Design Of Acoustic Metamaterials Research Articles

Sound absorption metamaterials designed by machine learning and their applications

Acoustic metamaterials are artificial materials composed of acoustic functional elements along the spatial order, which have extraordinary acoustic properties that are not possessed by homogeneous materials. Since the conception of phononic crystal in the 1990s, acoustic metamaterials have gradually matured, which prospects industrial application. In our report, we present an acoustic metamaterial design method based on deep learning for sound absorption. The design method is firstly set up with the array of Fabry-Perot resonators, then adapted for the array of Helmholtz resonators. The method uses a tandem inverse design model based on the convolution neural network(CNN), which is capable of on-demand design. It can generate acoustic metamaterial design of high absorption in targeted frequency range. Three designs of acoustic metamaterials for different purposes are presented. Firstly, sound absorption metamaterials with selective bandwidth absorption, are used to control tonal noise from electric transformers. Secondly, metamaterials with broadband absorption are used in vehicle cabin noise control. Lastly, full-band near-perfect absorption materials are created to construct acoustic anechoic chambers.

Comparison of traditional and deep learning optimisation for the design of acoustic metamaterials

This paper presents a comparative analysis of traditional and Deep learning (DL) optimisation approaches for AMM design. A case study comparing a generalised pattern search (GPS) optimisation to a previously trained inverse design deep neural network (IDDNN) of an acoustic meta-absorber using various metrics is considered. For benchmarking, a baseline design is realised with arbitrarily chosen geometric parameters in a CAD software. This design is 3D printed and experimentally tested. The peak absorption and corresponding resonant frequency obtained from experimental absorption, along with other geometric parameters, are used as inputs to IDDNN and GPS. Results show that IDDNN provides superior inference speed, requiring 7.24e-3 [s] to generate predictions on a single input instance, compared to GPS which took about 30.5464 [s]. While GPS exhibits slightly closer alignment to experimental curve based on Kullback-Leibler divergence (2.79e-3) compared to IDDNN (3.31e-3), IDDNN still achieves a slightly higher accuracy of 92%, compared to 90% for GPS. It is emphasised that trade-offs may be necessary in practice to determine the most suitable design approach for a given application. Traditional optimisation offers ease of design flexibility, allowing for on-the-fly model improvement and modification. In contrast, DL may require re-training, leading to delays in process workflow

Development and Characterization of a Flexible Soundproofing Metapanel for Noise Reduction

This study addresses the critical challenge of developing lightweight, flexible soundproofing materials for contemporary applications by introducing an innovative Flexible Soundproofing Metapanel (FSM). The FSM represents a significant advancement in acoustic metamaterial design, engineered to attenuate noise within the 2000–5000 Hz range—a frequency band associated with significant human auditory discomfort. The FSM’s novel structure, comprising a box-shaped frame and vibrating membrane, was optimized through rigorous finite element analysis and subsequently validated via comprehensive open field tests for enclosure-type soundproofing. Our results demonstrate that the FSM, featuring an optimized configuration of urethane rubber (Young’s modulus 6.5 MPa) and precisely tuned unit cell dimensions, significantly outperforms conventional mass-law-based materials in sound insulation efficacy across target frequencies. The FSM exhibited superior soundproofing performance across a broad spectrum of frequency bands, with particularly remarkable results in the crucial 2000–5000 Hz range. Its inherent flexibility enables applications to diverse surface geometries, substantially enhancing its practical utility. This research contributes substantially to the rapidly evolving field of acoustic metamaterials, offering a promising solution for noise control in applications where weight and spatial constraints are critical factors.

Combined acoustic metamaterial design based on multi-channel Fano resonance effect

In response to the increasing traffic noise problem, we designed a combined acoustic metamaterial (CAM) based on the multi-channel Fano resonance principle. By utilizing the Fano resonance coupling between the acoustic spiral structure and the hollow structure, efficient sound insulation under effective ventilation conditions is achieved. Simulation results of acoustic transmission loss show that the acoustic transmission loss of CAM is more than 13 dB in the frequency band of 520–989 Hz. The broadband sound insulation characteristic can block the oblique angle incident sound waves from different angles. Simulation results of the elastic strain energy and acoustic pressure field validate the sound insulation mechanism of the Fano resonance of the combined acoustic metamaterial. The experimental results in the impedance tube generally agree with the simulation results. To explore the possibility of wider engineering applications of CAM, we propose a combined CAM and CAM0.7 structure. The results show that a series structure of acoustic metamaterials can be selected to further realize broadband sound insulation within 500–1574 Hz.

Identifying Factors Influencing the Properties of Vibroacoustic Metamaterials Using Three Different Acoustic Methods

Vibroacoustic metamaterials offer an approach for the targeted damping of unwanted structural vibrations and noise by integrating periodically arranged resonators into a matrix of bulk material. Fabrication using the laser bed powder fusion process allows the targeted integration of bulk resonators and powder depots, leading to an extension of the designable damping properties. Herein, the adaptation of acoustic methods is focused on the characterization of the properties of metamaterial plates. The investigated vibroacoustic metamaterial plates are made of polyamide PA1.2, combining material and structural damping. The vibration behavior of the plates over a range of frequencies using acoustic impedance measurements in a custom‐built measurement tube is investigated and it is compared with structural dynamics experiments using an electrodynamic shaker. The measurements allow for the identification of stop bands (frequency range with high damping) and influencing factors such as metamaterial design, mass, powder amountand surface on the frequency‐dependent damping properties. The adapted technique investigated in this work provides an experimental platform to characterize the complex interplay of acoustic metamaterial design and holds promise for scaling up metamaterial technology for industrial applications due to its simplicity, small space requirement, and low cost.

Low-frequency vibration bandgaps and deep learning-based intelligent design method of Y-shaped core sandwich metabeams

In this paper, the wave propagation mechanics theoretical model of Y-shaped core sandwich metabeams with local resonators is established based on the spectral element method, and the flexural wave bandgaps and vibration isolation characteristics are studied. The reliability of the theoretical model of Y-shaped core sandwich metabeams is verified by the finite element method and experiment. On this basis, a deep learning-based intelligent design method for predicting the vibration transmission characteristics and structure design of Y-shaped core sandwich metabeams is proposed. A dataset is created using the theoretical model of wave dynamics, and deep neural networks are constructed to forward prediction of transmission characteristics and intelligent design of Y-shaped core sandwich metabeams, respectively. Results indicate that the bandgap range of Y-shaped core sandwich metabeams is 2.5 times that of Y-shaped core sandwich beams, and the start frequency of bandgap is reduced by 578 Hz. The prediction of the transmission characteristic curve is in good agreement with the target, and the average relative error of intelligent design is below 3 %, which verifies the precision of the intelligent design method. The innovative, intelligent design method provides a novel way to realize engineering vibration reduction design of acoustic metamaterials rapidly.

BEM-based fast frequency sweep for acoustic scattering by periodic slab

This paper presents a boundary element method (BEM) for computing the energy transmittance of a singly-periodic grating in 2D for a wide frequency band, which is of engineering interest in various fields with possible applications to acoustic metamaterial design. The proposed method is based on the Padé approximants of the response. The high-order frequency derivatives of the sound pressure necessary to evaluate the approximants are evaluated by a novel fast BEM accelerated by the fast-multipole and hierarchical matrix methods combined with the automatic differentiation. The target frequency band is divided adaptively, and the Padé approximation is used in each subband so as to accurately estimate the transmittance for a wide frequency range. Through some numerical examples, we confirm that the proposed method can efficiently and accurately give the transmittance even when some anomalies and stopband exist in the target band.

Machine learning in solid mechanics: Application to acoustic metamaterial design

AbstractMachine learning (ML) and Deep learning (DL) are increasingly pivotal in the design of advanced metamaterials, seamlessly integrated with material or topology optimization. Their intrinsic capability to predict and interconnect material properties across vast design spaces, often computationally prohibitive for conventional methods, has led to groundbreaking possibilities. This paper introduces an innovative machine learning approach for the optimization of acoustic metamaterials, focusing on Multiresonant Layered Acoustic Metamaterial (MLAM), designed for targeted noise attenuation at low frequencies (below 1000 Hz). This method leverages ML to create a continuous model of the Representative Volume Element (RVE) effective properties essential for evaluating sound transmission loss (STL), and subsequently used to optimize the overall topology configuration for maximum sound attenuation using a Genetic Algorithm (GA). The significance of this methodology lies in its ability to deliver rapid results without compromising accuracy, significantly reducing the computational overhead of complete topology optimization by several orders of magnitude. To demonstrate the versatility and scalability of this approach, it is extended to a more intricate RVE model, characterized by a higher number of parameters, and is optimized using the same strategy. In addition, to underscore the potential of ML techniques in synergy with traditional topology optimization, a comparative analysis is conducted, comparing the outcomes of the proposed method with those obtained through direct numerical simulation (DNS) of the corresponding full 3D MLAM model. This comparative analysis highlights the transformative potential of this combination, particularly when addressing complex topological challenges with significant computational demands, ushering in a new era of metamaterial and component design.

Mitigating low-frequency broadband aircraft noise through a structured assembly of acoustic material and devices

Addressing the challenge of attenuating low-frequency broadband noise emerges as a critical concern within the fields of aeronautics, ground transportation, and construction industries, requires innovative solutions for enhanced acoustic control. Over the last few decades, the literature has seen an increase in low-frequency noise control solutions centered around acoustic metamaterial designs. These proposed technologies exhibit promising acoustic performance, especially proving superior to conventional sound insulation materials in constrained spaces, such as in aerospace applications. Despite the efficacy of typical metamaterials in attenuating tonal noise through narrow resonant frequency maxima, practical applications reveal some challenges, as even slight variations in tonal noise frequencies can compromise the overall effectiveness of such solutions. In response to this, the present paper introduces a novel thin acoustic metamaterial design aimed at improving broadband noise attenuation at low frequencies. This design uses carefully arranged structured metamaterials within a fiberglass layer to create optimal resonance frequency bands for maximum low-frequency noise attenuation. Performance assessment in the low-frequency domain employed COMSOL Multiphysics finite element methods, predicting sound absorption coefficient and transmission loss. Results confirm the effectiveness of the proposed metamaterial design, showcasing broad noise attenuation at low frequencies.

Learning from failure: An analysis of a flawed nonlinear acoustic metamaterial design

Acoustic metamaterials (AMMs) are structured systems designed to exhibit specific, often exotic, effective material properties for acoustic wave motion. Most research on AMMs prioritize linear wave behavior, but a growing body of work has focused on nonlinear phenomena. While the primary approach to enhancing the nonlinear response of a system has been to place highly nonlinear inclusions in the system (such as bubbles, cracks, or buckling beams), an alternative approach is to control the linear material properties to enhance the relative strength of the nonlinearity. For example, one may reduce the shock formation distance of a system by reducing the effective mass density and wave speed even if the coefficient of nonlinearity is left unchanged. However, due to the nature of nonlinear waves, developing a practical design to accomplish this control can be challenging. We recently designed and built an experimental nonlinear AMM and found it to be fundamentally flawed. In this paper we discuss the thought process that led to the flawed design and present the lessons learned from an unsuccessful experiment.

Numerical extraction of three-dimensional acoustic polarizabilities for acoustically small scatterers

Polarizability is a convenient descriptor for scattering from low-ka inhomogeneities in both electromagnetism, where it originated, and in acoustics, where it is increasingly used in the design of metamaterial elements. In two or three dimensions, the polarizability is represented by a block matrix that couples the local pressure and particle velocity fields to the lowest-order components of the multipole expansion, usually truncated to dipole order. A fully dense acoustic polarizability matrix has components that couple spatially uniform pressure and velocity oscillations to dipole and monopole scattering, respectively. This unique coupling leads to acoustic bianisotropy, also known as Willis coupling, for a collection of scatterers. The design of Willis materials necessitates computationally efficient methods to extract all components of the polarizability matrix and, at present, only two-dimensional analytical extraction methods are found in the literature. In this work, we present an algorithm to extract all components of the three-dimensional polarizability matrix from a scatterer with arbitrary geometry and composition. The method presented here is numerically efficient and yields results that are in agreement with an analytically obtained benchmark polarizability, providing a useful tool for acoustic metamaterial design.

Tunable acoustic passive phased array based on double-opening resonant rings

The special structural design of acoustic metamaterials further extends acoustic properties of the materials. We design a tunable acoustic passive phased array based on double-opening resonant rings, which modulates the acoustic waves only by the rotational angle, making up for the defect of the fixed structure of ordinary metamaterials. The rotation angle is selected based on the generalized Snell’s law, which not only enables focusing in a large frequency band range but also meets the focusing demand of acoustic waves incident at different angles and controls the position of the focal point.

Analysis of Helmholtz resonator wall elasticity effects on the performance of periodic acoustic metamaterial

In this paper, a metamaterial made of a porous layer with embedded periodic Helmholtz resonators is studied and the effects of the resonator wall elasticity on the acoustic attenuation performance of the metamaterial are investigated numerically. The analytical transmission loss results using the parallel transfer matrix method show good agreement with finite element results for the rigid wall case. Elastic materials with different thicknesses are considered for the wall of the neck and the top, lateral and bottom walls of the resonator cavity. It is shown that the transmission loss of the metamaterial degrades when the bottom wall of the resonator cavity is elastic. The elasticity of the bottom wall has a significant impact on the performance of the metamaterial. This analysis will help for better design of acoustic metamaterials with periodic Helmholtz resonators.

Optimal design of low-frequency sound absorber based on Snake Optimizer

In this work, a low-frequency sound absorber composed of a micro-perforated panel (MPP) and a coiled-up space configured by grooved corrugations is proposed. Due to the intricate interactions caused by the hole diameter and hole separation distance, it is difficult to achieve optimal acoustic performance. Here, a high-efficient meta-heuristic optimization algorithm named Snake Optimizer (SO) is applied to flexibly obtain the prime configuration of acoustic absorbing and structure parameters. The expected sound spectrum characteristics are performed by substituting the optimum into the 3D finite element model (FEM). Good agreement verifies the effectiveness of the proposed method. Our work paves the way for broadening the application of algorithms in the optimal design of acoustic metamaterials.

Machine learning assisted design of acoustic metamaterials with broadband sound-absorbing and superior mechanical performance

It remains challenging to design lightweight metamaterials with superior sound-absorbing and load-bearing capacities. One promising approach is using multiple coherently coupled resonators to serve as sound absorbers and reinforced grid cores of sandwich panels. However, with too many design parameters each requiring careful tuning to reach the stringent critical coupling condition, achieving an optimal design based on experience alone is challenging. An autoencoder-like neural network is constructed that, once well trained, significantly promote the inverse design process thanks to the highly efficient computational speed. Particularly, a probabilistic model is inserted into the network to tackle ill-posed inverse problems requiring man-made and probably unreal spectrum as an input, and can provide multiple ultra-thin (32 mm) and broadband designs. We have fabricated and tested the optimized metallic sandwich structures, showing broadband capacity of using solely nine resonators to achieve quasi-perfect sound absorption (over 0.9) from 399 to 675 Hz. The static compression and dynamic impact testing also verify the superior mechanical performance with high yield strength (21.2 MPa) and large normalized energy absorption (0.29) at lower relative density (13.5%). We believe this work is encouraging to accelerate the design of multifunctional absorbers targeted especially for low-frequency noise control in engineering.

Acoustically Actuated Flow in Microrobots Powered by Axisymmetric Resonant Bubbles

Bubble‐driven microsystems inspired by the therapeutic use of microbubbles under clinical ultrasound actuation offer innovative remote manipulation in biological settings. Ultrasound‐powered microrobots, benefiting from a distribution of vibrating microbubbles (1–100 μm in diameters), exhibit localized fluid flow for self‐propulsion. Microbubbles also contribute to the design of acoustic metamaterials, where distributed actuation of bubbles enables exotic material properties (e.g., negative refractive index). Herein, a metamaterial‐inspired microrobot design, which exploits the streaming induced by the collective oscillation of microbubble arrays (> 10), is reported. Such a large distribution of bubbles offers twofold advantages: a mesoscale microrobot allowing ease of handling and motion at a considerably low acoustic driving pressure of 50 kPa. In this work, the oscillatory amplitude of a single bubble that acts as a unit cell of the metamaterial‐based microrobot is first characterized. Thereon, this amplitude is related to the flow generated by the collective vibration of all the bubbles close to the theoretically predicted resonant frequency of the bubbles. Finally, the hovering motion of the microrobot induced by the streaming and flow‐assisted debris clearance is demonstrated. Such auxiliary functionalities of the microrobot can be useful for applications like contactless sample extraction in inaccessible biological environments.

A mechanically adjustable acoustic metamaterial for low- frequency sound absorption with load-bearing and fire resistance

ABSTRACTBroadband sound absorption is limited to discrete noise with abrupt peaks in the spectrum. Here, we proposed a mechanically adjustable acoustical metamaterials (AAMM) for low-frequency sound absorption with deep-subwavelength (0.025λ), which integrates Helmholtz resonators and Fabry–Perot (FP) tubes by precise modular design. The calculation results based on the theoretical model demonstrate that the broad low frequency (from 100 Hz to 500 Hz) tunability of the composite adjustable sound absorbing materials. The adjustable design scheme is further verified by numerical simulation. Then a multi-impedance adjustment method is proposed to improve the local optimal defect and make it have quasi-perfect sound absorption effect in the range of 120 Hz–348 Hz. The sound absorbing material sample can withstand 2.7 tons of dynamic load and 1300° high temperature, presenting superior compression and fire resistance compared to conventional porous sound absorbing materials and membrane acoustic metamaterials. This research on assembled machine-adjustable sound absorption material enriches the conventional acoustic metamaterial design scheme, further improves the space utilization rate, and provides an effective solution for dealing with low-frequency complex variable noise.

The wave equation as a differentiable-programmable computer for the design of acoustic metamaterials

Designing new metamaterials enables fine-grain control of wave dynamics. Applications of these materials range from wave steering devices for seismic wave manipulation, to “super-focusing” devices for high-resolution ultrasound imaging and surgery. Control of systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is a challenging problem, because of the additional physical constraints and intrinsic properties of wave phenomena such as attenuation, reflection, and scattering. In this work, we propose a novel method for transient control of wave equations with Model Predictive Control. The proposed model incorporates the essential physical properties observed in the original dynamics directly into its lower dimensional latent space. We show that our model is capable of using its latent dynamics to predict scalar integral quantities over a variable length timespan. Moreover, it is fully interpretable by the corresponding physical quantities, which allows it to guarantee solution properties. We demonstrate this method by solving important cases of wave equation, which have not been solved before, such as control of transient waves. We make our code publicly available.

Design and analysis of periodic acoustic metamaterial sound insulator using finite element method

In this article, a design of acoustic metamaterial containing Helmholtz resonators periodically embedded in a porous material is investigated for aerospace applications using the finite element method (FEM). The results obtained using the FEM are compared with the results of the theory, and the proposed transfer matrix method and good agreements are obtained. The transfer matrix method was combined with FEM calculations for two different termination conditions (plane wave radiation and rigid wall) in order to retrieve the equivalent matrix of the porous layer with the integrated periodic resonator. The equivalent matrix is then coupled analytically in series with others matrices. Finite element method studies are carried out on single and double wall configurations, and the effects of different resonator parameters and the air gap on the transmission loss are illustrated. The influences of the orientation of the neck opening and the resistivity of the porous material are also studied. Finite element method results for different incident angles are presented for single and double wall configurations. The proposed design can potentially be integrated into the panels of aircraft cabins in order to reduce the noise level at low frequencies inside the cabin.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm.

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.