Design Of Acoustic Metamaterials Research Articles

A design method for accurate acoustic impedance matching under coherent coupling of sound-absorbing subunits

Acoustic metamaterials have garnered significant attention as an effective means to control low-frequency noise. However, the accurate design of complex structures composed of multiple subunits is still a challenge due to local coupling effects. To address this issue, in this work, a new design method is proposed that accurately achieves impedance matching at the target frequency when subunits are coupled in parallel. The method is demonstrated using six Fabry–Pérot (F–P) tubes to achieve perfect sound absorption in the continuous band of 405–445 Hz and the discontinuous bands of 400–410 and 430–440 Hz. Theoretical results show an average absorption coefficient of 99.3% in the target frequency band, which is verified through an impedance tube experiment. In addition, this paper explores the stability of this method under complex design conditions and discusses the mechanism of the influence of subunit parameters on sound-absorption performance from the perspective of impedance matching. Overall, the proposed design method offers a promising approach to achieving broadband sound absorption using multiple coupled subunits. The results of this study provide valuable insights for future research and the design of acoustic metamaterials.

Optimized Modular Design of Acoustic Metamaterials: Targeted Noise Attenuation

AbstractA modular design optimization method for acoustic metamaterial cells is proposed, which can ensure satisfying the targeted noise attenuation by using only the objective function of an arbitrary noise source and the constraints of the application at hand. The core algorithm is a fusion of the generalized particle swarm algorithm and wave finite element method specialized for structural and targeted optimization of metamaterials. The output is the optimized metamaterial cell and its sound barrier structure. The desired noise reduction performance is verified via acoustic testing of a 3D‐printed prototype. The simulation and experimental results of test cases show that the designed acoustic metamaterial can perfectly block the target noise band and have significant advantages in terms of design efficiency, light weight, and noise attenuation.

Study of acoustic transmission losses in particle-reinforced rubber-based membrane-type acoustic metamaterials

In this work, the mechanical properties of particle reinforced ethylene propylene diene monomer (EPDM)/ethylene tetrafluoroethylene (ETFE) copolymer material were determined by molecular dynamics (MD) method, and the copolymer material was used in the structural design of acoustic metamaterials. Secondly, based on the discrete point matching method, the acoustic transmission loss characteristics of the material are predicted, and the accuracy and effectiveness of the theory are verified through the multi physical field coupling finite element model. Finally, seven key parameters that affect the material structure are studied, and their influencing rules and mechanisms are analyzed. The results show that the structure makes up for the sound insulation defect of traditional ETFE film materials at low frequencies. Through reasonable selection of key parameters, high sound insulation design can be carried out for specific frequency bands, which is of great significance to the potential application in the construction field (new building materials).

Acoustic Metamaterial Design by Phase Delay Derivation Using Transfer Matrix

When acoustic elements such as quarter-wave, Helmholtz, labyrinthine-type or hook-type resonators are arranged sequentially, sound waves can be refracted in a specific frequency range. Thus, a metasurface may be designed to reduce noise by locating two sequentially arranged acoustic elements symmetrically. Phase delay, which can be calculated with a transfer function of the acoustic element, needs to be obtained to decide on acoustic element design parameters. However, in the case of a complex structure with labyrinthine-type or hook-type resonators, it can be difficult to calculate the phase delay accurately because each designer may have a different estimation method for the propagation direction of the sound wave. Therefore, this study presents a method for accurately deriving the phase delay required when designing a metasurface with a complex structure. The phase delay was calculated using the pressure and velocity derived from FEM and the transfer matrix of the main duct. Using the proposed method, a metasurface with symmetrically arranged acoustic elements was designed, and the noise reduction effect was confirmed through a speaker test. This study could be very helpful, since through it, any kinds of complex acoustic elements are able to be designed with accurate phase delay calculations.

Aerospace grade acoustic metamaterial design, modeling, and experimental validation

Vertical Take-Off and Landing Urban Aerial Mobility vehicle propulsion systems use rotors and blades to achieve lift, which results in heightened noise at the blade passing frequency. These frequencies must be attenuated to reduce cabin discomfort and comply with noise exposure limits. The design must absorb 350 Hz noise, be fire retardant to comply with aviation standards, and be maximally one inch thick. This paper outlines the design, computational simulation, and experimental validation of a novel aerospace-grade acoustic metamaterial. It contributes to the field of computational analysis of new metamaterial structures and experimental validation using prototype Helmholtz unit cells. Achieving maximum sound absorption with the aerospace requirements of minimal mass and fire safety led to the consideration of Nomex honeycomb Helmholtz resonator acoustic panels. Their sub-wavelength attenuation, tunability, lightweight and fire resistance make them an optimal fit for this application. A novel phenomenon was observed in experimental impedance tube testing where multiple Nomex honeycomb cells acted as one resonator cavity. This discovery allowed for samples of only one inch in thickness (cell depth) to achieve 83% sound absorption at 348 Hz. Experimental values match well with the calculated analytical solution using the Helmholtz equation and simulated sound absorption in COMSOL MultiPhysics. The acoustic metamaterial achieves tunable noise attenuation with minimal thickness, weight, and fire suppression using a novel design.

Deep-Learning-Based Acoustic Metamaterial Design for Attenuating Structure-Borne Noise in Auditory Frequency Bands

In engineering acoustics, the propagation of elastic flexural waves in plate and shell structures is a common transmission path of vibrations and structure-borne noises. Phononic metamaterials with a frequency band gap can effectively block elastic waves in certain frequency ranges, but often require a tedious trial-and-error design process. In recent years, deep neural networks (DNNs) have shown competence in solving various inverse problems. This study proposes a deep-learning-based workflow for phononic plate metamaterial design. The Mindlin plate formulation was used to expedite the forward calculations, and the neural network was trained for inverse design. We showed that, with only 360 sets of data for training and testing, the neural network attained a 2% error in achieving the target band gap, by optimizing five design parameters. The designed metamaterial plate showed a -1 dB/mm omnidirectional attenuation for flexural waves around 3 kHz.

Numerical design of Helmholtz resonators with multiple necks for multi-tonal noise control

The reduction of multi-tonal noise at multiple frequencies simultaneously is a challenge in many industrial fields. Different solutions such as metamaterials consisting of periodic Helmholtz resonators embedded into a porous layer have been studied in the literature. Generally, a classical resonator made of a cavity connected to a neck provides only one resonant transmission loss peak. In this study, a design of acoustic metamaterials is proposed numerically using the finite element method for multi-tonal noise reduction. The resonator is made of multiple necks extended into the cavity and is periodically distributed within a porous material. The cylindrical global cavity of the resonator is partitioned into several sub-cavities, which are separated from one another by a rigid wall, and each sub-cavity is connected to one neck. Helmholtz resonators with 2, 3, 4, and 5 necks are presented, they exhibit multiple resonance transmission loss peaks which correspond respectively to the number of the resonator necks. The proposed acoustic metamaterial designs can be used to reduce multi-total noise at several frequencies simultaneously.

Experimental investigation of a phase-cancelling slow-sound metamaterial with mean flow

Acoustic metamaterials have a wide variety of potential applications in various engineering disciplines. In many cases, the acoustic medium can be assumed to be at rest. However, for a lot of engineering applications a moving fluid is used to transport energy or substances, or to perform mechanical work. For those cases, acoustic waves are advected and acoustic energy can be dissipated or generated. These effects play a significant role for the design of acoustic metamaterials. In this work, an acoustic metamaterial with a low Mach number mean flow is presented. It is an array consisting of an even number of channels. Half of them are equipped with a slow-sound metamaterial, whereas the other half has unaltered sound propagation characteristics. Thus, the resonance frequencies of the channels are shifted. This results in a phase shift in the acoustic velocity response between both types of channels for a given pressure excitation, resulting in phase cancellation. However, this effect is weakened for higher mean flow velocities.

Vibration transmission characteristic prediction and structure inverse design of acoustic metamaterial beams based on deep learning

In this paper, an intelligent prediction and design method of acoustic metamaterial beams based on deep learning is presented. A theoretical model of acoustic metamaterial beams is derived by using the spectral element method to calculate the band structure and transmission characteristic of beam-type acoustic metamaterial. A high-degree-of-freedom design space dataset of band structure and transmission characteristics is constructed. In addition, the vibration transmission characteristics of acoustic metamaterial beams are predicted and the on-demand inverse design of acoustic metamaterial beams is realized by constructing a fully connected deep learning neural network model. Furthermore, the forward prediction and reverse design network model is verified by using the autoencoder neural network model. Results show that the predicted value of the autoencoder neural network structure is in good agreement with the target value, which indicates the feasibility of the intelligent design method of acoustic metamaterials based on deep learning. The presented intelligent design method could be potentially utilized in the field of fast and efficient acoustic metamaterial design for low frequency vibration isolation in engineering structures.

Design Method of Acoustic Metamaterials for Negative Refractive Index Acoustic Lenses Based on the Transmission-Line Theory

The design theory for electromagnetic metamaterials with negative refractive indices by using a distributed transmission-line model is introduced to the design of acoustic metamaterials, and a negative refractive index (NRI) acoustic lens is designed theoretically. Adjustments to the negative refractive indices of metamaterials have been carried out by calculations with numerical simulators in conventional design methods. As the results show, many calculations are needed to determine the shape of the unit structures and there are issues in that it is difficult to design those rigorously, meaning that limitations regarding the degree of freedom in the designs are many. On the other hand, the transmission-line model can rigorously design the unit cell structures of both the negative refractive index metamaterials and the background media with the positive refractive indices by calculations with the design formulas and modifying the error from the theory with a small calculation. In this paper, a meander acoustic waveguide unit cell structure is proposed in order to realize a structure with characteristics equivalent to the model, and the waveguide width and length for realizing an NRI acoustic lens are determined from the design formula of the model. The frequency dispersion characteristics of the proposed structure are also computed by eigenvalue analysis and the error in the waveguide length from the theoretical value is modified by a minor adjustment of the waveguide length. In addition, the NRI acoustic lens is constituted by periodically arranging the proposed unit cell structure with the calculated parameters, and the full-wave simulations are carried out to show the validity of the design theory. The results show that the designed lens operates at 2.5 kHz.

Wave Propagation Properties of a Spider‐Web‐Like Hierarchical Acoustic Metamaterial

Herein, a hierarchical acoustic metamaterial with a spider‐web‐like structure is proposed based on bionics theory. The wave propagation behaviors of the hierarchical structures are studied and discussed with the finite‐element method and Bloch theorem. The effects of the basic shape of the hierarchical structure, the levels (n), and the ambient temperature on the distribution of the bandgap are analyzed, respectively. The results show that the quadrilateral hierarchical structure has better bandgap properties than the same level's octagonal and hexagonal hierarchical structures. The level of the hierarchical structure has a significant effect on the distribution of the low‐frequency bandgap. When the level of the structure is 15, the lowest opening frequency is 99.875 Hz. When the temperature variable is introduced, the temperature‐induced deformation can significantly change the range of the first bandgap of the hierarchical structure. These findings can provide new ideas for the design of acoustic metamaterials.

Acoustic metamaterial design for noise reduction in vacuum cleaner

Acoustic metamaterial design for noise reduction in vacuum cleaner

Optimal Design of Acoustic Metamaterial of Multiple Parallel Hexagonal Helmholtz Resonators by Combination of Finite Element Simulation and Cuckoo Search Algorithm.

To achieve the broadband sound absorption at low frequencies within a limited space, an optimal design of joint simulation method incorporating the finite element simulation and cuckoo search algorithm was proposed. An acoustic metamaterial of multiple parallel hexagonal Helmholtz resonators with sub-wavelength dimensions was designed and optimized in this research. First, the initial geometric parameters of the investigated acoustic metamaterials were confirmed according to the actual noise reduction requirements to reduce the optimization burden and improve the optimization efficiency. Then, the acoustic metamaterial with the various depths of the necks was optimized by the joint simulation method, which combined the finite element simulation and the cuckoo search algorithm. The experimental sample was prepared using the 3D printer according to the obtained optimal parameters. The simulation results and experimental results exhibited excellent consistency. Compared with the derived sound absorption coefficients by theoretical modeling, those achieved in the finite element simulation were closer to the experimental results, which also verified the accuracy of this optimal design method. The results proved that the optimal design method was applicable to the achievement of broadband sound absorption with different low frequency ranges, which provided a novel method for the development and application of acoustic metamaterials.

Semi-analytical estimation of Helmholtz resonators’ tuning frequency for scalable neck-cavity geometric couplings

Innovative meta-materials offer great flexibility for manipulating sound waves and assure unprecedented functionality in the context of acoustic applications. Indeed, they can exhibit extraordinary properties, such as broadband low-frequency absorption, excellent sound insulation, or enhanced sound transmission. These amazing properties have drawn the eye of the transport industry, especially for aeronautic applications where objects like these can be combined and coupled with primary structures aiming to reduce exterior and interior noise without increasing weight. However, the design of acoustic meta-materials with exciting functionality still represents a challenge, therefore there is a huge interest about the conceptualization and design of innovative acoustic solutions making use of meta-material resonance effects. The main target of the present research work is to obtain an accurate prediction of the tuning frequency of a Helmholtz-resonating device, whose resonance properties are exploited in a wide part of acoustic meta-material design. In this context, an investigation on a correction factor for the classical formulation used to estimate the Helmholtz resonance frequency starting from its geometric characteristics, accounting for different-shaped resonators with varying neck/cavity ratios, is performed. More specifically, a set of numerical simulations for several geometric configuration is considered in order to demonstrate the limits of pre-existing formulas, and a new correction factor formula is developed after theoretical considerations where it is possible. In the end, results in terms of correction factors are provided in both graphical and semi-analytical form, compared with Finite Element data.

Slow-Sound-Based Delay-Line Acoustic Metamaterial

Periodic structures composed of quarter-wavelength or Helmholtz resonators have been widely used in the design of acoustic metamaterials. An interesting phenomenon achievable through hybridization in such structures is the slow sound, which results from the strong dispersion produced by the local resonances. It gives rise to many applications such as deep subwavelength sound absorbers or metadiffusers. All the applications proposed so far have been analyzed only in the frequency domain (steady state). In this work, we propose a passive treatment that can be used in room acoustics, which requires considering the time domain and all multiple reflections. We analytically design a delay line from a metasurface made of Helmholtz resonators, using slow-sound propagation. We prove numerically and experimentally that such structures can delay a pulse and thus reproduce the sound perception of a propagation over a given distance, larger than the actual size of the treatment. The limitations of real-time pulse propagation, dispersion, and losses on audio fidelity are discussed.

Generative design of acoustic metamaterials conditioned on desired transmission characteristics

Metamaterials gain increasing interest in acoustics due to their sound insulation abilities. The special arrangement of unit cells allows them to influence the way sound propagates in acoustic media. To date, a system-based approach is mainly adopted in the design process. This approach is accompanied with two drawbacks: Firstly, the design relies primarily on the expertise of specialists making the current process prone to subjective assessments. Secondly, the relevant target criteria can only be evaluated at the end of design phase. This is accompanied with substantial time and resource expenses and is even amplified when large scale simulations or physical experiments are involved. It is the aim of this contribution to introduce a design assistant which supports specialists in the design of acoustic metamaterials. The proposed assistant system aims at a criteria-centric design scheme. By this means, target criteria, which are only accessible at the final stages, can be considered early in the design process. Therefore, a conditional generative adversarial network is implemented. This network proposes cell candidates conditioned on the desired transmission characteristics for the metamaterial. To validate our method, simulations with the finite element method are performed. The findings of this investigation suggest an important role for generative adversarial networks in the design process of acoustic metamaterials. As such, the proposed framework allows to design cell candidates for problem-specific applications.

Acoustic metamaterial design framework using deep learning and generative modeling

This talk presents our findings and research performed on the application of deep learning and generative modeling in acoustic metamaterial design. Specifically, we will discuss our research findings published in recent papers on the application of deep learning algorithms, generative neural networks, reinforcement learning models, and global optimization for the inverse design of 2-D and 3-D acoustic metamaterial structures. The examples will be shown for the implementation of neural networks models for the inverse design of 3-D pentamode structures resulting in a low shear modulus, high bulk modulus, and an impedance matched with water. The generative 2-D GLO-Nets and the reinforcement learning models producing broadband low scattering effects for 2-D planar configurations of scatterers under plane wave incidence will be presented. The current challenges encountered during the application of deep learning methods in scaled metamaterial design will be discussed.

Efficient Modelling of Acoustic Metamaterials for the Performance Enhancement of an Automotive Silencer

Significant potential for acoustic metamaterials to provide a breakthrough in sound attenuation has been unlocked in recent times due to advancements in additive manufacturing techniques. These materials allow the targeting of specific frequencies for sound attenuation. To date, acoustic metamaterials have not been demonstrated in a commercial automotive silencer for performance enhancement. A significant obstacle to the practical use of acoustic metamaterials is the need for low cost and efficient modelling strategies in the design phase. This study investigates the effect of acoustic metamaterials within a representative automotive silencer. The acoustic metamaterial design is achieved using a combination of analytical and finite element models, validated by experiment. The acoustic metamaterial is then compared with commonly used techniques in the silencer industry to gauge the effectiveness of the acoustic metamaterials. COMSOL simulations were used to validate the developed test rig and were compared to experimental results which were obtained using the two-load transmission loss test method. Through this testing method, the implementation of a labyrinthine metamaterial cylinder proved to be a significant improvement in transmission loss within the silencer, with an increase in transmission loss of 40 dB at 1500 Hz. The research has successfully shown that acoustic metamaterials can be used in practical settings, such as an automotive silencer, to improve the overall sound attenuating performance. The described analytical model demonstrates the potential for industrially relevant low cost design tools.

Reinforcement learning for acoustic metamaterial design

This talk presents our findings and methodologies in applying reinforcement learning to the design of acoustic metamaterials [1]. Our reinforcement learning agents are capable of discovering configurations of cylindrical scatterers in water which minimize the scattering of an acoustic plane wave. These agents are successful in the optimization of two different parametric designs, i.e., radii and positions of each scatterer. The resultant designs produced by reinforcement learning algorithms such as double deep Q-learning network and deep deterministic policy gradient algorithms are comparable and in some cases superior to those produced by the gradient-based optimization solver such as fmincon. However, significant computational resources are required to train reinforcement learning models to completion. This poses a significant challenge when attempting to increase the complexity of a design; as training times increase to unfeasible levels. Methods to counteract this challenge are discussed in this talk. These methods include utilization of the Julia programming language as well as multiprocessing and multithreaded programming. Together they create a synergy which reduces training times by orders of magnitude. [1] T. Shah, L. Zhuo, P. Lai, A. Rosa-Moreno, F. Amirkulova, and P. Gerstoft, “Reinforcement learning applied to metamaterial design,” J. Acoust. Soc. Am. 150(1), 321–338 (2021).

Acoustic metamaterial design using Conditional Wasserstein Generative Adversarial Networks

This talk presents a method for generating planar configurations of scatterers with a reduced total scattering cross section (TSCS) by means of generative modeling and deep learning. The TSCS minimization via repeated forward modeling techniques, trial-error methods, and traditional optimization methods requires considerable computer resources and time. However, similar or better results can be achieved more efficiently by training a deep learning model to generate such optimized configurations producing low scattering effect. In this work, the Conditional Wasserstein Generative Adversarial Networks (cWGAN) is combined with Convolutional Neural Networks (CNN) to create the generative modeling architecture [1]. The generative model is implemented with a conditional proponent to allow the TSCS targeted design generation and is enhanced with the coordinate convolution (CordConv) layer to improve the model’s spatial recognition of cylinder configurations. The cWGAN model [1] is capable of generating images of 2D configurations of scatterers that exhibit low scattering. The method is demonstrated by giving examples of generating 2-cylinder and 4-cylinder planar configurations with minimal TSCS. [1]. P. Lai, F. Amirkulova, and P. Gerstoft. “Conditional Wasserstein generative adversarial networks applied to acoustic metamaterial design,” J. Acoust. Soc. Am. 150(6), 4362–4374 (2021).