Locally resonant sonic materials

Design and Robustness Evaluation of Valley Topological Elastic Wave Propagation in a Thin Plate with Phononic Structure

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic band and its robustness assessment in an elastic regime are still missing, hampering the realization of topological acoustic devices. We adopted a snowflake-like structure for the crystal unit cell and determined the optimal structure that exhibited the topological phase transition of the planar phononic crystal by changing the unit cell structure. The bandgap width could be adjusted by varying the length of the snow-side branch, and a topological phase transition occurred in the unit cell structure with threefold rotational symmetry. Elastic waveguides based on edge modes appearing at interfaces between crystals with different band topologies were designed, and their transmission efficiencies were evaluated numerically and experimentally. The results demonstrate the robustness of the elastic wave propagation in thin plates. Moreover, we experimentally estimated the backscattering length, which measures the robustness of the topologically protected propagating states against structural inhomogeneities. The results quantitatively indicated that degradation of the immunization against the backscattering occurs predominantly at the corners in the waveguides, indicating that the edge mode observed is a relatively weak topological state.

Constant intensity acoustic propagation in the presence of non-uniform properties and impedance discontinuities: Hermitian and non-Hermitian solutions

Propagation of sound through a non-uniform medium without scattering is possible, in principle, if the density and acoustic compressibility assume complex values, requiring passive and active mechanisms, also known as Hermitian and non-Hermitian solutions, respectively. Two types of constant intensity wave conditions are identified: in the first, the propagating acoustic pressure has constant amplitude, while in the second, the energy flux remains constant. The fundamental problem of transmission across an impedance discontinuity without reflection or energy loss is solved using a combination of monopole and dipole resonators in parallel. The solution depends on an arbitrary phase angle that can be chosen to give a unique acoustic metamaterial with both resonators undamped and passive, requiring purely Hermitian acoustic elements. For other phase angles, one of the two elements must be active and the other passive, resulting in a gain/loss non-Hermitian system. These results prove that uni-directional and reciprocal transmission through a slab separating two half spaces is possible using passive Hermitian acoustic elements without the need to resort to active gain/loss energetic mechanisms.

Omnidirectional acoustic cloaking against airborne sound realized by a locally resonant sonic material

We report that a locally resonant sonic material realizes omnidirectional acoustic invisibility in air. To achieve acoustic cloaking in the low-frequency regime, we axisymmetrically placed elastic rods comprised of silicone rubber and lead around a cloaked object. The radii of the rods are designed to minimize their total scattering cross section for a given frequency. The optimization is performed using an algorithm incorporating multiple scattering theory and gradient-based nonlinear programming. We numerically confirmed that the designed cloaking device suppressed the scattering cross section by almost 92% for all incident directions at the target frequency.

Metamaterial shields for inner protection and outer tuning through a relaxed micromorphic approach

In this paper, a coherent boundary value problem to model metamaterials' behaviour based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility of exploring the scattering patterns of finite-size metamaterial specimens. Thanks to the simplified model's structure (few frequency- and angle-independent parameters), we are able to unveil the scattering metamaterial's response for a wide range of frequencies and angles of propagation of the incident wave. These results are an important stepping stone towards the conception of more complex large-scale meta-structures that can control elastic waves and recover energy. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

A simple model for elastic wave propagation in hard sphere-filled random composites

A simple model is proposed to study wave propagation in hard sphere-reinforced elastic random composites. Compared to existing related models, the proposed model is featured by a modified form of classical elastodynamic equations in which the inertia term is substituted by the acceleration field of the mass centre of a representative unit cell, supplied with a derived simple differential relation between the displacement field of the composite and the displacement field of the mass centre of a representative unit cell. The present model enjoys conceptual and mathematical simplicity although it is restricted to hard sphere-filled elastic composites in which the elastic moduli of embedded spheres are much (at least 4-5 times) stiffer than those of a softer matrix. Explicit formulas are derived for the attenuation coefficient and the effective phase velocity of plane longitudinal P-waves and transverse S-waves. The efficiency and reasonable accuracy of the present model are demonstrated by reasonably good agreement between the predicted results and some established known data. The proposed model could offer a potential general method to study various three-dimensional dynamic problems of hard sphere-filled elastic random composites.

Unidirectional edge modes in time-modulated metamaterials

We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponding to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-modulation amplitude are illustrated by several numerical simulations.

Photo-responsive hydrogel-based re-programmable metamaterials

This paper explores a novel programmable metamaterial using stimuli-responsive hydrogels with a demonstration of bandgap formation and tuning. Specifically, a photo-responsive hydrogel beam that can achieve re-programmable periodicity in geometric and material properties through patterned light irradiation is designed. Hydrogels consist of polymeric networks and water molecules. Many unique properties of hydrogels, including bio-compatibility, stimuli-responsiveness, and low dissipation make them ideal for enabling re-programmable metamaterials for manipulating structural dynamic response and wave propagation characteristics. Bandgap generation and tunability in photo-responsive hydrogel-based metamaterial (in the form of a diatomic phononic chain) as well as the effects of system parameters such as light exposure pattern and photo-sensitive group concentration on the bandgap width and center frequency are systematically studied. In agreement with finite-element model simulations, it is observed that an increase in light exposure region size reduces both the bandgap width and center frequency, while an increase in the concentration of photo-sensitive group increases bandgap width, attenuation and reduces its center frequency. This work unveils the potential of stimuli-response hydrogels as a new class of low-loss soft metamaterials, unlike most other soft materials that are too lossy to sustain and exploit wave phenomena.

A Comparative Study and Analysis of Layered-Beam and Single-Beam Metamaterial Structures: Transmissibility Bandgap Development

Recently, layered-beam metamaterial structures have been gaining popularity in a variety of engineering applications including energy harvesting and vibration isolation. While both single-beam metamaterial structures and layered-beam metamaterial structures are capable of generating bandgaps, it is important to understand the limitations of each type of metamaterial structure in order to make informed design decisions. In this article, a comparative study of bandgap development in single-beam metamaterial structures and layered-beam metamaterial structures is presented. The results show that for the single-beam metamaterial structure, with equally spaced local resonator designs, only one significant bandgap is developed at approximately 300–415 Hz. This bandgap occurs near the resonant frequency of the local resonators, i.e., 309 Hz. The results also show that when the spacing and the design of the local resonators are desired to remain fixed, layering the horizontal beams offers a significant pathway for both lowering the bandgap and developing additional bandgaps. The double-layered beam-type metamaterial structure studied in this work generates two bandgaps at approximately 238–275 Hz and 298–410 Hz. When the goal is to keep the number of local resonators per beam constant, increasing the length of the unit cells offers an alternative technique for lowering the bandgaps.

Three-dimensional heating and patterning dynamics of particles in microscale acoustic tweezers

Acoustic tweezers facilitate a noninvasive, contactless, and label-free method for the precise manipulation of micro objects, including biological cells. Although cells are exposed to mechanical and thermal stress, acoustic tweezers are usually considered as biocompatible. Here, we present a holistic experimental approach to reveal the correlation between acoustic fields, acoustophoretic motion and heating effects of particles induced by an acoustic tweezer setup. The system is based on surface acoustic waves and was characterized by applying laser Doppler vibrometry, astigmatism particle tracking velocimetry and luminescence lifetime imaging. In situ measurements with high spatial and temporal resolution reveal a three-dimensional particle patterning coinciding with the experimentally assisted numerical result of the acoustic radiation force distribution. In addition, a considerable and rapid heating up to 55 °C depending on specific parameters was observed. Although these temperatures may be harmful to living cells, counter-measures can be found as the time scales of patterning and heating are shown to be different.

A Review of Recent Research into the Causes and Control of Noise during High-Speed Train Movement

Since the invention of the train, the problem of train noise has been a constraint on the development of trains. With increases in train speed, the main noise from high-speed trains has changed from rolling noise to aerodynamic noise, and the noise level and noise frequency range have also changed significantly. This paper provides a comprehensive overview of recent advances in the development of high-speed train noise. Firstly, the train noise composition is summarized; next, the main research methods for train noise, which include real high-speed train noise tests, wind tunnel tests, and numerical simulations, are reviewed and discussed. We also discuss the current methods of noise reduction for trains and summarize the progress in current research and the limitations of train body panels and railroad sound barrier technology. Finally, the article introduces the development and potential future applications of acoustic metamaterials and proposes application scenarios of acoustic metamaterials for the specific needs of railroad sound barriers and train car bodies. This synopsis provides a useful platform for researchers and engineers to cope with problems of future high-speed rail noise in the future.

Broadband Sound Insulation and Dual Equivalent Negative Properties of Acoustic Metamaterial with Distributed Piezoelectric Resonators

Aiming at the unsatisfactory sound transmission loss (STL) of thin-plate structures in the low-mid frequency range, this paper proposes an acoustic insulation metamaterial with distributed piezoelectric resonators. A complete acoustic prediction model is established based on the effective medium method and classical plate theory, and the correctness is verified by the STL simulation results of the corresponding acoustic-structure fully coupled finite-element model. Moreover, the intrinsic relationship between the dual equivalent negative properties and STLs is investigated to reveal the insulation mechanisms of this metamaterial. Then, the influence of the geometric and material parameters on the double equivalent negative characteristics is studied to explore the broadband STL for distributed multi-modal resonant energy-dissipation modes in the frequency band of interest. The results show that the two acoustic insulation crests correspond to the dual equivalent negative performances, and the sound insulation in the low-mid frequency range is improved by more than 5 dB compared with that of the substrate, even up to 44.49 dB.

Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension

In this study, a new type of 2D piezoelectric phononic crystal with a square hollow and convex structures is designed and established. A theoretical study of the piezoelectric phononic crystal is presented in this article to investigate the transmission properties of waves in terms of complex dispersion relations. Based on the finite discretization technique and plane wave expansion, the formula derivation of the real band structure is achieved as well as the complex band diagrams are obtained. The numerical results are presented to demonstrate the multiple broadband complete bandgaps produced by the designed piezoelectric phononic crystal and the propagation characteristics of the elastic waves for different directions. In addition, the transmission loss in the ΓX direction is calculated to verify the band structure. Finally, the effects of the thickness and the square hollow side length on the band structure are discussed.

Deeply subwavelength giant monopole elastodynamic metacluster resonators

The giant monopole resonance is a well-known phenomenon, employed to tune the dynamic response of composite materials comprising voids in an elastic matrix which has a bulk modulus much greater than its shear modulus, e.g. elastomers. This low frequency resonance (e.g. λp/a≈100 for standard elastomers, where λp and a are the compressional wavelength and void radius, respectively) has motivated acoustic material design over many decades, exploiting the subwavelength regime. Despite this widespread use, the manner by which the resonance arising from voids in close proximity is affected by their interaction is not understood. Here, we illustrate that for planar elastodynamics (circular cylindrical voids), coupling due to near-field shear significantly modifies the monopole (compressional) resonant response. We show that by modifying the number and configuration of voids in a metacluster, the directionality, scattering amplitude and resonant frequency can be tailored and tuned. Perhaps most notably, metaclusters deliver a lower frequency resonance than a single void. For example, two touching voids deliver a reduction in resonant frequency of almost 16% compared with a single void of the same volume. Combined with other resonators, such metaclusters can be used as meta-atoms in the design of elastic materials with exotic dynamic material properties.

Analysis of Floquet Waves in Periodic Multilayered Isotropic Media with the Method of Reverberation-Ray Matrix

The in-plane elastic waves in periodically multilayered isotropic structures, which are decoupled from the out-of-plane waves, are represented mainly by the frequency–wavenumber spectra and occasionally by the frequency–phase velocity spectra as well as being studied predominantly for periodic bi-layered media along and perpendicular to the thickness direction in the existing research. This paper investigates their comprehensive dispersion characteristics along arbitrary in-plane directions and in entire (low and high) frequency ranges, including the frequency–wavelength, wavenumber–phase velocity, wavelength–phase velocity spectra, the dispersion surfaces and the slowness curves with fixed frequencies, as well as the frequency–wavenumber and frequency–phase velocity spectra. Specially, the dispersion surfaces and the slowness curves completely reflect the propagation characteristics of in-plane waves along all directions. First, the method of reverberation-ray matrix (MRRM) combined with the Floquet theorem is extended to derive the dispersion equation of in-plane elastic waves in general periodic multilayered isotropic structures by means of the elastodynamic theory of isotropic materials and the state space formalism of layers. The correctness of the derivation and the numerical stability of the method in both low and high frequency ranges, particularly its superiority over the method of the transfer matrix (MTM) within the ranges near the cutoff frequencies, are verified by several numerical examples. From these demonstrations for periodic octal- and bi-layered media, the comprehensive dispersion curves are provided and their general characteristics are summarized. It is found that although the frequencies associated with the dimensionless wavenumber along thickness ql=nπ (n is an integer) are always the demarcation between pass and stop bands in the case of perpendicular incident wave, but this is not always exist in the case of the oblique incident wave due to the coupling between the two modes of in-plane elastic waves. The slowness curves with fixed frequencies of Floquet waves in periodically multilayered isotropic structures, as compared to their counterpart of body waves in infinite isotropic media obtained from the Christoffel equation now have periodicity along the thickness direction, which is consistent to the configuration of the structures. The slowness curves associated with higher frequencies have a smaller minimum positive period and have more propagation modes due to the cutoff properties of these additional modes.

A multiple scattering formulation for finite-size flexural metasurfaces

We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident wave generated by a harmonic source and the scattered fields induced by the flexural motion of the plates. The scattered field generated by each plate is calculated using an ad-hoc set of Green’s functions. The interaction between the incident field and the scattered fields is modelled through a multiple scattering formulation. Owing to the introduction of the multiple scattering formalism, the proposed technique can handle a generic set of plates arbitrarily arranged on the half-space surface. The method is validated via comparison with finite element simulations considering Rayleigh waves interacting with a single and a collection of thin plates. Our framework can be used to investigate the interaction of vertically polarized surface waves and flexural resonators in different engineering contexts, from the design of novel surface acoustic wave devices to the interpretation of urban vibration problems.

Sound Transmission Loss of Metamaterial Honeycomb Core Sandwich Plate Elastically Connected with Periodic Subwavelength Arrays of Shunted Piezoelectric Patches

Honeycomb core sandwich plates are widely used as a lightweight, high-strength sound insulation material. However, they do not perform well in specific frequency bands. Acoustic metamaterials can break the law of mass in specific frequency bands and have high sound transmission loss (STL); however, the resonance frequency is difficult to regulate. To solve this problem, this paper first proposes an infinitely large metamaterial honeycomb core sandwich plate, which can generate newly tuned piezoelectric resonance frequencies, and we study its STL. The structure has piezoelectric patches arranged in sub-wavelength arrays with inductance shunting circuits that are elastically connected to both sides of the honeycomb core sandwich plate. The effective dynamic mass density and effective dynamic bending stiffness of the metamaterial plates were obtained using the effective medium (EM) method. A theoretical model for the numerical calculation of oblique STL and diffuse-field STL was established by the structural bending wave method. The finite element simulation method was used to verify that the metamaterial plates can generate three peaks at 1147 Hz, 1481 Hz and 1849 Hz in oblique or diffuse-field STL curves, which reached 57 dB, 86 dB and 63 dB, respectively, and are significantly better than the plate rigidly connected with piezoelectric sheets and the bare plate with the same mass. In order to better understand the characteristics of STL, the explicit functions of the resonance frequencies were derived. Key influencing factors were analyzed, and the regulation law of new piezoelectric resonance frequencies was clarified.

Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators

The wave propagation and vibration transmission in metamaterial-based elastic rods with periodically attached multi-degree-of-freedom (MDOF) dynamic anti-resonant vibration isolator (DAVI) resonators are investigated. A methodology based on a combination of the transfer matrix (TM) method and the Bloch theorem is developed, yielding an explicit formulation for the complex band structure calculation. The bandgap behavior of the periodic structure arrayed with single-degree-of-freedom (SDOF) DAVI resonators and two-degree-of-freedom (2DOF) DAVI resonators are investigated, respectively. A comparative study indicates that the structure consisting of SDOF DAVI resonators periodically jointed on the metamaterial-based elastic rod can obtain an initial locally resonant band gap 500 Hz smaller than the one given in the published literature. The periodic structure containing 2DOF DAVI resonators has an advantage over the periodic structure with SDOF DAVI resonators in achieving two resonance band gaps. By analyzing the equivalent dynamic mass of a DAVI resonator, the underlying mechanism of achieving a lower initial locally resonant band gap by this periodic structure is revealed. The parameters of the 2DOF DAVI resonator are optimized to obtain the lowest band gap of the periodic structure. The numerical results show that, with the optimal 2DOF DAVI parameters, the periodic structure can generate a much lower initial locally resonant band gap compared with the case before the optimization.

Scattering Properties of an Acoustic Anti-Parity-Time-Symmetric System and Related Fabry–Perot Resonance Mode

The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time (PT) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry–Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-PT-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-PT-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-PT-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry–Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-PT-symmetric system and the design of associated bidirectional response prototype devices.

Influence Mechanism of a New-Style Resonator on Band Gap of Locally Resonant Phononic Crystal Double Panel Structure

Based on the previous studies on the stubbed-on locally resonant phononic crystal (LRPC) double panel structure (DPS) made of a two-dimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower plates, the stubbed-on LRPC DPS with soft shell surrounded and simplified model with additional springs surrounded are proposed. According to the changes in structural form, the wider band gap is opened, and the novel formation mechanism of the band gap is revealed. Finite element method (FEM) is applied to calculate the band structures. Numerical results and further analysis demonstrate that the soft shell only affects the bands corresponding to symmetric vibration mode and makes the bands shift up. In addition, the influences of density and Poisson’s ratio of soft shell on the band gap can be ignored, but the starting frequency keeps still, and band gap width increases first and then keeps constant with the increase of elasticity modulus. All the results provide a theoretical basis for the study of vibration and noise resistance in engineering.

Low-Frequency Low-Reflection Bidirectional Sound Insulation Tunnel with Ultrathin Lossy Metasurfaces

We report both numerical and experimental constructions of a tunnel structure with low-frequency low-reflection bidirectional sound insulation (BSI). The designed tunnel was constructed from a pair of lossy acoustic metasurfaces (AMs), which consists of six ultrathin coiled unit cells, attached on both sides. Based on the generalized Snell′s law and phase modulations for both AMs, the tunnel with the low-frequency BSI was constructed based on sound reflections and acoustic blind areas created by the AMs. The obtained transmittances were almost the same for sound incidences from both sides and were lower than −10 dB in the range 337–356 Hz. The simulated and measured results agreed well with each other. Additionally, we show that the low-reflection characteristic of the tunnel can be obtained simultaneously by thermoviscous energy loss in coiled channels of the unit cells. Finally, an interesting application of the designed tunnel in an open-window structure with low-frequency low-reflection BSI is further simulated in detail. The proposed tunnel based on the ultrathin lossy AMs has the advantages of ultrathin thickness (about λ/35), low-frequency low-reflection BSI, and high-performance ventilation, which may have potential applications in architectural acoustics and noise control.

Waves Propagating in Nano-Layered Phononic Crystals with Flexoelectricity, Microstructure, and Micro-Inertia Effects

The miniaturization of electronic devices is an important trend in the development of modern microelectronics information technology. However, when the size of the component or the material is reduced to the micro/nano scale, some size-dependent effects have to be taken into account. In this paper, the wave propagation in nano phononic crystals is investigated, which may have a potential application in the development of acoustic wave devices in the nanoscale. Based on the electric Gibbs free energy variational principle for nanosized dielectrics, a theoretical framework describing the size-dependent phenomenon was built, and the governing equation as well as the dispersion relation derived; the flexoelectric effect, microstructure, and micro-inertia effects are taken into consideration. To uncover the influence of these three size-dependent effects on the width and midfrequency of the band gaps of the waves propagating in periodically layered structures, some related numerical examples were shown. Comparing the present results with the results obtained with the classical elastic theory, we find that the coupled effects of flexoelectricity, microstructure, and micro-inertia have a significant or even dominant influence on the waves propagating in phononic crystals in the nanoscale. With increase in the size of the phononic crystal, the size effects gradually disappear and the corresponding dispersion curves approach the dispersion curves obtained with the conventional elastic theory, which verify the results obtained in this paper. Thus, when we study the waves propagating in phononic crystals in the micro/nano scale, the flexoelectric, microstructure, and micro-inertia effects should be considered.

Ultra-Broadband Bending Beam and Bottle Beam Based on Acoustic Metamaterials

We report the realization of an ultra-broadband bending beam based on acoustic metamaterials by the theoretical prediction and the numerical validation. The proposed structure is composed of a series of straight tubes with spatially modulated depths. We analytically derive the depth profile required for the generation of an ultra-broadband bending beam, and examine the performance of the metastructure numerically. The design is then extended for the generation of a three-dimensional bottle beam. The transverse trapping behaviours on small rigid objects by the bottle beam are investigated based on the force potential. Our work will help the further study of broadband acoustic meta-structures, and may also find applications in a variety of fields such as ultrasound imaging, health monitoring and particle manipulations.

Extremely low frequency wave localization via elastic foundation induced metamaterial with a spiral cavity

We proposed a metamaterial which exhibits elastic wave localization at extremely low frequencies. First, we opened an extremely low bandgap via elastic foundations. Subsequently, we investigated wave localization by imposing normal defect, which is widely used to capture waves in conventional wave localization systems. However, there were limitations: wave localization was not achieved when a weak bandgap is generated, and the operating frequency of localization is still in the upper part of the bandgap. To overcome wave localization via the normal defect, we proposed a novel metamaterial with a spiral cavity which can tune the resonating frequency depending on the length of the spiral path. By imposing on the spiral cavity inside the elastic foundation-induced metamaterial, we can shift the resonating frequency of the cavity down. Finally, we carried out wave simulations, not only to support the previous eigenfrequency study for the supercell, but also to verify that the finite-size metamaterial can also achieve wave localization at the extremely low frequencies. Through wave simulations, we could observe wave localization even at 77.3 Hz, which is definitely the lower part of the extremely low bandgap.

Achieving Enhanced Sound Insulation through Micromembranes-Type Acoustic Metamaterials

Acoustic micromembranes (AμMs) are attracting more and more attention due to their unparalleled light weight but high sound transmission loss (STL) at low frequencies. Previous works showed that AμMs feature remarkable sound insulation compared to homogeneous plates with the same surface mass density, while some follow-up works claimed that the outstanding insulation capability of small AμMs samples disappears when the sample size grows. To uncover the working mechanisms underpinning the unique behavior of AμMs, in this paper, we present theoretical and numerical studies of AμMs that couple the vibrations of the supporting frame and the AμMs within the lattice. The results show how the global response in the STL of the AμMs assembly is related to the geometrical parameters of AμMs cells and the lattice. This study provides a theoretical foundation for designing a large-scale yet high-insulation assembly of AμMs, and paves the way for applying AμMs for blocking low-frequency noise.

Acoustic Equivalent Lasing and Coherent Perfect Absorption Based on a Conjugate Metamaterial Sphere

Acoustic conjugate metamaterials (ACMs), in which the imaginary parts of the effective complex mass density and bulk compressibility are cancelled out in the refractive index, possess the elements of loss and gain simultaneously. Previous works have focused on panel ACMs for plane wave incidence. In this paper, we explore the extraordinary scattering properties, including the acoustic equivalent lasing (AEL) and coherent perfect absorption (CPA) modes, of a three-dimensional ACM sphere, where incident spherical waves with specific topological orders could be extremely scattered and totally absorbed, respectively. Theoretical analysis and numerical simulations show that the AEL or CPA mode with a single order can be realized with a small monolayer ACM sphere with appropriate parameters. A huge (relative to incident wavelength) ACM sphere with pure imaginary parameters could support the even- (or odd-) order AEL and odd- (or even-) order CPA modes simultaneously. In addition, the AEL and/or CPA with multiple orders could be realized based on a small multilayered ACM sphere. The proposed ACM sphere may provide an alternative method to design acoustic functional devices, such as amplifiers and absorbers.

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation

Structural vibration induced by low frequency elastic waves presents a great threat to infrastructure such as buildings, bridges, and nuclear structures. In order to reduce the damage of low frequency structural vibration, researchers proposed the structure of seismic metamaterial, which can be used to block the propagation of low frequency elastic wave by adjusting the frequency range of elastic wave propagation. In this study, based on the concept of phononic crystal, a ternary seismic metamaterial is proposed to attenuate low frequency vibration by generating band gaps. The proposed metamaterial structure is periodically arranged by cube units, which consist of rubber coating, steel scatter, and soft matrix (like soil). The finite element analysis shows that the proposed metamaterial structure has a low frequency band gap with 8.5 Hz bandwidth in the range of 0-20 Hz, which demonstrates that the metamaterial can block the elastic waves propagation in a fairly wide frequency range within 0-20 Hz. The frequency response analysis demonstrates that the proposed metamaterial can effectively attenuate the low frequency vibration. A simplified equivalent mass-spring model is further proposed to analyze the band gap range which agrees well with the finite element results. This model provides a more convenient method to calculate the band gap range. Combining the proposed equivalent mass-spring model with finite element analysis, the effect of material parameters and geometric parameters on the band gap characteristic is investigated. This study can provide new insights for low frequency vibration attenuation.

Flexible Manipulation of the Reflected Wavefront Using Acoustic Metasurface with Split Hollow Cuboid

This work proposes a method for actively constructing acoustic metasurface (AMS) based on the split hollow cuboid (SHC) structure of local resonance, with the designed AMS flexibly manipulating the direction of reflected acoustic waves at a given frequency range. The AMS was obtained by precisely adjusting any one or two types of structural parameters of the SHC unit, which included the diameter of the split hole, the length, width, height, and shell thickness of the SHC. The simulation results showed that the AMS can flexibly manipulate the direction of the reflected acoustic waves, and the anomalous reflection angle obeys the generalized Snell’s law. Furthermore, among the five structural parameters, the AMS’s response frequency band is widest with the hole diameter and height, followed by the length and width, and narrowest with the shell thickness. It is worth noting that comprehensive manipulation of two parameters not only broadens the response frequency band, but also strengthens the effect of the anomalous reflection at the same response frequency. The subwavelength size of the AMS constructed with such a comprehensive method has the advantages of a small size, wide response band, simple preparation, and flexible modulation, and can be widely used in various fields, such as medical imaging and underwater stealth.

A transfer matrix method for calculating the transmission and reflection coefficient of labyrinthine metamaterials

Labyrinthine unit cells have existed for many years and have been central to the design of numerous metamaterial solutions. However, the literature does not present a reproducible analytical model to predict their behaviour both in transmission and reflection, thus limiting design optimization in terms of bandwidth of operation and space occupied. In this work, we present an analytical model based on the transfer matrix method for phase shift and intensity of transmission/reflection-based labyrinthine unit cells. We benchmark our analytical model by finding agreement with finite element method simulations - using commercial software - within 1 dB in amplitude and a 1° in phase. Finally, we compare our predictions with measurements on transmissive/reflective units with 4 and 6 horizontal baffles ("bars"), using different experimental methods. We found that some of the measurement methods lead to an agreement within 2 dB, while others are completely out of range, thus pointing out the challenges in characterizing this type of acoustic metamaterial.

A metamaterial ultrasound mode convertor for complete transformation of Lamb waves into shear horizontal waves

This article reports a new mechanism involving a non-perforated resonant elastic metamaterial to achieve the complete conversion of Lamb waves (A₀ and S₀) into the fundamental shear horizontal (SH₀) wave. The proposed metamaterial ultrasound mode convertor is studied via the observation of the special resonant shear motion of its unit cells, initiating with a conventional additive stub design. Thereafter, such a stubbed structure is further modified to fully couple the Lamb modes with the shear horizontal stub motion. By investigating the band structure of the metamaterial unit cell through modal analysis and tuning the shear resonant motions, a complete SH₀ mode generation band within the simultaneous Lamb modes bandgap can be established in a wide frequency range. Such a special bandgap situation enables the complete mode conversion from Lamb waves into shear horizontal waves. The transformation capability of the proposed ultrasound mode convertor is further substantiated via the harmonic analysis of metamaterial chain model, showcasing the frequency spectrum of the transmitted wave modes. The optimal configuration is determined by conducting a parametric study to identify the most effective mode conversion performance. Finally, a coupled-field transient finite element simulation is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis of the transmitted wave field illuminates the successful realization of the mode conversion behavior. Experimental demonstrations are presented to validate the numerical predictions. The proposed complete mode conversion capability may possess great potential for wave control and manipulation.

Quantization of Acoustic Modes in Dumbbell Nanoparticles

The vibrational eigenmodes of dumbbell-shaped polystyrene nanoparticles are recorded by Brillouin light spectroscopy (BLS), and the full experimental spectra are calculated theoretically. Different from spheres with a degeneracy of (2l+1), with l being the angular momentum quantum number, the eigenmodes of dumbbells are either singly or doubly degenerate owing to their axial symmetry. The BLS spectrum reveals a new, low-frequency peak, which is attributed to the out-of-phase vibration of the two lobes of the dumbbell. The quantization of acoustic modes in these molecule-shaped dumbbell particles evolves from the primary colloidal spheres as the separation between the two lobes increases.

Mechanical Shunt Resonators-Based Piezoelectric Metamaterial for Elastic Wave Attenuation

The conventional piezoelectric metamaterials with operational-amplifier-based shunt circuits have limited application due to the voltage restriction of the amplifiers. In this research, we report a novel piezoelectric metamaterial beam that takes advantage of mechanical shunt resonators. The proposed metamaterial beam consisted of a piezoelectric beam and remote mechanical piezoelectric resonators coupled with electrical wires. The local resonance of the remote mechanical shunt resonators modified the mechanical properties of the beam, yielding an elastic wave attenuation capability. A finite-length piezoelectric metamaterial beam and mechanical shunt resonators were considered for conceptual illustration. Significant elastic wave attenuation can be realized in the vicinity of the resonant frequency of the shunt resonators. The proposed system has the potential in the application of wave attenuation under large-amplitude excitations.

Monochannel Demultiplexer Phononic Crystal Slab Based on Hollow Pillars

A mono-channel waveguide with alternate hollow pillars of different radius to passively select and reject particular frequencies for filtering applications are numerically simulated based on the Finite Element Method (FEM). The waves are guided while the frequencies can be filtered according to pillar inner radius as its waveguiding mechanism. The computations of dispersion relation, transmission coefficient and stress displacement profile of the waveguides were carried out to understand the propagation behaviour of elastic waves on the waveguide structure. The proposed model shows a complete bandgap around 700 kHz, while its respective blocking phenomenon is demonstrated using square-ring shapes. The introduction of defect lines in linear and L-Shaped form enables a tailorable frequency shift within the bandgap region with optimized inner radius of hollow pillar. The proposed model eliminates the need for a multi-channel filtering system with conventional several separated lines thus reduces the dimension of filtering device.

Parametric Optimization of Local Resonant Sonic Crystals Window on Noise Attenuation by Using Taguchi Method and ANOVA Analysis

Local resonant sonic crystals (LRSCs) window as a novel design has recently been proposed to achieve a good balance between noise mitigation, natural ventilation and natural lighting. In an effort to explore the feasibilities of such designs in civil residential buildings, an optimization methodology was proposed to develop a more compact LRSCs window with high noise attenuation performance in the present study. Specifically, the Taguchi method was adopted for the design of experiments on the parameters of interest and their corresponding levels, and SN ratio analysis was then applied for the parametric evaluations on the noise attenuation on specified frequencies in traffic noise (concentrated sound energy frequency range: 630–1000 Hz). Three optimal sets of design parameters on the interested frequencies, namely, 630 Hz, 800 Hz and 1000 Hz were obtained. ANOVA analysis was conducted to quantificationally identify the design parameters with statistical significance and remarkable contribution to the desired performance. Results indicate that the slit size has the most significant influence on the overall noise attenuation performance, followed by cavity width. An optimal set of design parameters to achieve the overall best noise reduction performance in the frequency range of 630–1000 Hz was finally determined by combining the SN ratio and ANOVA analysis. A prototype of the final optimized LRSCs window was then fabricated and tested in a semi-anechoic chamber. Good agreement was found between the experiment and numerical simulation. In comparison to the benchmark case, the final optimized design can achieve a further noise reduction by 2.84 dBA, 3.48 dBA and 5.56 dBA for the frequencies of 630 Hz, 800 Hz and 1000 Hz, respectively. The overall noise reduction for the interested frequency range can be promoted by 3.28 dBA. The results indicate that the proposed optimization methodology is practical and efficient in designing a high-performance LRSCs window or improving similar applications.

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.

Intelligent on-demand design of phononic metamaterials

With the growing interest in the field of artificial materials, more advanced and sophisticated functionalities are required from phononic crystals and acoustic metamaterials. This implies a high computational effort and cost, and still the efficiency of the designs may be not sufficient. With the help of third-wave artificial intelligence technologies, the design schemes of these materials are undergoing a new revolution. As an important branch of artificial intelligence, machine learning paves the way to new technological innovations by stimulating the exploration of structural design. Machine learning provides a powerful means of achieving an efficient and accurate design process by exploring nonlinear physical patterns in high-dimensional space, based on data sets of candidate structures. Many advanced machine learning algorithms, such as deep neural networks, unsupervised manifold clustering, reinforcement learning and so forth, have been widely and deeply investigated for structural design. In this review, we summarize the recent works on the combination of phononic metamaterials and machine learning. We provide an overview of machine learning on structural design. Then discuss machine learning driven on-demand design of phononic metamaterials for acoustic and elastic waves functions, topological phases and atomic-scale phonon properties. Finally, we summarize the current state of the art and provide a prospective of the future development directions.

Controlling terahertz sound propagation: some preliminary Inelastic X-Ray Scattering result

The control of sound propagation in materials via the design of their elastic properties is an exciting task at the forefront of Condensed Matter. It becomes especially compelling at terahertz frequencies, where phonons are the primary conveyors of heat flow. Despite the increasing focus on this goal, this field of research is still in its infancy; To achieve a few advances in this field, we performed several Inelastic X-Ray Scattering (IXS) measurements on elementary systems as dilute suspensions of nanoparticles (NPs) in liquids. We found that nanoparticles can effectively impact the sound propagation of the hosting liquid. We also explored the possibility of shaping terahertz sound propagation in a liquid upon confinement on quasi-unidimensional cavities. These results are here reviewed and discussed, and future research directions are finally outlined.

A mechanical metamaterial with reprogrammable logical functions

Embedding mechanical logic into soft robotics, microelectromechanical systems (MEMS), and robotic materials can greatly improve their functional capacity. However, such logical functions are usually pre-programmed and can hardly be altered during in-life service, limiting their applications under varying working conditions. Here, we propose a reprogrammable mechanological metamaterial (ReMM). Logical computing is achieved by imposing sequential excitations. The system can be initialized and reprogrammed via selectively imposing and releasing the excitations. Realization of universal combinatorial logic and sequential logic (memory) is demonstrated experimentally and numerically. The fabrication scalability of the system is also discussed. We expect the ReMM can serve as a platform for constructing reusable and multifunctional mechanical systems with strong computation and information processing capability.

Low-Frequency, Open, Sound-Insulation Barrier by Two Oppositely Oriented Helmholtz Resonators

In this work, a low-frequency, open, sound-insulation barrier, composed of a single layer of periodic subwavelength units (with a thickness of λ/28), is demonstrated both numerically and experimentally. Each unit was constructed using two identical, oppositely oriented Helmholtz resonators, which were composed of a central square cavity surrounded by a coiled channel. In the design of the open barrier, the distance between two adjacent units was twice the width of the unit, showing high-performance ventilation, and low-frequency sound insulation. A minimum transmittance of 0.06 could be observed around 121.5 Hz, which arose from both sound reflections and absorptions, created by the coupling of symmetric and asymmetric eigenmodes of the unit, and the absorbed sound energy propagating into the central cavity was greatly reduced by the viscous loss in the channel. Additionally, by introducing a multilayer open barrier, a broadband sound insulation was obtained, and the fractional bandwidth could reach approximately 0.19 with four layers. Finally, the application of the multilayer open barrier in designing a ventilated room was further discussed, and the results presented an omnidirectional, broadband, sound-insulation effect. The proposed open, sound-insulation barrier with the advantages of ultrathin thickness; omnidirectional, low-frequency sound insulation; broad bandwidth; and high-performance ventilation has great potential in architectural acoustics and noise control.

Broadband square cloak in elastic wave metamaterial plate with active control

Cloaking invisibility is a novel technique that prevents the object from being detected in the background field. The development of new artificial materials and structures promotes the emergence of new achievements in cloaking research. In this work, a broadband square cloaking configuration of elastic wave metamaterial plate is designed and fabricated by the external active control system. The approximate parameters of the flexural wave cloak can be obtained by the coordinate transformation and achieved by alternating layers of the Acrylonitrile Butadiene Styrene (ABS), polydimethylsiloxane (PDMS), and piezoelectric (PZT) patches. With the introduction of active control systems, the square cloak has a wide effective frequency range. The simulation and experimental results show that the square cloak of flexural waves exhibits a good invisible performance in the frequency region of 500-2200 Hz. Compared to the structure without active control systems, the frequency region 2200-2750 Hz is extended for the active cloak. The design and fabrication of the broadband cloak is wished to be helpful during the practical engineering.

Two-Dimensional Composite Acoustic Metamaterials of Rectangular Unit Cell from Pentamode to Band Gap

Pentamode metamaterials have been receiving an increasing amount of interest due to their water-like properties. In this paper, a two-dimensional composite pentamode metamaterial of rectangular unit cell is proposed. The unit cells can be classified into two groups, one with uniform arms and the other with non-uniform arms. Phononic band structures of the unit cells were calculated to derive their properties. The unit cells can be pentamode metamaterials that permit acoustic wave travelling or have a total band gap that impedes acoustic wave propagation by varying the structures. The influences of geometric parameters and materials of the composed elements on the effective velocities and anisotropy were analyzed. The metamaterials can be used for acoustic wave control under water. Simulations of materials with different unit cells were conducted to verify the calculated properties of the unit cells. The research provides theoretical support for applications of the pentamode metamaterials.

Vibration Band Gap Characteristics of Two-Dimensional Periodic Double-Wall Grillages

In this article, the wave finite element method (WFEM) is used to calculate the band gap characteristics of two-dimensional (2D) periodic double-wall grillages (DwGs), which are verified by the grillage model vibration measurement experiment and finite element calculation. To obtain the band gap characteristics of periodic DwGs, the finite element calculation model is established according to the lattice and energy band theory and the characteristic equation of the periodic unit cell under the given wave vector condition is solved based on Bloch theorem. Then, the frequency transfer functions of finite-length manufactured and finite element models are obtained to verify the band gap characteristics of periodic DwGs. Finally, the effects of material parameters and structural forms on band gap characteristics and transfer functions are analyzed, which can provide a reference for engineering structure vibration and noise reduction design.

Progress of low-frequency sound absorption research utilizing intelligent materials and acoustic metamaterials

In recent years, increasing attention has been paid to the impacts of environmental noises on living creatures as well as the accuracy and stability of precise instruments. Due to inherent properties induced by large wavelength, the attenuation and manipulation of low-frequency sound waves is quite difficult to realize with traditional acoustic absorbers, yet particularly critical to modern designs. The advent of acoustic metamaterials and intelligent materials provides possibilities of energy dissipation mechanisms other than viscous dissipation and heat conduction in conventional porous sound absorbers, and therefore inspires new strategies on the design of subwavelength-scale structures. This short review aims to trace the current advancement on the low-frequency sound absorption research utilizing intelligent materials and metamaterials, including Helmholtz resonators and acoustic metamaterials based on micro-perforated plates, porous media, and decorated membrane, along with the tunable absorbing structures regulated with the function of electroactive polymers or magnetically sensitive materials. The effective principles and prospects were concluded and presented for future investigations of subwavelength-scale acoustic structures.

Lotus Metasurface for Wide-Angle Intermediate-Frequency Water-Air Acoustic Transmission

Only 0.1% of the acoustic energy can transmit across the water-air interface because of the huge acoustic impedance mismatch. Enhancing acoustic transmission across the water-air interface is of great significance for sonar communications and sensing. However, due to the interface instability and subwavelength characteristics of acoustic metamaterials, wide-angle intermediate-frequency (10 kHz-100 kHz) water-air acoustic transmission remains a great challenge. Here, we demonstrate that the lotus leaf is a natural low-cost acoustic transmission metasurface, namely, the lotus acoustic metasurface (LAM). Experiments demonstrate the LAM can enhance the acoustic transmission across the water-air interface, with an energy transmission coefficient of about 40% at 28 kHz. Furthermore, by fabricating artificial LAMs, the operating frequencies can be flexibly adjusted. Also, the LAM allows a wide-angle water-to-air acoustic transmission. It will enable various promising applications, such as detecting and imaging underwater objects from the air, communicating between ocean and atmosphere, reducing ocean noises, etc.

Enhanced Vibration Isolation with Prestressed Resonant Auxetic Metamaterial

Metamaterials designate structures with properties exceeding bulk materials. Since the end of the 1990s, they have attracted ever-growing attention in many research fields such as electromagnetics, acoustics, and elastodynamics. This paper presents a numerical and experimental study on a locally resonant auxetic metamaterial for vibration isolation. The designed materials combine different mechanisms—such as buckling, local resonances, and auxetism—to generate enhanced isolation properties. This type of structure could help to improve the isolation for machines, transportation, and buildings. First, the static properties of the reference and resonant structures are compared. Dispersion curves are then analysed to describe their periodic dynamic behaviour. An experimental validation carried out on a specially designed test bench is then presented and compared to corresponding finite structure simulation. As a result, huge bandgaps are found for the resonant case and strong isolation properties are also confirmed by the experimental data.

Multichannel Piezo-Ultrasound Implant with Hybrid Waterborne Acoustic Metastructure for Selective Wireless Energy Transfer at Megahertz Frequencies

Ultrasound energy transfer (UET) is developed and integrated into various bioelectronics with diagnostic, therapeutic, and monitoring capabilities. However, existing UET platforms generally enable one function at a time due to the single ultrasound channel architecture, limiting the full potential of bioelectronics that requires multicontrol modes. Here, a multichannel piezo-ultrasound implant (MC-PUI) is presented that integrates a hybrid waterborne acoustic metastructure (HWAM), multiple piezo-harvesters, and a miniaturized circuit with electronic components for selective wireless control via ultrasound frequency switching. The HWAM that utilizes both a 3D-printed air-diffraction matrix and a half-lambda Fabry-Perot resonator is optimized to provide the advantage of ultrasound selectivity at megahertz frequencies. Complying with U.S. Food and Drug Administration regulations, frequency-controlled multifunctional operations, such as wireless charging (≈11.08 µW) at 3.3 MHz and high-sensitivity wireless switch/control (threshold ≈0.55 MPa) of micro-light-emitting diode/motor at 1 MHz, are demonstrated ex vivo using porcine tissue and in vivo in a rat. The developed MC-PUI enhances UET versatility and opens up a new pathway for wireless implant design.