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

Loss-induced modal selection by a resistive wiremesh

This work examines the impact of local losses produced by a resistive wiremesh on the modes of an acoustic cavity. In the one-dimensional case, we demonstrate the ability to selectively affect the modes, ranging from being completely unaffected by the wiremesh to being fully absorbed by it. This effect can be used to filter the cavity modes. In the two-dimensional case, higher order modes are considered and we discuss the effect of wiremesh tilt on the cavity modes. A new type of mode that is localized on the wiremesh with a purely imaginary eigenfrequency has been identified. These findings show that wiremeshes are ultrabroadband lossy metasurfaces offering a straightforward way to explore passive non-Hermitian systems.

Perfect Resonant Absorption of Guided Water Waves by Autler-Townes Splitting

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

Recent Progress in Resonant Acoustic Metasurfaces

Acoustic metasurfaces, as two-dimensional acoustic metamaterials, are a current research topic for their sub-wavelength thickness and excellent acoustic wave manipulation. They hold significant promise in noise reduction and isolation, cloaking, camouflage, acoustic imaging, and focusing. Resonant structural units are utilized to construct acoustic metasurfaces with the unique advantage of controlling large wavelengths within a small size. In this paper, the recent research progresses of the resonant metasurfaces are reviewed, covering the design mechanisms and advances of structural units, the classification and application of the resonant metasurfaces, and the tunable metasurfaces. Finally, research interest in this field is predicted in future.

Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.

Passive earplug including Helmholtz resonators arranged in series to achieve broadband near zero occlusion effect at low frequencies

The use of passive earplugs is often associated with the occlusion effect: a phenomenon described as the increased auditory perception of one's own physiological noise at low frequencies. As a notable acoustic discomfort, the occlusion effect penalizes the use and the efficiency of earplugs. This phenomenon is objectively characterized by the increase in sound pressure level in the occluded ear canal compared to the open ear canal. Taking inspiration from acoustic metamaterials, a new design of a three-dimensional printed "meta-earplug," made of four Helmholtz resonators arranged in series, is proposed for achieving near zero objective occlusion effect measured on artificial ear in a broadband frequency range (300 Hz to 1 kHz). For this purpose, the geometry of the meta-earplug is optimized to achieve a null occlusion effect target based on an analytical model of the phenomenon. It results from the optimization process that the input impedance of the meta-earplug medial surface approximately matches the input impedance of the open ear canal, weighted by the ratio of volume velocity imposed by the ear canal wall to the ear canal cavity between open and occluded cases. Acoustic properties of the meta-earplug are also shown to significantly improve its sound attenuation at the piston-like mode of the system.

The acoustic performances of a subwavelength hierarchical honeycomb structure: Analytical, numerical, and experimental investigations

This paper proposes a subwavelength hierarchical honeycomb structure (SHHS) with a compact lateral dimension and double-band perfect absorption in low frequencies. Unlike the conventional micro-perforated panel (MPP)-honeycomb sandwich absorber, this structure has an additional internal honeycomb with a perforated wall. Therefore, there are two resonant cavities in the SHHS to realize multiple absorption peaks. Analytical, numerical, and experimental investigations are performed to study the proposed system's acoustic performance in absorption. The SSHS is simplified into four parts and its analytical model is constructed by combining various analytical models by acoustic-electro analogy. The analytical model is presented to explore the physical properties of sound absorption and the influence of parameters, which has been validated by comparisons with the numerical model, and the experimental data is measured by an impedance tube. It is found that the main incident energy is lost by the inside hole, which is different from the conventional absorbers with surface MPP. Moreover, the side length of the internal honeycomb can adjust the resonant frequencies to achieve an absorber with the subwavelength. A SSHS is designed with a perfect absorption at 320 Hz whose thickness is 1/31 of the resonant frequency wavelength. The SHHS has excellent potential for noise control engineering applications.

Multifunctional sound-absorbing and mechanical metamaterials via a decoupled mechanism design approach

Multifunctional materials are in high demand for practical engineering applications. Owing to the ubiquitous noise and impact energy hazards in many settings, traditional materials and conventionally designed metamaterials are incapable of preventing these types of hazard simultaneously. Herein, we report a new paradigm, via a decoupled approach, in the design of acousto-mechanical multifunctional metamaterials. We leverage the morphology of a Helmholtz resonator, such that the sound-absorbing and mechanical components are designed independently. For sound absorption, we adopt a coherent coupling design for a favorable resonant response, while for the mechanical response, we adopt customized struts. We then demonstrate our concept via 3D printing. Experimentally measured remarkable broadband absorption in the practical low-frequency range (<1.0 kHz) is achieved. Absorption mechanisms are attributed to viscous and thermal boundary dissipation. Compression tests also reveal that the metamaterials are highly deformation resilient with a recovery of up to 98%, owing to both the lattice structure design and the viscoelastic behavior of the base material. Through this decoupled design, we further demonstrate the potential of our metamaterials in customizable absorption, strength, pseudo-reusability, and impact resistance. The proposed design paradigm broadens the horizon for the design of multifunctional materials, offering an impetus to their exploration for practical applications.

Adjustable Sound Absorber of Multiple Parallel-Connection Helmholtz Resonators with Tunable Apertures Prepared by Low-Force Stereolithography of Photopolymer Resin

The variable noise spectrum for many actual application scenarios requires a sound absorber to adapt to this variation. An adjustable sound absorber of multiple parallel-connection Helmholtz resonators with tunable apertures (TA-MPCHRs) is prepared by the low-force stereolithography of photopolymer resin, which aims to improve the applicability of the proposed sound absorber for noise with various frequency ranges. The proposed TA-MPCHR metamaterial contains five metamaterial cells. Each metamaterial cell contains nine single Helmholtz resonators. It is treated as a basic structural unit for an array arrangement. The tunable aperture is realized by utilizing four segments of extendable cylindrical chambers with length l₀, which indicates that the length of the aperture l is in the range of [l₀, 4l₀], and that it is tunable. With a certain group of specific parameters for the proposed TA-MPCHR, the influence of the tunable aperture with a variable length is investigated by acoustic finite element simulation with a two-dimensional rotational symmetric model. For the given noise spectrum of certain actual equipment with four operating modes, the TA-MPCHR sample with a limited total thickness of 40 mm is optimized, which is made of photopolymer resin by the low-force stereolithography, and its actual average sound absorption coefficients for the frequency ranges of 500-800 Hz, 550-900 Hz, 600-1000 Hz and 700-1150 Hz reach 0.9203, 0.9202, 0.9436 and 0.9561, respectively. Relative to common non-adjustable metamaterials, the TA-MPCHR made of photopolymer resin can reduce occupied space and improve absorption efficiency, which is favorable in promoting its practical applications in the noise pollution prevention.

Reduction of the occlusion effect induced by earplugs using quasi perfect broadband absorption

Passive earplugs are used to prevent workers from noise-induced hearing loss. However, earplugs often induce an acoustic discomfort known as the occlusion effect. This phenomenon corresponds to an increased auditory perception of the bone-conducted part of physiological noises at low-frequency and is associated with the augmentation of the acoustic pressure in the occluded earcanal. In this work, we report a new concept of passive earplugs for mitigating the occlusion effect between 100 Hz and 1 kHz. The strategy consists in reducing the input impedance of the earplug seen from the earcanal by using quasi-perfect broadband absorbers derived from the field of meta-materials. The proposed "meta-earplug" is made of 4 critically coupled Helmholtz resonators arranged in parallel. Their geometry is optimized using an evolutionary algorithm associated with a theoretical model of the meta-earplug input impedance. The latter is validated against a finite-element approach and impedance sensor measurements. The meta-earplug is manufactured by 3D printing. Artificial test fixtures are used to assess the occlusion effect and the insertion loss. Results show that the meta-earplug induces an occlusion effect approximately 10 dB lower than foam and silicone earplugs while it provides an insertion loss similar to the silicone earplug up to 5 kHz.

Absorption characteristics of large acoustic metasurfaces

Metasurfaces formed of arrays of subwavelength resonators are often tuned to 'critically couple' with incident radiation, so that at resonance dissipative and radiative damping are balanced and absorption is maximized. Such design criteria are typically derived assuming an infinite metasurface, whereas the absorption characteristics of finite metasurfaces, even very large ones, can be markedly different in certain frequency intervals. This is due to the excitation of surface waves, intrinsic to resonant metasurfaces and especially meta-resonances, namely collective resonances where the surface waves form standing-wave patterns over the planar metasurface domain. We illustrate this issue using a detailed model of a Helmholtz-type acoustic metasurface formed of cavity-neck pairs embedded into a rigid substrate, with geometric and dissipation effects included from first principles (R. Brandão and O. Schnitzer, Wave Motion, 97, 102583, 2020). This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

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.

Design of broadband Helmholtz resonator arrays using the radiation impedance method

This paper describes the design process of a low-frequency sound absorptive panel composed of differently tuned Helmholtz resonators (HRs), considering size and fabrication constraints relevant for applications in the building sector. The paper focuses on cylindrical and spiral resonators with embedded necks that are thin and can achieve high absorption. the mutual interaction between the resonators was modeled based on the radiation impedance method and it plays a key component in enhancing the absorption performance of the array. The differential evolution search algorithm was used to design the resonators and modify their mutual interaction to derive the absorption performance of multiple HR arrays for comparison. Optimizations to the resonator configuration and the neck resistance were implemented to produce a unit panel that has a broadband absorption performance with emphasis on the low to mid frequencies and is thin and light in weight. Unit panels with dimensions of 20 cm×20 cm, consisting of 29 cylindrical HRs designed to absorb in the 25-900 Hz frequency range, were constructed and tested in a custom-built impedance tube. The measured absorption performance of these panels is consistent with the theoretical predictions.

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.

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.

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.

Compact broadband acoustic sink with coherently coupled weak resonances

Broadband sound sink/absorber via a structure with deep sub-wavelength thickness is of great and continuing interest in physics and engineering communities. An intuitive technique extensively used is to combine components (resonators) with quasi-perfect absorption to piece together a broad absorbing band, but the requirement of quasi-perfect absorption substantially places a very strict restriction on the impedance and thickness of the components. Here, we theoretically and experimentally demonstrate that a compact broadband acoustic sink that quasi-perfectly absorbs broadband arriving sound waves can be achieved with coherently coupled "weak resonances" (resonant sound absorbing systems with low absorption peaks). Although each component exhibits rather low absorption peak alone, via manipulating the coherent coupling effect among the components, they collectively provide a remarkably improved performance over a wide frequency range with a significantly compressed thickness. To illustrate the design principle, a hybrid metasurface utilizing the coaction of parallel and cascade couplings is presented, which possesses an average absorption coefficient of 0.957 in the quasi-perfect band (α>0.9) from 870 to 3224 Hz with a thickness of only 3.9 cm. Our results open new avenues for the development of novel and highly efficient acoustic absorbers against low frequency noise, and more essentially, suggest an efficient approach towards on-demand acoustic impedance engineering in broadband.

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.

Sound Absorption Properties of Perforated Recycled Polyurethane Foams Reinforced with Woven Fabric

The acoustic properties of recycled polyurethane foams are well known. Such foams are used as a part of acoustic solutions in different fields such as building or transport. This paper aims to seek improvements in the sound absorption of these recycled foams when they are combined with fabrics. For this aim, foams have been drilled with cylindrical perforations, and also combined with different fabrics. The effect on the sound absorption is evaluated based on the following key parameters: perforation rate (5% and 20%), aperture size (4 mm and 6 mm), and a complete perforation depth. Experimental measurements were performed by using an impedance tube for the characterization of its acoustic behavior. Sound absorption of perforated samples is also studied—numerically by finite element simulations, where the viscothermal losses were considered; and analytically by using models for the perforated foam and the fabric. Two textile fabrics were used in combination with perforated polyurethane samples. Results evidence a modification of the sound absorption at mid frequencies employing fabrics that have a membrane-type acoustic response.

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.

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.

Composite honeycomb metasurface panel for broadband sound absorption

Composite honeycomb sandwich panels have been adopted in a wide range of applications owing to their excellent mechanical properties. This paper demonstrates a design of a composite honeycomb metasurface panel that can achieve 90% sound absorption from 600 to 1000 Hz with a thickness less than 30 mm. The panel is comprised of periodically and horizontally arranged honeycomb "supercells" which consist of unit cells of different geometric parameters (pore size). Two different analytical models (Helmholtz resonator model and micro-perforated panel model) are used to calculate the sound absorption of the panel, and they are further validated by a numerical model. The relatively broadband sound absorption is found to be attributed to the coupling between unit cells, which is illustrated by both the complex frequency plane theory and the calculated sound intensity field.

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.

Modelling resonant arrays of the Helmholtz type in the time domain

We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. This is of practical importance if the numerical implementations of the effective problem in the time domain is sought.

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.

PT-Symmetric Scattering in Flow Duct Acoustics

We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amounts of mean-flow-induced effective gain and loss, displays all the features of a parity-time (PT) symmetric system. Using a scattering matrix formalism, we observe, experimentally, the properties which reflect the PT symmetry of the scattering acoustical system: the existence of spontaneous symmetry breaking with symmetry-broken pairs of scattering eigenstates showing amplification and reduction, and the existence of points with unidirectional invisibility.

Coherent perfect absorption induced by the nonlinearity of a Helmholtz resonator

In this work, coherent perfect absorption of sound waves induced by the nonlinear response of a Helmholtz Resonator side loaded to a waveguide, is reported. It is shown that this two-port system can perfectly absorb two high amplitude symmetric incident waves under a certain condition. For the one-sided incidence configuration, this condition leads to an absorption equal to 0.5. Experiments verify these results and are in agreement with an analytical nonlinear impedance model for the resonator. The nonlinear control of perfect absorption opens new possibilities in the design of high amplitude sound attenuators for aero-engine applications.