency selection properties of a space-saving design consisting of Helmholtz resonators arranged at sub-wavelength intervals along a cochlear-inspired spiral tube. The height of the Helmholtz resonators was varied gradually, which induced bandgap formation at different frequencies along the length of the spiral tube. Numerical simulations and experimental measurements of acoustic wave propagation through the structure showed that frequencies in the range of 1–10 kHz were transmitted to different extents along the spiral tube. These rainbow trapping results were achieved with a footprint that was up to 70 times smaller than the previous structures operating at similar bandwidths, and the channels are 2.5 times of the previous structures operating at similar bandwidths.

Theoretical requirements and inverse design for broadband perfect absorption of low-frequency waterborne sound by ultrathin metasurface

Effective absorption of low-frequency waterborne sound with subwavelength absorbers has always been a challenging work. In this paper, we derive two theoretical requirements for broadband perfect absorption of low-frequency waterborne sound by ultrathin acoustic metasurface under a finite-thickness steel plate followed by semi-infinite air. Based on the theoretical requirements, an acoustic metasurface, a rubber layer embedded periodically with cavities, is inversely designed to achieve perfect absorption at 500 Hz. The metasurface is as thin as 1% of the working wavelength and maintains a substantially high absorptance over a relatively broad bandwidth. The perfect absorption peak is attributed to the overall resonance mode of the metasurface/steel plate system. Besides, high absorption can still be achieved even if the loss factor of the given rubber material cannot meet the ideal requirement. Finally, a strategy to utilize the inherent frequency-dependent characteristics of dynamic parameters of rubber material is suggested to achieve an ultra-broadband perfect absorption. When the frequency-dependent characteristics of the given rubber matrix cannot meet the theoretical requirements, a broadband super-absorption can still be realized by properly designing the frequency position of perfect absorption of the cavity-based metasurface.

Reconfigurable sound anomalous absorptions in transparent waveguide with modularized multi-order Helmholtz resonator

Helmholtz resonators offer an ideal platform for advanced sound absorbers, but their utility has been impeded by inherent frequency range limitations and the lack of function reconfiguration. Here, we introduce a multi-order Helmholtz resonator (MHR) that allows multiple monopolar resonant modes theoretically and experimentally. The combination of these modularized MHRs further creates reconfigurable multi-band anomalous absorbers in a two-port transparent waveguide while maintaining undisturbed air ventilation. In asymmetric absorption state through coupling of artificial sound soft boundary with preposed MHR, sound energy is almost totally absorbed in multiple frequency ranges when sound waves are incident from one side while it is largely reflected back from the opposite side. Interestingly, the original asymmetric absorber would turn into symmetric bidirectional absorber if one post MHR concatenates after the soft boundary. Using combination of identical MHRs, we demonstrate function selective asymmetric/symmetric absorber in multi-bands, highlighting the potential to use MHRs in the design of diverse devices for more versatile applications.

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.

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.

Sound attenuation optimization using metaporous materials tuned on exceptional points

A metamaterial composed of a set of periodic rigid resonant inclusions embedded in a porous lining is investigated to enhance the sound attenuation in an acoustic duct at low frequencies. A transmission loss peak is observed on the measurements and corresponds to the crossing of the lower two Bloch modes of an infinite periodic material. Numerical parametric studies show that the optimum modal attenuation can be achieved at the exceptional point in the parameter plane of inclusion position and frequency, where the two lower modes merge.

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.

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 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.