Labyrinthine Acoustic Metamaterials Research Articles

Effect of micro-slit entries on the sound absorption and size of a labyrinthine acoustic metamaterial

Low frequency noise attenuation is a pressing issue in the field of acoustics and noise control. In this regard, labyrinthine acoustic metamaterials have shown high potential in achieving low frequency sound absorption. This paper presents two new acoustic metamaterial designs consisting of a labyrinthine of sub-wavelength straight folded air channels with a rectangular cross-section surrounded by sound hard boundaries, combined with a micro-perforated slit panel. Design 1 has two micro-slits at the end channels, whose lengths are the same as the width of labyrinthine channels. Design 2 has two micro-slits of unequal length at the end channels. A simulation study using COMSOL Multiphysics is conducted to check the effect of the slit lengths on the sound absorption of these metamaterials. It is found that having micro-slits with unequal lengths for sound wave entry leads to a higher absorption peak and a lower peak absorption frequency compared to that of micro-slits with equal lengths. Moreover, it leads to a better sound absorption performance with increasing thickness. The experimental results of the sound absorption coefficient are in good agreement with the simulation results. Thus, Design 2 can be used for extremely low frequency sound absorptions in machinery with space constraints.

Labyrinthine acoustic metamaterials with triangular self-similarity for low-frequency sound insulation at deep subwavelength dimensions

Labyrinthine acoustic metamaterials are good choices for realizing sound insulation, acoustic stealth, and acoustic lenses by virtue of their stable performance and rich modes. We design a labyrinthine acoustic metamaterial with eight resonance units by utilizing triangular self-similarity. First, with the help of eigenstate analysis, it is demonstrated that it has monopolar resonance and multipolar resonance modes. Then, the physical mechanisms that generate transmission valleys and acoustic isolation peaks are analyzed by applying the equivalent medium theory and the vibrational velocity field. Finally, we designed an ultra-sparse distribution (fill rate of 20 %) hypersurface for effective acoustic isolation and noise reduction at 417 Hz (normalized frequency of about λ/12). This study can provide useful assistance in the design of labyrinthine acoustic metamaterials, as well as potential applications in areas where ventilation is required (e.g., acoustic barriers for transportation systems).

Scattering properties of labyrinthine metamaterials with different numbers of resonance units

This paper describes a series of labyrinthine acoustic metamaterials with different numbers of resonance units. The research is carried out based on numerical modeling of impedance tubes. We find that the realization of slit sound transmission using resonant dimers is related to the coupling interaction between the samples and the distribution spacing, and that each order of metamaterials can realize full slit sound transmission only at the corresponding distribution spacing. For labyrinth-type acoustic metamaterials with higher refractive indices, the phenomenon of acoustic capture is more pronounced for samples capable of acoustic capture at the monopolar resonance frequency. The acoustic isolation under sparse spacing distribution can be improved by increasing the pressure difference between the sample center and the background medium. This work can be useful for the design of labyrinth-type acoustic metamaterials in terms of sound insulation, acoustic capture, and acoustic lensing.

Influence of right-angled elbows on the modal response of labyrinthine meta-materials

This article studies how right-angled 90 degrees elbows modify the resonance properties of labyrinths. The resonance properties are evaluated by considering the dispersion curves obtained by performing a band structure calculation. The response to the bandgaps width and positions in the presence of one, then two and finally a large number of elbows has then been studied to quantify the influence of the path tortuosity on the modal response of the labyrinth’s geometry. The end-goal is to provide the elementary understanding tools leading to more refined predictive models for labyrinthine acoustic metamaterials (LAM).

Labyrinthine Acoustic Metamaterials with a Subwavelength Bandgap Inspired by Topology‐Optimized Structural Design

Herein, a structural design for labyrinthine acoustic metamaterial is proposed using a topology optimization method to realize a subwavelength bandgap preventing the transmission of low‐frequency sounds. The optimized design is composed of air‐filled channels of different widths, which exhibit the subwavelength bandgap based on the monopole resonance induced in the meta‐atom. In addition to the optimized meta‐atom design, a simplified meta‐atom design with a small coiling coefficient is proposed by extracting structural features of the optimized design. The bandwidth and central frequency of the subwavelength bandgap can be controlled by adjusting the size parameters of the simplified meta‐atom. Numerical analysis for acoustic waves based on the finite‐element method is conducted to demonstrate the low transmission coefficients of the obtained designs for a wide‐ and low‐frequency range. Furthermore, using a 3D printer, experimental specimens of optimized and simplified meta‐atoms are constructed, and impedance tube experiments are performed to show their functionality.

Near-perfect sound absorptions in low-frequencies by varying compositions of porous labyrinthine acoustic metamaterial

Low-frequency sound absorption is the key challenge in acoustics, and even the remarkable labyrinthine acoustic metamaterials with sound-hard boundaries are unable to attain an increase in the range of sound absorption under 500 Hz. This paper presents a new Porous Labyrinthine Acoustic Metamaterial (PLAM) that contains a folded slit labyrinthine structure in a micro-porous matrix, such that the matrix also participates in sound propagation. Theory, simulations, and experiments show that PLAM gives near-perfect sound absorptions at low frequencies (200–500 Hz) for different compositions. These near-perfect sound absorptions are due to particles vibrating in resonance in folded slit entry and dissipating acoustic energy into micro-porous matrix, which leads to zero acoustic pressure at the transmission end. For this purpose, labyrinthine structure and micro-porous matrix must acoustically couple, for which the characteristic frequency should be less than the resonance peak of the labyrinthine. Under these conditions, changing the Johnson-Champoux-Allard parameters of the micro-porous matrix changes the magnitude and frequency of the absorption peak. Increasing the number of folds of the labyrinthine structure shifts the sound absorption peak to lower frequencies but narrows the peak. However, parallel combination of PLAMs with different fold numbers, together, broadens the absorption peak at the low frequencies. The PLAM has been validated to attenuate noise level of an HVAC appliance by 6 dB without affecting the airflow performance. Hence, the presented work paves way for designing labyrinthine metamaterials with enhanced low-frequency sound absorptions and broader sound absorption range for aerodynamic noise control applications.

Level set-based topology optimization for the design of labyrinthine acoustic metamaterials

We present a topology optimization method for the design of labyrinthine metamaterials with a large path length for acoustic wave propagation. An objective function maximizes the pressure gradient in an air-filled region at a low frequency, and a level set-based optimization method enables the optimal design of the labyrinthine structure with high computational efficiency owing to the concept of topological derivative. First, we explain the design settings of labyrinthine metamaterials. Next, the objective functions to obtain labyrinthine structures are introduced, and the corresponding topological derivatives are obtained. The optimization problem is formulated in the framework of the level set topology optimization method, and two-dimensional numerical examples are provided to demonstrate the validity of the proposed method. Based on the frequency responses of the effective parameters and dispersion analysis, the optimized designs are characterized by a negative refractive index over a wide frequency interval, which can be controlled by a parameter introduced in the objective function.

Labyrinthine acoustic metastructures enabling broadband sound absorption and ventilation

There is growing interest in the development of path coiling-based labyrinthine acoustic metamaterials for realizing extraordinary acoustical properties such as low-to-mid frequency sound absorption. We present a subwavelength labyrinthine acoustic metastructure (≤3 cm) exhibiting a superior sound absorption with a high bandwidth (more than one octave in the range of 400–1400 Hz). The metastructure is orchestrated of multiple labyrinthine unit cells of different configurations in a hexagonal array, and broadband absorption has been achieved by the dissipation of incident propagating sound waves inside the labyrinthine zigzag channels. Furthermore, the unique design of the metastructure allows for simultaneous air circulation for facilitating natural ventilation and sound absorption. The proposed unique designs may find potential applications in architectural acoustics and noise shielding where simultaneous natural ventilation and noise mitigation are required.

Subwavelength multiple topological interface states in one-dimensional labyrinthine acoustic metamaterials

Acoustic analogies of topological insulators reside at the frontier of ongoing metamaterials research. Of particular interest are the topological interface states that are determined by the Zak phase, which is the geometric phase characterizing the topological property of the bands in one-dimensional systems. Here we design double-channel Mie resonators based on the so-called labyrinth acoustic metamaterials, which can be considered equivalent to a ultraslow medium of large refractive index, inevitably containing structural features on a subwavelength scale. The metamolecule containing two cells is engineered to host the degenerated states through a zone-folding mechanism, whereupon the Zak phase transition takes place when the interval between two cells changes from shrunk to expanded. Furthermore, the topological interface state displays strong robustness against randomly introduced perturbations whose acoustic intensity is enhanced by nearly a factor 1600 in comparison to an ordinary waveguide.

Porous labyrinthine acoustic metamaterials with high transmission loss property

This study systemically investigates a porous labyrinthine type of acoustic metamaterials (LAMs), a sort of acoustic metasurface, analytically, numerically, and in laboratory tests. The LAMs are composed of a series of porous elements, where stainless steel plates with various lengths are inserted into the melamine foam. At the frequency of interest 2000 Hz, porous elements with a thickness smaller than one-eighth of the target wavelength are designed to generate a linearly varied phase gradient on the refracting surface and slightly varied phase responses on the reflecting surface; the elements play key roles in refracted and reflected wave manipulations, respectively. Two porous LAMs with different periodical lengths are designed based on the generalized Snell’s law to study the effect of the periodical length on refraction and reflection phenomena in the scattered sound pressure fields. By reducing the length to smaller than one-half of the target wavelength, the high-order wave modes will disappear in the refracted and reflected sound pressure fields at omnidirectional incidence, resulting in enhancements of transmission loss and also sound absorption coefficient in a wide range of incidence angles compared with the uniform melamine foam with the same thickness. The thin porous LAMs provide a method to improve sound transmission loss and sound absorption properties of an uniform porous material and show potentials to be used in cabins of high-speed trains and aircraft.

3D Hilbert fractal acoustic metamaterials: low-frequency and multi-band sound insulation

In this work, we present a class of three-dimensional (3D) labyrinthine acoustic metamaterials with self-similar fractal technique, which can produce multiple frequency-band sound insulation in deep-subwavelength scale. By simultaneously exploiting the multi-frequency bandgaps and the low-frequency characteristics, the Hilbert cubes are explored to design the 3D Hilbert fractal acoustic metamaterials (HFAMs). The multiple-band features of the HFAMs are examined by the finite element method and the effective medium theory, in which the negative bulk modulus and the mass density are responsible for the formation of the multi-bandgaps. These multi-frequency properties are induced by the Fabry–Perot multi-resonance of 3D HFAMs, which possess an ultra-high refractive index. Hence, the multi-band sound insulations of 3D HFAMs with the negative effective property are achieved below 500 Hz. These properties of the designed 3D HFAMs provide an effective way for acoustic metamaterials to achieve multi-band filtering and noise attenuation in the low-frequency regime.

Labyrinthine Acoustic Metamaterials with Space-Coiling Channels for Low-Frequency Sound Control

We numerically analyze the performance of labyrinthine acoustic metamaterials with internal channels folded along a Wunderlich space-filling curve to control low-frequency sound in air. In contrast to previous studies, we perform direct modeling of wave propagation through folded channels, not introducing effective theory assumptions. As a result, we reveal that metastructures with channels, which allow wave propagation in the opposite direction to incident waves, have different dynamics as compared to those for straight slits of equivalent length. The differences are attributed to activated tortuosity effects and result in 100% wave reflection at band gap frequencies. This total reflection phenomenon is found to be insensitive to thermo-viscous dissipation in air. For labyrinthine channels generated by iteration levels, one can achieve broadband total sound reflection by using a metamaterial monolayer and efficiently control the amount of absorbed wave energy by tuning the channel width. Thus, the work contributes to a better understanding of labyrinthine metamaterials with potential applications for reflection and filtering of low-frequency airborne sound.

Fractal and bio-inspired labyrinthine acoustic metamaterials

Control of low-frequency sound is a challenge, despite numerous advances in the field. Recently emerged acoustic metamaterials have already proven their efficiency for the development of innovative systems for sound control and demonstration of such fascinating phenomena as super-resolution imaging, transformation acoustics, acoustic cloaking, etc. For sound attenuation, a common attenuation mechanism relies on dispersion induced by local resonances that results in the generation of slow sound inside a metastructure at resonant frequencies. However, the selective bandwidth of metamaterials with identical resonators restricts their practical applications. To overcome this limitation, one can introduce rainbow-type resonators that leads to the increase of structural sizes and raises manufacturing costs. We present fractal and bio-inspired labyrinthine acoustic metamaterials with non-resonant elements for low-frequency sound control. Designed configurations contain sets of narrow channels extending wave propagation paths that leads to reduction of effective sound speed within a structure. We show that by folding these channels into fractal space-filling curves or bio-inspired geometries, one can induce strong artificial Mie-type resonances that allow the achievement of total broadband sound reflection at deep subwavelength scales. This unique phenomenon can be used to develop small-size metastructures with total reflectance of low-frequency sound for versatile applications.

Spider web-structured labyrinthine acoustic metamaterials for low-frequency sound control

Attenuating low-frequency sound remains a challenge, despite many advances in this field. Recently-developed acoustic metamaterials are characterized by unusual wave manipulation abilities that make them ideal candidates for efficient subwavelength sound control. In particular, labyrinthine acoustic metamaterials exhibit extremely high wave reflectivity, conical dispersion, and multiple artificial resonant modes originating from the specifically-designed topological architectures. These features enable broadband sound attenuation, negative refraction, acoustic cloaking and other peculiar effects. However, hybrid and/or tunable metamaterial performance implying enhanced wave reflection and simultaneous presence of conical dispersion at desired frequencies has not been reported so far. In this paper, we propose a new type of labyrinthine acoustic metamaterials (LAMMs) with hybrid dispersion characteristics by exploiting spider web-structured configurations. The developed design approach consists in adding a square surrounding frame to sectorial circular-shaped labyrinthine channels described in previous publications (e.g. ()). Despite its simplicity, this approach provides tunability in the metamaterial functionality, such as the activation/elimination of subwavelength band gaps and negative group-velocity modes by increasing/decreasing the edge cavity dimensions. Since these cavities can be treated as extensions of variable-width internal channels, it becomes possible to exploit geometrical features, such as channel width, to shift the band gap position and size to desired frequencies. Time transient simulations demonstrate the effectiveness of the proposed metastructures for wave manipulation in terms of transmission or reflection coefficients, amplitude attenuation and time delay at subwavelength frequencies. The obtained results can be important for practical applications of LAMMs such as lightweight acoustic barriers with enhanced broadband wave-reflecting performances.

Fractal labyrinthine acoustic metamaterial in planar lattices

Labyrinthine acoustic metamaterial provides a flexible and unprecedented ability to manipulate the sound wave propagation, such as sound blocking, cloaking, supertunneling etc. However, the design of labyrinthine acoustic metamaterial with excellent properties remains challenging with a traditional zigzag channel. Here, we develop a class of fractal-inspired labyrinthine acoustic metamaterials with hierarchical zigzag channels and highlight the influences of the self-similar fractal hierarchies on their band structures. Band structures of fractal-inspired labyrinthine acoustic metamaterials in the five representative Bravais lattices are also investigated. Our results show that the self-similar fractal can be effectively used to widen the total band gaps and lower the frequency of the first bandgap. Furthermore, for the second order fractal labyrinthine acoustic metamaterial arranged in different Bravais lattices, several excellently wide bandgaps appear in the different frequency ranges. By actively-tuning the Bravais lattice, we have a chance to yield excellently wide and tunable bandgaps. Thus, this work provides an insight into the critical role of the self-similar fractal on the band structure of the labyrinthine acoustic metamaterial, and gives a guidance for the selection of Bravais lattices with a desired band structure.

Subwavelength diffractive acoustics and wavefront manipulation with a reflective acoustic metasurface

Acoustic metasurfaces provide useful wavefront shaping capabilities, such as beam steering, acoustic focusing, and asymmetric transmission, in a compact structure. Most acoustic metasurfaces described in the literature are transmissive devices and focus their performance on steering sound beam of the fundamental diffractive order. In addition, the range of incident angles studied is usually below the critical incidence predicted by generalized Snell's law of reflection. In this work, we comprehensively analyze the wave interaction with a generic periodic phase-modulating structure in order to predict the behavior of all diffractive orders, especially for cases beyond critical incidence. Under the guidance of the presented analysis, a broadband reflective metasurface is designed based on an expanded library of labyrinthine acoustic metamaterials. Various local and nonlocal wavefront shaping properties are experimentally demonstrated, and enhanced absorption of higher order diffractive waves is experimentally shown for the first time. The proposed methodology provides an accurate approach for predicting practical diffracted wave behaviors and opens a new perspective for the study of acoustic periodic structures. The designed metasurface extends the functionalities of acoustic metasurfaces and paves the way for the design of thin planar reflective structures for broadband acoustic wave manipulation and extraordinary absorption.

A broadband acoustic absorber based on phase-modulating reflective metasurfaces

Most high performance acoustic absorbers exhibit outstanding absorption capabilities at resonant frequencies, thus their bandwidth are significantly limited. Acoustic metasurfaces enabled unprecedented wave manipulation with their planar profiles, subwavelength thicknesses, and large degree of design freedom. However, studies have been primarily focused on extraordinary wavefront shaping functionalities, and little explorations has been made on manipulating transmitted/reflected power of diffracted beams. By carefully tailoring the design and arrangement of acoustic metamaterial cells, enhanced absorption can be achieved for a broad range of frequencies. Building on our previous works on transmissive and reflective metasurfaces with exotic properties, including anomalous refraction, surface mode conversion, and extraordinary beam-steering (Xie et al. Nat. Commun. 2014), we present in this work a broadband acoustic absorber built with an expanded library of labyrinthine acoustic metamaterials. We demonstrate that by engineering the phase modulation profile of phase-modulating metasurfaces, incident waves can be effectively converted to surface modes that propagate along the air-metasurface interface, thus minimal reflection is observed in the far field. Our work extends functionalities of acoustic metasurfaces, demonstrates an alternative route to the design of broadband acoustic absorbers, and can be potentially applicable to noise control.

Compact acoustic antenna design using labyrinthine metamaterials

We present an effective design and architecture for a class of acoustic antennas in air. The work begins with a conformal transformation method that yields the preliminary design, which is constructed using an isotropic but inhomogeneous material. However, the desired material parameters have been unavailable until now. Here we show that by scaling up the refractive index and optimizing the geometry in the preliminary design, a series of square antennas can be achieved to exhibit an excellent beam-collimating effect. An important part of our strategy is that the device’s thickness and material properties can be tailored easily to greatly facilitate its realization. It is also demonstrated that the proposed antenna can be made very thin and readily implemented using labyrinthine acoustic metamaterials.

Design and demonstration of broadband thin planar diffractive acoustic lenses

We present here two diffractive acoustic lenses with subwavelength thickness, planar profile, and broad operation bandwidth. Tapered labyrinthine unit cells with their inherently broadband effective material properties are exploited in our design. Both the measured and the simulated results are showcased to demonstrate the lensing effect over more than 40% of the central frequency. The focusing of a propagating Gaussian modulated sinusoidal pulse is also demonstrated. This work paves the way for designing diffractive acoustic lenses and more generalized phase engineering diffractive elements with labyrinthine acoustic metamaterials.

Tapered labyrinthine acoustic metamaterials for coherent controlling of acoustic wave

Acoustic metamaterials with their exotic material properties enable unprecedented control over acoustic wave propagation and reflection. Besides utilizing locally resonating structures or non-resonant composite effective media, non-locally resonating spatial coiling structures have recently been adopted to design negative or high positive refractive index metamaterials. We have in the past experimentally demonstrated the unit cell characteristics of one kind of labyrinthine metamterial (Xie et al. PRL 2013) and its impedance matching improved versions (Xie et al. APL 2013). In this work, we present several coherent modulation devices based on our recently proposed tapered labyrinthine metamaterials. With thickness of only one or two metamaterial cell layers, we can create an acoustic blazed diffraction grating, a phase conjugation lens, or a flat lens that can perform plane wave-cylindrical wave conversion. The design process and experimental demonstrations will be presented. The coherent controlling devices feature precise phase modulation, high-energy throughput, broad operating bandwidth, and sub-wavelength thickness. Our work demonstrates that labyrinthine metamaterials can be the unit cells of choice for functional coherent acoustic modulation devices.