An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials.

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Design of Locally Resonant Acoustic Metamaterials with Specified Band Gaps Using Multi-Material Topology Optimization.

Locally Resonant Acoustic Metamaterials (LRAMs) have significant application potential because they can form subwavelength band gaps. However, most current research does not involve obtaining LRAMs with specified band gaps, even though such LRAMs are significant for practical applications. To address this, we propose a parameterized level-set-based topology optimization method that can use multiple materials to design LRAMs that meet specified frequency constraints. In this method, a simplified band-gap calculation approach based on the homogenization framework is introduced, establishing a restricted subsystem and an unrestricted subsystem to determine band gaps without relying on the Brillouin zone. These subsystems are specifically tailored to model the phenomena involved in band gaps in LRAMs, facilitating the opening of band gaps during optimization. In the multi-material representation model used in this method, each material, except for the matrix material, is depicted using a similar combinatorial formulation of level-set functions. This model reduces direct conversion between materials other than the matrix material, thereby enhancing the band-gap optimization of LRAMs. Two problems are investigated to test the method's ability to use multiple materials to solve band-gap optimization problems with specified frequency constraints. The first involves maximizing the band-gap width while ensuring it encompasses a specified frequency range, and the second focuses on obtaining light LRAMs with a specified band gap. LRAMs with specified band gaps obtained in three-material or four-material numerical examples demonstrate the effectiveness of the proposed method. The method shows great promise for designing metamaterials to attenuate specified frequency spectra as required, such as mechanical vibrations or environmental noise.

An adjustable acoustic metamaterial cell using a magnetic membrane for tunable resonance.

Acoustic metamaterials are growing in popularity for sound applications including noise control. Despite this, there remain significant challenges associated with the fabrication of these materials for the sub-100 Hz regime, because acoustic metamaterials for such frequencies typically require sub-mm scale features to control sound waves. Advances in additive manufacturing technologies have provided practical methods for rapid fabrication of acoustic metamaterials. However, there is a relatively high sensitivity of their resonant characteristics to sub-mm deviations in geometry, pushing the limits of additive manufacturing. One way of overcoming this is via active control of device resonance. Here, an acoustic metamaterial cell with adjustable resonance is demonstrated for the sub-100 Hz regime. A functionally superparamagnetic membrane-devised to facilitate the fabrication process by eliminating magnetic poling requirements-is engineered using stereolithography, and its mechanical and acoustic properties are experimentally measured using laser Doppler vibrometry and electret microphone testing, with a mathematical model developed to predict the cell response. It is demonstrated that an adjustable magnetic acoustic metamaterial can be fabricated at ultra-subwavelength dimensions ( ≤ λ /77.5), exhibiting adjustable resonance from 88.73 to 86.63 Hz. It is anticipated that this research will drive new innovations in adjustable metamaterials, including wider frequency ranges.

Acoustic Skyrmionic Mode Coupling and Transferring in a Chain of Subwavelength Metastructures.

Skyrmions, a stable topological vectorial textures characteristic with skyrmionic number, hold promise for advanced applications in information storage and transmission. While the dynamic motion control of skyrmions has been realized with various techniques in magnetics and optics, the manipulation of acoustic skyrmion has not been done. Here, the propagation and control of acoustic skyrmion along a chain of metastructures are shown. In coupled acoustic resonators made with Archimedes spiral channel, the skyrmion hybridization is found giving rise to bonding and antibonding skyrmionic modes. Furthermore, it is experimentally observed that the skyrmionic mode of acoustic velocity field distribution can be robustly transferred covering a long distance and almost no distortion of the skyrmion textures in a chain of metastructures, even if a structure defect is introduced in the travel path. The proposed localized acoustic skyrmionic mode coupling and propagating is expected in future applications for manipulating acoustic information storage and transfer.

Information encoding and encryption in acoustic analogues of qubits.

Cryptography is crucial in protecting sensitive information and ensuring secure transactions in a time when data security and privacy are major concerns. Traditional cryptography techniques, which depend on mathematical algorithms and secret keys, have historically protected against data breaches and illegal access. With the advent of quantum computers, traditional cryptography techniques are at risk. In this work, we present a cryptography idea using logical phi-bits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phi-bits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multi-phi-bit systems. The state vector of multiple phi-bits system lies in a complex exponentially scaling Hilbert space and is used to encode information or messages. By changing the driving conditions of the metamaterial, the information can be encrypted with exceptional security and efficiency. We illustrate experimentally the practicality and effectiveness of encoding and encryption of a message using a 5 phi-bits system and emphasize the scalability of this approach to an N phi-bits system with the same processing time.

Construction and Observation of Flexibly Controllable High-Dimensional Non-Hermitian Skin Effects.

Non-Hermitian skin effect (NHSE) is one of the most fundamental phenomena in non-Hermitian physics. It is established that 1D NHSE originates from the nontrivial spectral winding topology. However, the topological origin behind the higher-dimensional NHSE remains unclear, which poses a substantial challenge in constructing and manipulating high-dimensional NHSEs. Here, an intuitive bottom-to-top scheme to construct high-dimensional NHSEs is proposed, through assembling multiple independent 1D NHSEs. Not only the elusive high-dimensional NHSEs can be effectively predicted from the well-defined 1D spectral winding topologies, but also the high-dimensional generalized Brillouin zones can be directly synthesized from the 1D counterparts. As examples, two 2D nonreciprocal acoustic metamaterials are experimentally implemented to demonstrate highly controllable multi-polar NHSEs and hybrid skin-topological effects, where the sound fields can be frequency-selectively localized at any desired corners and boundaries. These results offer a practicable strategy for engineering high-dimensional NHSEs, which can boost advanced applications such as selective filters and directional amplifiers.

Observation of an acoustic topological Euler insulator with meronic waves.

Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling a new horizon in topological physics beyond the conventional paradigm. Here, we report on the first experimental realization of a topological Euler insulator phase with unique meronic characterization in an acoustic metamaterial. We demonstrate that this topological phase has several nontrivial features: First, the system cannot be described by conventional topological band theory, but has a nontrivial Euler class that captures the unconventional geometry of the Bloch bands in the Brillouin zone. Second, we uncover in theory and probe in experiments a meronic configuration of the bulk Bloch states for the first time. Third, using a detailed symmetry analysis, we show that the topological Euler insulator evolves from a non-Abelian topological semimetal phase via. the annihilation of Dirac points in pairs in one of the band gaps. With these nontrivial properties, we establish concretely an unconventional bulk-edge correspondence which is confirmed by directly measuring the edge states via. pump-probe techniques. Our work thus unveils a nontrivial topological Euler insulator phase with a unique meronic pattern and paves the way as a platform for non-Abelian topological phenomena.

Multi-Order Asymmetric Acoustic Metamaterials with Broad Bandgaps at Subwavelength Scales.

Noise manipulation at the subwavelength scale remains a challenging problem. To obtain better broadband sound isolation within the subwavelength range, a class of asymmetric acoustic metamaterials (AAMs) based on rotation is proposed, and this class of AAMs can further improve subwavelength sound isolation performance by introducing multi-orders. The influences of changing the alternate propagation length of the coiled channel and the square cavity in the unit cell on the band frequency distribution and the omnidirectional band structure were investigated. The effective parameters are calculated with the S-parameter retrieval method, and the generation and change mechanisms of the bandgaps were elucidated. The calculation of sound transmission characteristics showed that, in the asymmetric mode, the overall sound isolation performance of the structure was greatly improved, and the relative bandwidth expanded as the alternate propagation length of the coiled channel and square cavity increased. The omnidirectional bandgaps from the first-order to the third-order AAMs occupied 63.6%, 75.96%, and 76.84% of the subwavelength range, respectively. In particular, the first bandgap moves to the low frequency and becomes wider. Both the experimental results and numerical analyses consistently showed that disrupting structural symmetry enhances acoustic metamaterials for superior broadband sound isolation, inspiring broader applications for asymmetry in this field.

Multimodal Local Resonators for Low-Frequency Amelioration of Acoustic Black Holes.

Acoustic black holes (ABHs) are effective at suppressing vibrations at high frequencies, but their performance at low frequencies is limited. This paper aims to improve the low-frequency performance of ABH plates through the design of a metamaterial acoustic black hole (MMABH) plate. The MMABH plate consists of a double-layer ABH plate with a set of periodic local resonators installed between the layers. The resonators are tuned to the low-frequency peak points of the ABH plate, which are identified using finite element analysis. To dissipate vibration energy, the beams of the resonators are covered with damping layers. A modal analysis of the MMABH plate is performed, confirming its damping effect over a wide frequency band, especially at low frequencies.

Underwater acoustic metamaterials.

Acoustic metamaterials have been widely investigated over the past few decades and have realized acoustic parameters that are not achievable using conventional materials. After demonstrating that locally resonant acoustic metamaterials are capable of acting as subwavelength unit cells, researchers have evaluated the possibility of breaking the classical limitations of the material mass density and bulk modulus. Combined with theoretical analysis, additive manufacturing and engineering applications, acoustic metamaterials have demonstrated extraordinary capabilities, including negative refraction, cloaking, beam formation and super-resolution imaging. Owing to the complexity of impedance boundaries and mode transitions, there are still challenges in freely manipulating acoustic propagation in an underwater environment. This review summarizes the developments in underwater acoustic metamaterials over the past 20 years, which include underwater acoustic invisibility cloaking, underwater beam formation, underwater metasurfaces and phase engineering, underwater topological acoustics and underwater acoustic metamaterial absorbers. With the evolution of underwater metamaterials and the timeline of scientific advances, underwater acoustic metamaterials have demonstrated exciting applications in underwater resource development, target recognition, imaging, noise reduction, navigation and communication.

Metamaterials for Acoustic Noise Filtering and Energy Harvesting.

Artificial methods for noise filtering are required for the twenty-first century's Factory vision 4.0. From various perspectives of physics, noise filtering capabilities could be addressed in multiple ways. In this article, the physics of noise control is first dissected into active and passive control mechanisms and then further different physics are categorized to visualize their respective physics, mechanism, and target of their respective applications. Beyond traditional passive approaches, the comparatively modern concept for sound isolation and acoustic noise filtering is based on artificial metamaterials. These new materials demonstrate unique interaction with acoustic wave propagation exploiting different physics, which is emphasized in this article. A few multi-functional metamaterials were reported to harvest energy while filtering the ambient noise simultaneously. It was found to be extremely useful for next-generation noise applications where simultaneously, green energy could be generated from the energy which is otherwise lost. In this article, both these concepts are brought under one umbrella to evaluate the applicability of the respective methods. An attempt has been made to create groundbreaking transformative and collaborative possibilities. Controlling of acoustic sources and active damping mechanisms are reported under an active mechanism. Whereas Helmholtz resonator, sound absorbing, spring-mass damping, and vibration absorbing approaches together with metamaterial approaches are reported under a passive mechanism. The possible application of metamaterials with ventilation while performing noise filtering is reported to be implemented for future Smart Cities.

Acoustic Insulation Characteristics and Optimal Design of Membrane-Type Metamaterials Loaded with Asymmetric Mass Blocks.

Membrane-type acoustic metamaterials (MAMs) are the focus of the current research due to their lightweight, small size, and good low-frequency sound insulation performance. However, there exists difficulties for extensive application because of the narrow sound insulation band. In order to achieve broadband sound isolation under the premise of lightweight, a novel MAM with asymmetric rings is firstly proposed in this paper. The sound transmission loss (STL) of this MAM is calculated by an analytical method and is verified by the finite element model. The different properties of the membrane when it is loaded with one, two, or four mass blocks are analyzed. The comparison with the traditional MAM proves the superior performance of this novel MAM. Moreover, by discussing the influence of the eccentricity and distribution position of the masses on the results, the tunability of the sound insulation performance of this MAM is proven. Finally, the Isight platform is used to optimize the MAM to further improve the broadband sound insulation performance: the average STL of the MAM is improved by 15.7%, the bandwidth above 30 dB is improved by 11.5%, and the mass density is reduced by 30.01%.

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.

Chirality-switchable acoustic vortex emission via non-Hermitian selective excitation at an exceptional point.

Artificial structures provide an efficient method to generate acoustic vortices carrying orbital angular momentum (OAM) essential for applications ranging from object manipulation to acoustic communication. However, their flexibility in terms of chirality control has thus far been limited by the lack of reconfigurability and degrees of freedom like spin-orbit coupling. Here we show that this restriction can be lifted by controlling the individual on-off states of two coherent monopolar sources inside a passive parity-time-symmetric ring cavity at an exceptional point where the counter-propagating waves coalesce into one chiral eigenmode. One of the sources satisfies the chirality-reversal condition, generating a travelling wave field fully decoupled from and opposite to the chiral eigenmode, while the other source is phase-shifted such that the wave generated by the first source can be canceled out, and the remaining sound field circulates in the same direction as the chiral eigenmode. Such non-Hermitian selective excitation enables our experimental realization of acoustic vortex emission with switchable OAM but free of system reconfiguration. Our work offers opportunities for chiral sound manipulation as well as integrated and tunable acoustic OAM devices.

Observation of fractal higher-order topological states in acoustic metamaterials.

Topological phases of matter have been extensively investigated in solid-state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain almost unexplored. Fractals, being self-similar on different scales, are one of the intriguing complex geometries with non-integer dimensions. Here, we demonstrate fractal higher-order topological states with unprecedented emergent phenomena in a Sierpinski acoustic metamaterial. We uncover abundant topological edge and corner states in the acoustic metamaterial due to the fractal geometry. Interestingly, the numbers of the edge and corner states depend exponentially on the system size, and the leading exponent is the Hausdorff fractal dimension of the Sierpinski carpet. Furthermore, the results reveal the unconventional spectrum and rich wave patterns of the corner states with consistent simulations and experiments. This study thus unveils unconventional topological states in fractal geometry and may inspire future studies of topological phenomena in non-Euclidean geometries.

Viscoelastic reduced enhanced isotropic continua as acoustic metamaterials.

We consider a linear enhanced viscoelastic continuum of general nature but of specific type. Namely, we consider a reduced elastic continuum, satisfying Lagrange equations, where the strain energy depends on a certain (special) vectorial generalized coordinate, but does not depend on its gradient, and then add linear dissipation to the existing elastic connections. We may also represent this model as a 'bearing continuum', where all the connections are present (described by one vectorial generalized coordinate), enriched in each point by a 'distributed dynamic absorber' (described by 'special' vectorial generalized coordinate). We look for free harmonic waves in this infinite medium and obtain a reduced spectral problem for the vectorial generalized coordinate of the bearing continuum, for an arbitrary number of degrees of freedom. It was shown earlier that under certain symmetry conditions in the elastic case we obtain a single negative acoustic metamaterial, i.e. a medium that has band gaps. Further, we consider isotropic and gyrotropic reduced media, described by two three-dimensional vectorial generalized coordinates. First, we generalize results of previous studies for more complex elastic coupling, discovering a polarized shear wave, which has both bandgaps and zones of anomalous refraction. Then we introduce linear dissipation of different kinds. We find that viscosity yields in existence of travelling harmonic waves for all frequencies, possibly except for some points. Logarithmic decrement, infinite for the elastic material in bandgaps, becomes finite and decreases as the dissipation increases, at least for small viscosity. An important observation is: an infinitesimal dissipation in most cases transforms bandgaps into zones of travelling evanescent waves that partially are zones of anomalous refraction (decreasing parts of dispersion curves), where the medium is a double negative acoustic metamaterial. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Topological Supercavity Resonances in the Finite System.

Acoustic resonant cavities play a vital role in modern acoustical systems. The ultrahigh quality-factor resonances are highly desired for some applications such as high-resolution acoustic sensors and acoustic lasers. Here, a class of supercavity resonances is theoretically proposed and experimentally demonstrated in a coupled acoustic resonator system, arising from the merged bound states in the continuum (BICs) in geometry space. Their topological origin is demonstrated by explicitly calculating their topological charges before and after BIC merging, accompanied by charges annihilation. Compared with other types of BICs, they are robust to the perturbation brought by fabrication imperfection. Moreover, it is found that such supercavity modes can be linked with the Friedrich-Wintgen BICs supported by an entire rectangular (cuboid) resonator sandwiched between two rectangular (or circular) waveguides and thus more supercavity modes are constructed. Then, these coupled resonators are fabricated and such a unique phenomenon-moving, merging, and vanishing of BICs-is experimentally confirmed by measuring their reflection spectra, which show good agreement with the numerical simulation and theoretical prediction of mode evolution. The results may find exciting applications in acoustic and photonics, such as enhanced acoustic emission, filtering, and sensing.

Magnetoactive Acoustic Topological Transistors.

Topological field-effect transistor is a revolutionary concept that physical fields are used to switch on and off quantum topological states of the condensed matter. Although this emerging concept has been explored in electronics, how to realize it in the acoustic realm remains elusive. In this work, a class of magnetoactive acoustic topological transistors capable of on-demand switching on and off topological states and reconfiguring topological edges with external magnetic fields is presented. The key mechanism is to harness magnetic fields to tune air-cavity volumes within acoustic chambers, thus breaking or preserving the inversion symmetry to manifest or conceal the quantum valley Hall effect. To switch the topological transport beyond the in-plane routes, a magneto-tuned non-topological band gap to allow or forbid the wave transport out-of-plane is harnessed. With the reversible magnetic control, on-demand switching of topological routes to realize topological field-effect waveguides and wave regulators is demonstrated. Analogous to the impact of semiconductor transistors on modern electronics, this work may expand the scope of topological acoustics by achieving unprecedented functions in acoustic modulation.

Acoustic Insulation Mechanism of Membrane-Type Acoustic Metamaterials Loaded with Arbitrarily Shaped Mass Blocks of Variable Surface Density.

Membrane-type acoustic metamaterials (MAMs) have recently received widespread attention due to their good low-frequency sound-transmission-loss (STL) performance. A fast prediction method for the STL of rectangular membranes loaded with masses of arbitrary shapes and surface density values is proposed as a semi-analytical model for calculating the STL of membrane-type acoustic metamaterials. Through conformal mapping theory, the mass blocks of arbitrary shapes were transformed into regular shapes, which simplified the calculation model of acoustic propagation loss prediction, and the prediction results were verified by finite element simulations. The results show that the change in mass surface density was closely related to the size and frequency distribution of STL. The influence of the mass center on the STL and characteristic frequency of the film metamaterial is discussed.

Low-Frequency Bandgaps of the Lightweight Single-Phase Acoustic Metamaterials with Locally Resonant Archimedean Spirals.

In order to achieve the dual needs of single-phase vibration reduction and lightweight, a square honeycomb acoustic metamaterials with local resonant Archimedean spirals (SHAMLRAS) is proposed. The independent geometry parameters of SHAMLRAS structures are acquired by changing the spiral control equation. The mechanism of low-frequency bandgap generation and the directional attenuation mechanism of in-plane elastic waves are both explored through mode shapes, dispersion surfaces, and group velocities. Meanwhile, the effect of the spiral arrangement and the adjustment of the equation parameters on the width and position of the low-frequency bandgap are discussed separately. In addition, a rational period design of the SHAMLRAS plate structure is used to analyze the filtering performance with transmission loss experiments and numerical simulations. The results show that the design of acoustic metamaterials with multiple Archimedean spirals has good local resonance properties, and forms multiple low-frequency bandgaps below 500 Hz by reasonable parameter control. The spectrograms calculated from the excitation and response data of acceleration sensors are found to be in good agreement with the band structure. The work provides effective design ideas and a low-cost solution for low-frequency noise and vibration control in the aeronautic and astronautic industries.