Abstract
Recent advancements in acoustic research have increasingly emphasized the dual consideration of sound insulation performance and air circulation efficiency. Traditional sound insulation materials exhibit significant limitations in fulfilling adequate ventilation requirements. Acoustic ventilated metamaterials, however, can simultaneously achieve both sound insulation and air circulation. In this review, we trace the development of many promising works from single-type resonant principles of sound insulation, including Helmholtz, Fabry-Pérot, Fano and membrane resonances. Significantly, we sort out some efforts taken to explore acoustic ventilated metamaterials based on hybrid-type resonances. They may show wider ranges of operating frequency than those based on a single-type. Finally, we discuss the future directions of this rapidly growing field by analyzing the prominent challenges it faces.
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Introduction
Noise can cause many physiological and psychological illnesses apart from disrupting people’s daily lives1. The severe impact arising from noise on environment cannot be ignored in modern society. The need for noise control is increasingly urgent in many fields, such as construction engineering, traffic engineering, manufacturing industry, etc2,3,4. However, the traditional sound insulation materials may obstruct airflow5. It will exert a negative effect on ventilation systems in noise control. In the area of architectural design, the demand for reducing energy consumption and improving indoor air quality drive the need for natural ventilation6,7,8. While the external ambient noise will inevitably permeate indoor spaces and potentially disrupt people’s living or working environment if windows or vents are opened. Similarly, in air-conditioning equipment, engine compartment and various electrical machinery systems, heat dissipation and air exchange are critical to maintaining steady works9. Many efforts have been made to solve such problems.
Traditional ventilation soundproofing methodologies can be classified into two primary categories: mechanical ventilation systems10 and natural ventilation approaches11. Mechanical ventilation systems typically involve the installation of air circulation devices with noise reduction capabilities on sealed windows. These systems use mechanical components such as fans to provide adequate airflow12. They can be adjusted in real-time and are therefore referred to as active ventilation. Inside the equipment, resistive silencers made from sound-absorbing materials are used to minimize the transmission and diffusion of external noise13. However, the introduction of mechanical components increases both energy consumption and operational costs. Moreover, fans require regular maintenance and generate additional noise14,15. They may also disperse the fibers of sound-absorbing materials into the air, raising potential health concerns for residents.
For a natural ventilation system, it faces an inherent conflict between sound insulation and airflow16. Various methods have been employed to mitigate this issue. For example, double-glazed windows with staggered inner and outer openings are commonly installed in high-rise residential buildings17,18. This design creates an S-shaped airflow path between the two layers of glass. Also, sound-absorbing materials applied to metal louvered windows further reduce noise19. Recent advances have enhanced the noise attenuation capabilities of natural ventilation systems. These improvements include the installation of micro-perforated panels20 and the arrangement of rigid cylinder arrays21 within the air passages between glass layers. Additionally, active noise control by setting secondary sound sources within the channels that sound waves pass through can be explored to dissipate acoustic energy22. This technology helps to further improve noise reduction while maintaining passive ventilation. The effectiveness of these systems depends on the precise positioning of the secondary sound sources and the accuracy of their control mechanisms23,24.
The traditional ventilation and sound insulation structures mentioned above are mainly applied in buildings. Ventilation and sound insulation effects can be improved to a certain extent with the design of local active components or passive configurations. However, these structures generally do not provide a direct, unobstructed airflow path, which is not beneficial to high-standard air and acoustic environments. In industry, to obtain higher mechanical efficiency and stability for productive process, the performances of ventilation and sound insulation for cabin covers of various motor devices also need to be strengthened25. Relatively few related studies are reported yet.
The emergence of acoustic metamaterials (AMs) has significantly contributed to addressing these limitations. As a kind of artificial material, AMs are usually composed of periodically arranged microstructures26,27,28,29,30,31,32. They can exhibit extraordinary physical properties that conventional materials do not possess through the orderly structural design. With the abilities of sound wave control, they can be used in the fields of acoustic stealth33,34,35, acoustic lens36,37, noise reduction38,39,40,41,42,43,44,45,46, etc. Wherein, noise reduction is one of the most popular topics due to the potential applications. In recent years, Acoustic ventilated metamaterials (AVMs), which can both achieve highly efficient sound isolation and maintain a certain degree of air circulation in deep subwavelength scale, have gradually become a significant research object47,48,49. AVMs with diverse spatial geometric configurations, classified as meta-mufflers, meta-barriers, meta-cages, have been extensively investigated and demonstrated significant potential for achieving simultaneous sound insulation and ventilation in applications. In addition, the emergence of additive manufacturing technology also provides a new way to manufacture AMs with complex structures50,51.
In this survey, we systematically summarize and elucidate recent developments of AVMs employing resonance-based principles for sound insulation. Distinct from the previous review articles on AVMs47,48,49, the present work provides a more comprehensive analysis focusing on AVMs based on single-type principle of resonance, while also incorporating the most recent advancements in this rapidly evolving field. Furthermore, the study firstly offers a thorough investigation of hybrid-type resonance principles in AVMs, which typically demonstrate enhanced application potential and superior design flexibility. Figure 1 shows a framework of physical principles for AVMs. In the second section, the transmission characteristics of an AVMs unit are demonstrated briefly. In the third section, AVMs based on single-type resonant principles, including Helmholtz resonance, Fabry-Pérot resonance, Fano resonance, and Membrane resonance are discussed, respectively. Resonance-based AVMs effectively attenuate sound energy through the manipulation of resonance and dissipation. Exceptional performance in low-frequency sound isolation is observed. This is significantly practical because low-frequency noise is common in urban environments52. Moreover, AVMs with Helmholtz resonator have the advantage of easily controlling the resonance frequency. The Fabry-Pérot resonance and Fano resonance feature a more compact structure that integrates better with ventilation channels. While the Membrane resonance is characterized by a thinner and lighter structure. The fourth section is the review of the AVMs based on hybrid-type resonance principles. They are characterized by better low-frequency and broadband sound isolation. Meanwhile, the structure can be designed as ultra-open and lightweight. Finally, the paper provides an outlook on the future development of AVMs.
A framework that shows different resonance principles for ventilated sound insulation.
Transmission characteristics of an AVM unit
As shown in Fig. 2, an unit cell of AVM is placed in a cylindrical waveguide. The cylindrical structure retains certain openings to ensure the free flow of air accompanied with sound insulation. The relationship between the sound pressure P and the particle velocity V of the input and output parts across the metamaterial can be related with a transfer matrix T0 as follows42:
Conceptual diagram of an AVM unit in cylindrical waveguide.
For the present system, T0 can be rewritten as53,54:
Herein, \(\iota =\sqrt{-1}\); \({Z}_{{\rm{Air}}}=\rho c\) is the air impedance; ρ is the density of air; c is the velocity of sound wave in air; k is the wave number of air; ZAVM and l are the total impedance and thickness of unit, respectively. The various regions of the sound field are connected by the continuity of sound pressure and the particle velocity. The first and third terms in Eq. (2) correspond to the contributions from the area change in the front and rear half parts of the cylindrical tube, respectively. The second term represents the contribution from resonance-based AVM. The acoustic transmission coefficient T of AVM can be given as:
where T0mn represents each element of the 2 × 2 matrix T0, and m,n = 1, 2.
The cross sections of waveguides discussed in this review are primarily categorized into two types: circular and square. In principle, the waveguide and the unit depicted in Fig. 2 can be substituted with units of arbitrary cross sections55,56. It only needs to be satisfied that the system must operate in a plane wave regime within the frequency range below the cutoff frequency of the waveguide.
The AVMs based on single-type resonance
Resonance is a fundamental concept in physics, characterized by a substantial amplification of system response at specific frequencies57. For AVMs, our investigation specifically concentrates on the implementation of resonance in acoustics. AVMs achieve sound isolation primarily through two mechanisms: sound absorption and sound reflection. Sound absorption predominantly occurs within the cavities of metamaterials, where intense resonances localize sound energy53,58,59,60. For the other one, sound reflection is typically related to destructive interference61,62,63,64. Taking account of sound absorption or reflection, various resonance principles have been successfully applied in AVMs, including Helmholtz resonance, Fabry-Pérot resonance, Fano resonance, and Membrane resonance.
In this review, AVMs based on single-type resonance are specifically defined as metastructures that employ exclusively one of the aforementioned resonance effects as the dominant mechanism for sound insulation. Such resonators commonly exhibit multiple-order resonances at different frequencies. However, current review mainly focuses on exploiting fundamental resonance (i.e., first-order resonance) modes65,66,67,68. Higher-order resonance modes may also be utilized to achieve sound isolation of AVMs69,70. The relative investigations are not too much and will not be discussed in detail in this review.
Helmholtz resonance
In typical Helmholtz resonance phenomena, acoustic waves propagate through a narrow neck into an enclosed cavity71,72. The whole system can be simplified as a spring-mass model. The resonator’s neck functions as an oscillating mass while the contained air volume acts as a spring element73. When the frequency of the incident sound wave matches the natural frequency of the system, the air column in the aperture vibrates intensely due to resonance, thereby sound energy can be attenuated74. Helmholtz resonators have three key design parameters: neck length, opening area, and cavity volume. By adjusting these geometric parameters, the resonant frequency can be precisely manipulated53,75,76. Due to efficient effect of resonance, Helmholtz resonators show a surprising advantage in low-frequency sound absorption71,77,78. In this part, we will review AVMs driven by Helmholtz resonance dominantly according to the classification of spatial structures: meta-mufflers, meta-barriers, meta-cages.
Meta-muffler
In general, meta-mufflers are employed to address sound insulation challenges in waveguide-aligned structures, particularly in one-dimensional systems such as piping networks where sound propagation follows linear transmission paths39,40,53,58,59. Such kind of structures are usually laid on the surface of airflow channel to attenuate sound waves and keep the channel unobstructed79,80,81,82,83,84,85. In several research, AVMs referred to this category of metastructures are also called meta-liners82,83,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102.
The simplest meta-muffler contains only one resonator in an unit cell70,81,99,103. Anderson103 conduct an experiment, setting the Helmholtz resonator in a single side branch of the circular pipe that allows both sound and airflow to pass through. It is observed that the fundamental resonant frequency will rise with the increase of airflow velocities. The results reveal a remarkable dependence of resonant properties on airspeed. Wang et al.70 integrate one resonator into the side branch of a waveguide, as shown in Fig. 3a. The resonator exhibits near-zero acoustic energy transmission at 335.6 Hz. They reveal how the excitation of evanescent guided waves affects the transmission cancellation of resonant frequencies. Wen et al.81 develop similar configurations into origami-based AMs, which integrates accordion origami into Helmholtz resonators as the side cavity. The configuration exploits the single-degree-of-freedom characteristic of accordion origami, enabling facile adjustment of sound attenuation properties via air pressure changes. Their design not only achieves a significant transmission loss (TL) of over 10 dB in the frequency range of 271–790 Hz but also maintains airflow permeability. As can be observed, AVM with only a single resonator usually generates narrow band sound isolation, which limits the practical utility in complex noise control scenarios requiring broadband attenuation.
a The transmission coefficient of the individual resonator integrated into the waveguide. The illustration shows the resonance modes of the resonators. Reproduced with permission from ref. 70. b Complex band structures and sound attenuation for the cascaded resonators. Reproduced with permission from ref. 70. c Configurations of the meta-liner and the supercell. The spectrum presents the sound transmission loss for the airflow velocity of 10 m/s. Reproduced with permission from ref. 79. d The ring-shape meta-muffler with six unit cells and the absorption coefficient spectrum. Reproduced with permission from ref. 53.
Seo and Kim104 propose a solution to this problem. The working bandwidth of the muffler is significantly expanded through cascaded Helmholtz resonators with different geometric parameters. Based on the structure shown in Fig. 3a, Wang et al.70 also propose a metastructure composed of cascaded resonators in periodicity. This configuration introduces additional Bragg bandgaps, further improving the effect of sound isolation. The corresponding results are presented in Fig. 3b. Huang et al.79 developed an acoustic liner with considering grazing flow, see Fig. 3c. The liner consists of a perforated plate and a meta-surface with neck-embedded Helmholtz resonators. The supercell is composed of multiple Helmholtz resonators with different geometric parameters arranged in a periodic two-dimensional array. The equivalent acoustic impedance of the liner could be modulated by changing several key geometric parameters, and sound insulation in the frequency range of 800–3000 Hz is obtained. Moreover, the metastructure is also analyzed with considering airflow. Particularly, as the velocity of airflow is within the range of 10–60 m/s, significant sound energy dissipation can be observed. It reveals that the influence of airflow velocity on the acoustic properties cannot be ignored for ventilated acoustic matamaterials. A number of studies have taken this factor into consideration79,82,84,89,92,105,106. For example, Meng et al.106 investigate the monopolar and dipolar acoustic responses of a passive single point scatterer subjected to low-Mach-number grazing airflow. Wang et al.82 develope a coiled-up meta-liner with nonuniform cross sections to effectively attenuate low-frequency sound under conditions of grazing flow.
By cascading multiple unit cells with gradient dimensions, Gao et al.53 design a ring-shape meta-muffler with high ventilation. It consists of an ultra-thin annular cavity and a hole opening on the inner wall, as shown in Fig. 3d. The experiment shows an average absorption of 98% in the frequency range of 380–470 Hz. The ventilation rate, ratio of opening area to total occupied area, is up to 70.56%. Similarly, they develop a cascaded arrangement with structural gradient in another AVM and achieve optimized sound absorption by coupling modulation of resonant energy leakage and loss75.
Although the cascaded configuration enables broadband sound isolation, it imposes significant thickness requirements on the metamaterials, which raises practical concerns. Recent studies have investigated parallel configurations to achieve broadband acoustic attenuation while maintaining reduced thickness79,80,83,84,107,108,109,110,111. Nguyen et al.72 propose an acoustic muffler that achieves low-frequency sound insulation with broadband and high ventilation by using a compact slot Helmholtz resonators (SHRs), as shown in Fig. 4a. The structure is constructed with a double-layer acoustic muffler. Each layer consists of five SHRs with different geometric parameters. The design performs well within the frequency range of 480–950 Hz, with transmission losses of over 30 dB and a maximum of 50 dB. The thickness of the muffler is only 0.04λ. Wherein λ is the wavelength, corresponding to 480 Hz here. Meanwhile, excellent ventilation performance is also ensured. A configuration involving both cascading and parallel arrangements is proposed by Meng et al.59. To reveal the absorption behaviors of both reflected and radiated acoustic waves for one-dimensional open pipeline problem, they develop an acoustic absorption metamaterial by cascading several monopolar point scatterers. A monopolar point scatterer is composed of multiple Helmholtz resonators distributed in a ring array in parallel. For the single ring of monopolar point scatterer consisting of 14 Helmholtz resonators with different geometric parameters, the maximum sound absorption in the frequency range of 250–500 Hz could be achieved due to the weakly coupling effects between 14 resonators. As a comparison, utilizing the strong coupling between multiple layers of ring-shaped scatterers, an approximate perfect sound absorption is able to be achieved between 450 and 1000 Hz demonstrated by experiments, see Fig. 4b. In this configuration, the multiple Helmholtz resonators in each ring are identical, while varying across different layers.
a The double-layer acoustic muffler and sound transmission loss spectrum. Reproduced with permission from ref. 72. b The acoustic metamaterial consists of multiple layers of monopolar point scatterers cascaded together, along with the configurations of a monopolar point scatterer and an individual resonator within it. The spectrum presents the sound absorption coefficient. Reproduced with permission from ref. 59.
Meta-barrier
Meta-barrier is composed of unit cells arranging in a two-dimensional array. It has a remarkable adaptability for planar sound insulation problems, such as building sound insulation and noise reduction for mechanical equipment54,65,112,113,114,115,116,117. Kumar et al.114 propose a metastructure for both ventilation and sound isolation, illustrated in Fig. 5a. The unit cell consists of a Helmholtz cavity with two openings and a central airflow vent. Due to the high impedance match between the structure and air, sound absorption of 96% at 1000 Hz is obtained, with sound TL of 18 dB. Meanwhile, a ventilation area accounting for 45% of the total area is reserved. Furthermore, multiple unit cells are assembled into an acoustic barrier by applying a jigsaw puzzle approach. The efficient acoustic performances of the meta-barrier in low-mid frequency range are experimentally validated. Dong et al.54 report an acoustic barrier with ultra-broadband sound attenuation, as shown in Fig. 5b. The supercell is composed of multiple resonators that are independently arranged, possessing a combination of dissipation and interference effects. The multi-layer helical structure demonstrates remarkable sound absorption (over 90%) in the frequency range of 650–2000Hz. The thickness of the structure is only λ/10. In addition, the meta-barrier also provides a wind speed ratio of about 34%, allowing air to flow freely. Origami metamaterials are also utilized for fabricating the meta-barrier due to their excellent fold-ability and dynamic adjustment performance. Jin et al.65 present a reconfigurable silencing window. The window consists of numerous origami modules that are assembled into a barrier, see Fig. 5c. Each module is composed of interconnected origami “tiles” that form a “tile-void” structure. Owing to the distinctive characteristics of origami, the structure can undergo shape transformation via a straightforward folding mechanism. This mechanism enables the areas between the tiles and voids to change in a flexible manner. As a result, the window is able to dynamically adapt to both acoustic and ventilation functions. It is validated that the average sound TL of the origami window significantly outperforms the conventional sliding window. The sound attenuation for specific frequency bands are further optimized through strategic adjustments of origami geometry, internal partitions, and folding angles.
a The unit cell consists of a Helmholtz cavity with two openings and a central airflow vent, along with the transmission loss spectrum of the meta-barrier. Reproduced with permission from ref. 114. b The meta-barrier and the multi-layer helical supercell, along with the power transmission spectrum. Reproduced with permission from ref. 54. c The reconfigurable origami acoustic meta-barrier, as well as the variation of ventilation and average transmission loss with the opening angle \(\theta\). Reproduced with permission from ref. 65.
In addressing the problem of typically low ventilation in meta-barriers, ultra-open structures are developed38,60,118,119,120,121,122,123, which are characterized by a high ventilation rate. He et al.121 propose an ultra-open and omnidirectional meta-barrier, as shown in Fig. 6a. Through the arrangement of units consisting of two central-symmetric cavities with a ventilation of 80%, the barrier attains a thickness of merely ~0.12λ. This configuration not only efficiently obstructs sound waves approaching from all directions but also ensures the maintenance of a wind velocity ratio exceeding 90%. Wind velocity ratio is defined as the ratio between the wind speed measured with the metamaterial structure and that measured without it. Ye et al.60 design an reconfigurable ultra-open acoustic meta-barrier. The unit cell is constructed with three independently configured Helmholtz resonators, see Fig. 6b. It features a wind velocity ratio of 95.9% and a ventilation of 80.5%. By mechanically changing the blades angle β, the proposed metamaterial enables continuous frequency tuning of acoustic absorption, across a bandwidth from 600 Hz to 950 Hz. Xiang et al.118 develop an ultra-open ventilated meta-barrier with creating a more spacious ventilation area beyond the confines of units, see Fig. 6c. The unit cell consists of two symmetrical split-tube resonators and the slit between them. The slit leads to the coupling of two spilt-tube resonators. The configuration results in the merger of symmetric mode and antisymmetric mode resonance peaks, which further enhances the sound absorption performances of the unit cells. The experiments show that the ultra-open meta-barrier achieves a sound absorption coefficient larger than 50% within the frequency range of 476–726 Hz, and maintains a ventilation of 52.4%. They also put forward an adjustable design for analogous structures119,120. This design is realized through physical tuning and electromechanical adaptive adjustments. Similarly, Shrestha et al.117 design a micro-perforation actuator which can reduce the perforation size by voltage sensing to achieve tunable broadband sound absorption.
a The ultra-open and omnidirectional meta-barrier and the unit, as well as the transmission coefficient for incident angle of 0°. Reproduced with permission from ref. 121. b The reconfigurable ultra-open meta-barrier and the absorption coefficient for the blades angle β = 10°. Reproduced with permission from ref. 60. c The unit cell consists of two symmetrical split-tube resonators, and the absorption coefficient spectra for the ultra-open meta-barrier. Reproduced with permission from ref. 118.
Meta-cage
Meta-cage is a stereo structure which is designed to overcome the challenges of three-dimensional ventilation and sound insulation124,125,126,127. The device employs a cage-like structural configuration, serving to either trap noise within or block it from entering. For wrap-around noise control, the meta-cage has shown specific advantages. Kumar et al.125 propose an acoustic meta-cage comprising multiple cylindrical pillars assembled in an axisymmetric shape. Each column unit consists of two-sided half-cylindrical weakly coupled Helmholtz resonator cavities with respective openings, illustrated in Fig. 7a. Two types of cavities with different configurations observed from the top view are intentionally designed. These resonators are arranged according to a specific geometry, forming a ring-shape structure. The insertion losses reach 20.8 dB and 11.9 dB at 2500 Hz when the sound source is placed inside and outside the cage, respectively. Meanwhile, this meta-cage ensures effective direct ventilation to prevent overheating. The design provides a new solution for practical applications, such as industrial noise control and heat dissipation. Xiao et al.126 develop an acoustic metamaterial composed of a number of periodically arranged resonant cavities in series, with a star-shaped opening in the middle to facilitate free airflow in each unit, as shown in Fig. 7b. Sound transmission can be controlled directly through rotating the opening. By configuring resonant cavities around a central air passage, the metamaterial reduces noise by more than 30 dB in the frequency range of 625–1695 Hz. A meta-cage is constructed with six units assembled in a cuboid structure, is capable of reducing of more than 60 dB in the frequency range of 650–1410 Hz.
a The meta-cage comprises an axisymmetric array of cylindrical columns which are constructed from Helmholtz resonators, with corresponding transmission loss spectra for both internal and external acoustic source configurations. Reproduced with permission from ref. 125. b The meta-cage constructed with the metamaterial, which is composed of periodically arranged resonant cavities in series, with a star-shaped opening. Reproduced with permission from ref. 126.
Overall, for meta-mufflers, AVMs with only one resonator feature a simplified structural configuration and ease of fabrication, but the practical applications are constrained by inherent narrowband limitations. Using multiple resonators can broaden the frequency band, which often involves cascading and paralleling of unit cells. However, critical challenges arise where cascading configurations lead to increased thickness of metamaterial layers while parallel arrangements reduce ventilation efficiency, necessitating a trade-off analysis. For meta-barriers, while the metastructure formed by compact arrangement of supercells can easily achieve broadband sound isolation, the design inherently compromises the ventilation capabilities. This technical challenge can be effectively mitigated through the implementation of an ultra-open structural configuration.
Fabry-Pérot resonance
As demonstrated in previous analyses, the application of Helmholtz resonance principle enables effective sound isolation of both low-frequency and broadband. However, it cannot be ignored that low-frequency sound isolation always depend on a large enough cavity volume, while broadband is often related to the splicing of the resonator59,114. Both treatments will result in a relatively large size of structure. In certain cases, structural design flexibility in structural design has to be compromised. AVMs based on Fabry-Pérot resonance can address this issue due to the compact structure128,129,130,131,132. Fabry-Pérot resonance (FP resonance) typically occurs in closed channels with limited length, where sound waves are scattered repeatedly inside the cavity. When a stable standing wave pattern is formed, the wave will interfere with the reflected wave, generating the FP resonance128. Under the resonance modes, sound energy is significantly attenuated. The key geometric parameters of FP resonators are usually the effective path length and the thickness of the channel130. A longer effective length corresponds to a lower resonant frequency. A larger thickness corresponds to a stronger sound insulation performance. In addition, the space coiled structure, as a typical FP resonator, can realize low-frequency sound insulation regardless of the volume of cavity129,132. Therefore, the space required for the structure can be reduced, which is favorable of the requirement of compact structure.
Meta-muffler
Similar to Helmholtz resonators, some studies have sought to extend the working frequency band by integrating FP resonators with different geometric parameters105,128,129,130,131,132,133,134,135. Liu et al.130 design a broadband muffler utilizing cascaded labyrinthine meta-surfaces. Each unit cell includes an open central hole connected to a bypass space coiling tunnel (Fig. 8a). By optimizing the geometric parameters of the multi-layer unit cell, they have improved the TL to over 15 dB within the frequency range of 198–412 Hz. However, due to the extensive distribution of metamaterial on the windward side, similar structures have difficulty to maintain a high ventilation rate.
a The circular labyrinthine metamaterial and the transmission loss spectra. Reproduced with permission from ref. 130. b The muffler consisting of a series of crimped FP resonators and the absorption coefficient spectra. Reproduced with permission from ref. 132. c The labyrinth acoustic metamaterial and the coiled portion, as well as the absorption coefficient spectra. Reproduced with permission from ref. 129.
Ventilation is also a key requirement for many equipment91,124,132,136,137,138. To improve the performance of air circulation, Yang et al.132 design a muffler for noise control of high voltage direct current (HVDC) converter stations by incorporating a series of crimped FP resonators, see Fig. 8b. The configuration not only achieves broadband noise absorption in the frequency range of 600–900 Hz but also provides efficient ventilation of 25%. Sound insulation of the muffler is mainly due to the slow wave effect. The effect enables acoustic waves to resonate within the structure for an extended duration, thereby promoting more interactions between the waves and the structure. To enhance airflow, Kumar et al.129 develop a labyrinth acoustic metamaterial, see Fig. 8c. The design integrates multiple maze-like units in parallel within a hexagonal structure, achieving a sound absorption coefficient of over 0.8 at 325–600 Hz while ensuring sufficient air circulation.
Meta-barrier
Recent research efforts have also explored the development of meta-barrier based on FP resonance139,140,141,142. Ma et al.140 develop a ventilation meta-barrier with low-frequency and broadband sound insulation by applying the space coiled structure, as shown in Fig. 9a. By introducing multiple resonant modes in internal channels, the meta-barrier effectively controls sound waves, especially at low frequencies. The design achieves sound isolation performance in multiple frequency bands by stacking different meta-barrier layers. Meanwhile the opening rate of the structure is 10.2%. A bidirectional sound barrier is presented by Du et al.141. The unit cell includes a ventilation duct and a curled single-ended closed channel, as shown in Fig. 9b. By employing a bilayer structure and introducing the asymmetric loss, the design achieves near-perfect absorption (98.6%) at the resonance frequency for sound waves incident from the front, while maintaining a ventilation of 50%. The relative bandwidth of the absorption peak can be adjusted from 12% to 80% by changing the ventilation of the structure. For sound waves incident from the rear, the bilayer meta-surface still acts as a low-transmission sound barrier. To further improve ventilation rate, Shao et al.142 present an ultra-open metamaterial with broadband low-frequency sound absorption, see Fig. 9c. Broadband sound insulation is achieved by parallel coupling through four vented metamaterial absorbers with different resonant frequencies, each of which comprises three folded FP resonators. The three resonators are designed as dark, intermediate, and bright modes. They effectively manage sound energy through different damping levels. The dark mode is highly overdamped to absorb sound energy, the bright mode is highly underdamped to simulate effective acoustic soft boundaries, and the intermediate mode is slightly overdamped to enhance absorption. The experiment confirmed that the sound barrier maintained an absorption rate of more than 90% in the frequency range of 307–341 Hz and ventilation of 46.3%.
a The sound barrier composed of an array of the space coiled structure and transmission loss. Reproduced with permission from ref. 140. b The meta-barrier with a bilayer structure and reflection, transmission and absorption coefficients. Reproduced with permission from ref. 141. c The ultra-open sound barrier, along with reflection, transmission, and absorption coefficients. Reproduced with permission from ref. 142.
Meta-cage
Although there is rather few research on acoustic meta-cages driven by FP resonances for sound insulation, some outstanding work still needs to be highlighted. Considering three-dimensional sound insulation, Liu et al.143 design a acoustic meta-cages consisting of six metamaterial plates, as shown in Fig. 10a. Each of which hides bypass space-folding channels connected to the opening. The FP resonance constructed by the channels ensures that the acoustic metacage can effectively achieve sound isolation around 1030 Hz. In addition, this design shows robustness to airflow disturbances and is suitable for scenarios that require sound insulation and ventilation. Yin et al.144 also make a great progress in both broadband sound insulation and ventilation. They designed an acoustic local rainbow trapping meta-cage, see Fig. 10b. The underlying mechanism involves FP resonance induced by radially gradient grooves carved along the circumferential direction. By strategically designing the distribution and dimensions of these grooves, the structure can achieve a TL of at least 10 dB within 1500–1800 Hz while maintaining a ventilation of 55%.
FP resonance is favored by many researchers due to excellent low-frequency sound insulation performance and compact structure. However, the multi-layer coiling design on the windward side will also affect the ventilation performance of metamaterials105,128,130,131,133. This is an issue that needs to be addressed.
Fano resonance
Fano resonance is also inseparable from space-coiled structure. It is widely used in AVMs because of its excellent sound insulation performance in the low and middle frequencies and compact structure56,67,145,146,147,148,149,150,151,152,153,154. The space-coiled resonator guided by Fano resonance has an inlet and an outlet for sound waves. The sound waves entering from the inlet are repeatedly scattered due to the coiled path during propagation. A discrete state wave is generated. When the sound wave passes through the ventilation passage, the waveform is unchanged. It is a continuous state wave. The two waveforms are symmetrical. After the two waves are coupled near the outlet. Due to the phase difference between them, the coupled waveform becomes asymmetric155. This corresponds to the destructive interference and constructive interference between the two sound waves, in which the destructive interference realizes the sound energy dissipation.
Ghaffarivardavagh et al.62 design an ultra-open acoustic muffler (Fig. 11a). The unit cell consists of two layers of media with significant contrast in acoustic properties. This significant contrast results in asymmetric acoustic transmission of the unit cell, which is the result of Fano resonance. They achieve a 94% reduction in transmitted sound energy by adjusting the acoustic impedance contrast and refractive index contrast between the two layers. In particular, the metamaterial unit has an open area of about 60%, allowing for air circulation in applications where ventilation is required. Zhang et al.63 develop an omnidirectional ventilated barrier using a binary structure consisting of a coiled unit and a hollow pipe, see Fig. 11b. The principle behind this barrier is the Fano resonance between binary structures. It allows the structure to not only effectively block noise from multiple directions but also allows up to 63% of the air flow through. Furthermore, the sound insulation performance is maintained when the sound barrier faces the sound from different incidence angles. This indicates the robustness of the omnidirectional sound insulation of the structure. In an innovation based on traditional Herschel-Quincke tubes, Kim et al.156 integrate multiple resonators into a silencer. The device involves two parallel tubes: one rigid and the other lined with a periodic resonator that promotes destructive interference and enhances sound attenuation by varying the phase velocity. The muffler exhibits high sound performance while keeping the system pressure drop to a minimum. Meanwhile, they considered the impact of airflow velocity on the proposed structure.
In engineering applications, narrow-band nature of Fano resonance is inevitably limited in dealing with some sound insulation problems62,63. Such as discrete noise sources, which usually require a broadband sound insulation. Sun et al.64 apply Fano resonance designing an acoustic ventilation barrier to broadband effect, as shown in Fig. 12a. The unit cell possesses a central vent and a spiral channel around it. Their design blocks 90% of sound transmission from 900–1418 Hz while guaranteeing a ventilation of 20.25%. The efficient sound blocking is mainly attributed to the design of multi-layer spiral structures, which achieve a balanced response between the monopole mode and dipole mode. This broadband sound isolation phenomenon is defined as acoustic consecutive Fano resonance56,64,66,147,148,149,150,151,152,153.
a The helical metamaterial and sound transmission loss spectra. Reproduced with permission from ref. 64. b The metamaterial for attenuating broadband diffused sound and sound transmission loss spectra. Reproduced with permission from ref. 56. c The reconfigurable metamaterial and sound transmission loss spectra at s’ = 5 mm and s’ = 25 mm. s’ is the spacing of the zigzag channel after sliding. Reproduced with permission from ref. 66.
Consecutive Fano resonances are generated by inducing the space-coiled structure to produce consecutive resonant modes. The discrete state acoustic waves under resonant modes interfere with the continuous state acoustic waves in the ventilated region. The interference shapes multiple asymmetric Fano responses into a symmetrical continuous Fano response. This results in low sound transmission between multiple Fano resonance peaks, enabling broadband sound isolation. Xu et al.152 further optimize similar structures by employing a machine learning-based inverse design method. To address the attenuation of diffuse sound, Dong et al.56 apply the concept consecutive Fano resonances to a space-coiled barrier through simulation and experimental validation, see Fig. 12b. The core principle underpinning the structure is the consecutive Fano resonances (destructive interference) that occur between the spiral structure and the central hole. The thickness of the meta-barrier is only 1/11 of the wavelength corresponding to the lowest working frequency, and the structure maintains a ventilation rate of 20%. Although the AVM is designed in the plane wave regime, over 10 dB of sound TL is measured in the regime of 610–1120 Hz for a diffuse sound field. Li et al.66 propose a tunable design driven by consecutive Fano resonances. They develop a reconfigurable acoustic metamaterial with a maze-like structure (Fig. 12c). The innovative design includes separable zigzag channels, which can adjust the frequency for sound insulation without affecting the structural thickness. The adjustment is achieved through a simple sliding principle. It allows tuning the frequency between 360 and 575 Hz while maintaining a constant free ventilation of over 36.3%.
Compared to FP resonance, space coiled structures driven by Fano resonance are often more compact or have higher ventilation. The possible reason is that the emergence of broadband characteristics does not depend on the splicing of resonators but is related to the FP resonance mode of coiled channels. To further expand the bandwidth, Tang et al.149 introduce three consecutive resonance modes in a helical structure (Fig. 13). They designed a broadband ventilated sound barrier utilizing mode superposition and consecutive Fano resonances. This design features a central hollow orifice and four surrounding spiral blades in a bilayer meta-structure. The continuous Fano resonances and the superposition of monopolar and dipolar modes enable the device to achieve up to 90% sound attenuation in the frequency range of 1145–1815 Hz.
Reproduced with permission from ref. 149.
Through the above research, it can be found that most space-coiled structures based on Fano resonance appear in the form of meta-barriers. They are usually compact and have a high ventilation rate. The consecutive Fano resonances endow the structure with broadband acoustic performance. However, metamaterials based on such a principle have poor sound insulation performance at low frequencies. How to improve the contribution of Fano resonance in low-frequency sound insulation is also an unexplored area.
Membrane resonance
Membrane Acoustic Metamaterials (MAMs) are characterized by their lightness and ease of adjustment. Their sound absorption performance at low frequencies is outstanding. MAMs are mainly composed of rigid frames and membranes61,157,158,159,160,161,162,163,164,165. When sound waves are incident on the membrane, the membrane structure triggers resonance, thus consuming the energy of the sound waves.
Wang et al.61 design an ultra-thin and durable open membrane metamaterial, see Fig. 14a. The structure consists of a rigid frame and a membrane with perforations. Sound transmission is reduced due to the interference effect of sound waves between the hole area and the membrane area. The experiment shows a significant sound TL of 20 dB at 430 Hz, despite the minimal thickness of only 1.5 mm. In addition, the large hole in each cell ensures air flow and the rigid framework ensures the durability.
a schematic diagram of the open membrane metamaterial, along with sound transmission loss and transmission coefficient spectra. Reproduced with permission from ref. 61. b Metamaterial consists of an array of four tunable membrane resonators and transmission loss spectra. Reproduced with permission from ref. 157.
Moreover, the acoustic properties of the membrane structure can be adjusted by changing the tension of the membrane. Yu et al.157 explore a tunable acoustic metamaterial composed of an array of resonators (Fig. 14b). Each resonator consists of a cavity and a pre-stretched dielectric elastomer membrane. The acoustic properties of resonators are adjusted by changing the voltage applied to the dielectric elastomer membrane. Therefore the overall TL of the device can be controlled. Experiments demonstrated that the configuration formed by an array of four resonators achieved a TL greater than 10 dB in the frequency range of 295–420 Hz. Additionally, the configuration also showed up to 14% tunability (frequency shift rate regulated by voltage) in sound attenuation due to changes in the voltage applied to the dielectric elastomer membrane.
Membrane resonators have the advantages of being lightweight, providing low-frequency sound insulation, and being easy to tune. However, due to the large area of obstruction and the difficulty of manufacturing and processing, research on AVMs based on membrane structures is very scarce. The durability of the membrane structure also is a concern.
The AVMs based on hybrid-type resonances
With the rapid development of AMs, the study in structures with single principles for sound insulation is becoming more and more mature80,143,151. To improve sound insulation performance, AVMs based on hybrid-type resonances gradually developed. The hybrid-type resonance principles refer to using multiple resonance principles in a structure to achieve sound insulation.
Coupling of Helmholtz resonance and Fabry-Pérot resonance
As mentioned above, both Helmholtz resonance and FP resonance can isolate low-frequency noise. The advantage of Helmholtz resonance lies in the resonant frequency can be precisely controlled. For FP resonance, the advantage lies in the compact size of the structure. Utilizing these advantages, sound insulation with a wider frequency range can be achieved without significantly increasing the structure thickness89,92,93,166,167,168,169,170,171. Liu et al.167 design a structure for sound insulation, which includes an open waveguide tube with a spiral throat (FP resonator), as well as a single Helmholtz cavity connected to the tube, as shown in Fig. 15a. Using coupled Helmholtz and FP resonances within the compact labyrinth units, the structure not only achieves broadband sound isolation in the frequency range of 120–3100 Hz but also maintains natural ventilation.
a The meta-muffler coupled with a FP resonator and a single Helmholtz resonator, and transmission coefficient. Reproduced with permission from ref. 167. b The meta-muffler composed with a layer of Mie resonator and a layer consisting of eight Helmholtz resonators in a parallel array and transmission coefficient and transmission loss. Reproduced with permission from ref. 169. c The meta-muffler constructed with Helmholtz resonators and FP resonators laid along the inner wall of the pipeline and transmission loss. Reproduced with permission from ref. 93. d Structures providing monopole and dipole resonance modes as well as transmission coefficient. The illustration is the experimental test system. Reproduced with permission from ref. 170.
Similarly, Chen et al.169 present another design. The composite acoustic metamaterial consisting of a Mie resonator and a Helmholtz resonator array (Fig. 15b). The Mie resonator achieves multi-mode resonance utilizing the high contrast in refractive indices, and the HR array achieves broadband sound attenuation through the parallel arrangement of different geometric structures. More than 90% of the incident acoustic energy is blocked in the frequency range of 350–1600 Hz. A meta-muffler constructed with Helmholtz resonators and FP resonators laid along the inner wall of the pipeline is proposed by Liu et al.93, as shown in Figure 15c. The compact design transfers the inherent thickness for sound insulation to the length direction of the pipeline, resulting in an ultra-thin structural design and a ventilation of 55.5%. The measured results show that the average TL of the structure is 12 dB. The TL is more than 10 dB within the frequency range of 404–1169 Hz, and more than 15 dB within the range of 419–540 Hz and 835–1083 Hz.
In addition, specially designed Helmholtz resonator and space-coiling structure can inspire monopole and dipole modes, respectively. These correspond to the negative effective bulk modulus and negative effective mass density, respectively. Gao et al.170 couple monopole and dipole resonance modes into a four-element meta-surface (Fig. 15d). Each unit consists of a central cavity and open-ended pipes on both sides, forming a Helmholtz resonator (monopole mode). The central channel formed by connecting four units constructs a FP resonator (dipole mode). Due to the coupling effects, the meta-surface achieves effective sound insulation in the frequency range of 1040–1465 Hz. Meanwhile, the thickness of the structure is only 0.127λ.
Coupling of Helmholtz resonance and membrane resonance
There have been some works on combining membrane structures with Helmholtz resonators to enhance low frequency performance91,172,173,174. Kim et al.172 design an AVMs with low-frequency broadband (Fig. 16(a)). In this design, the membrane structure exhibits negative mass density in the frequency range of 290–435 Hz and the Helmholtz resonator exhibits negative bulk modulus in the range of 440–600 Hz. By adjusting the cavity height of the Helmholtz resonator to match the frequency range of the two structures, a continuous negative effective region in the frequency range of 290–600 Hz is realized. The results show that the muffler has a TL of more than 10 dB in the frequency range of 275–500 Hz. In addition, the structure supports a ventilation rate of about 50%. Different from this type of separated composite material, Shao et al.173. introduce a membrane metamaterial constructed within a Helmholtz cavity, in which multiple membranes are embedded in the cavity, see Fig. 16b. The investigation shows that increasing the number of membranes can reduce the resonance frequency caused by negative mass density. The increase in the number of Helmholtz cavities directly expands the frequency bandwidth for sound insulation. The metamaterial can achieve a TL of more than 20 dB at 380 Hz and retain a certain ventilation area.
a AVM composed with a membrane structure and a side Helmholtz resonator and transmission loss. Reproduced with permission from ref. 172. b Meta-muffler constructed with a layer of membrane material in ring-shape embedding in a circle Helmholtz cavity, and transmission loss spectra. Reproduced with permission from ref. 173.
Coupling of Fano resonance and Fabry-Pérot resonance
Both Fano resonance and FP resonance are inseparable from the space-coiled structure. Designing a structure by combining the two different resonances to achieve a novel acoustic effect seems to be an interesting idea. Zhu et al.68 present a ventilated meta-surface with non-local effects, which combines a central hole and its surrounding spiral blades (Fig. 17a). Non-local effects are achieved through the synergistic effect between radiation coupling and direct coupling. This effectively broadens the working bandwidth and improves the acoustic performance. The results show that the meta-surface can continuously block more than 90% of the incoming sound energy in the range of 600–1900 Hz, while maintaining a wind speed ratio of 27%.
a The meta barrier with each unit composed of a central hole and its surrounding spiral blades, as well as the transmission coefficient spectrum. Reproduced with permission from ref. 68. b The meta-surface composed of a labyrinthine resonator and a coiled space resonator as well as the reflection, transmission, and absorption coefficients. Reproduced with permission from ref. 171.
Liu et al.171 propose a method to enhance the acoustic performance by the superposition coupling of monopole resonance modes and dipole resonance modes generated by FP resonators and Fano resonators, respectively. They designed a meta-surface for absorbing cylindrical sound waves by combining monopoles and dipoles. These are synthesized using a coiled space resonator and a labyrinthine resonator, respectively, as shown in Fig. 17b. The monopoles and dipoles generate composite multipoles in the structure, which can effectively absorb cylindrical sound waves through destructive interference between them. By arranging 32 absorbers in an annular pattern, the meta-surface experimentally achieves 91% sound absorption for omnidirectionally radiated cylindrical sound waves at 722 Hz and has a ventilation rate of 46%.
Combined by resonance and porous material
As a traditional material for sound insulation, porous materials show the advantages of broadband sound absorption88,90,162,175,176,177,178,179,180,181. By introducing porous materials into the metamaterial, the broadband sound absorption performance can be significantly improved.
To reduce the noise of propellers in small unmanned aerial vehicles, Xiao et al.90 propose a subwavelength meta-liner composed of porous materials and hollow coiling slits. These unit cells are uniformly arranged along the axial direction of the pipeline and periodically distributed along the radial direction. Through its unique design, the proposed system exhibits great sound absorption performance in the frequency range of 900–1200 Hz, specifically achieving a sound absorption coefficient exceeding 0.9. It effectively reduces the noise level of the propeller system in the target frequency range. Similarly, Ding et al.88 design a broadband acoustic meta-line. The structure is composed of three layers: Helmholtz resonators, micro-perforated plates and metal foam respectively (Fig. 18). Due to the weak coupling effect of multiple resonators, the multi-layer design demonstrates broadband sound absorption performance with an average sound absorption coefficient of 0.96 in the frequency range of 800–3200 Hz.
Reproduced with permission from ref. 88.
In general, most of the structures combined with Helmholtz resonance and FP resonance can achieve low-frequency broadband acoustic isolation while maintaining a compact structure or high opening rate. The structures combined with Helmholtz resonance and membrane resonance focus more on low-frequency sound isolation. The design combined with Fano resonance and FP resonance improves bandwidth and acoustic performance for sound insulation. The structures combined with Resonance and porous material have a more stable acoustic performance. These results combine the advantages of different resonance types, demonstrating the great flexibility of structural design and the great potential of sound isolation.
Conclusions and outlook
In this paper, we systematically investigate the development and new advances of AVMs, including concepts, configurations, mechanisms, and applications. According to different principles of sound insulation, we classify AVMs into three main categories, namely AVMs based on single-type resonance and hybrid-type resonances. On this basis, a review is conducted on the achievements for each type of AVMs. Considering the dimensions of sound insulation structures, they are further discussed as meta-muffler, meta-barrier, and meta-cage. Overall, Helmholtz resonance, FP resonance, and membrane resonance can all achieve excellent low-frequency sound isolation. Among them, the resonant frequency of Helmholtz resonance can be precisely manipulated. FP resonance ensures the compactness of structural design. Membrane resonance can be inspired by rather thin structures; Structures driven by Fano resonance are often more compact or have higher ventilation. Moreover, splicing unit cells including cascading and arranging in a parallel array will improve the performance of sound insulation significantly. And various hybrid resonances in one AVM are favored of low-frequency and broadband, as well as a higher ventilation or smaller thickness of structure.
Although various AVMs are reported, their working frequencies are hardly changed when the samples are fabricated. However, the change of the environment may require consequent modification of the working frequencies. It is noted that tunable control of sound insulation is also achieved via fluid fillings182. Other tunable designs via mechanical reconfigurability or multi-field coupling are highly expected183.
With the development of intelligent optimization algorithms and machine learning184,185,186, AMs are inversely customized for multiple objectives under multiple constraints. Both high ventilation and broadband acoustic isolation with high efficiency of AVMs can be realized simultaneously187,188,189. While similar optimization algorithms are still rarely applied in the design of AVMs.
The impact of airflow velocity on the sound insulation performance of the AVMs cannot be ignored. Previous studies have systematically analyzed the effect of grazing flow velocity on the acoustic performance of AVMs82,84,106. However, most of the studies have primarily focused on meta-mufflers, with the examined airflow velocities being relatively low. Therefore, the development of rigorous theoretical frameworks and advanced computational methodologies for AVMs is critical to account for coupled fluid-structure interactions under high-velocity flow regimes.
Although AVMs have demonstrated promising potential in theoretical studies, their engineering implementations in real-world applications remain limited. At present, there have been some explorations in the application prospects38,91,93,136,190. But the sample is still measured under laboratory conditions. It is difficult to keep consistent with the actual working conditions. Future works are recommended to focus more on proposing scenario-oriented designs. Moreover, it is necessary to develop standards and common indicators for manufacturing and installation deviations resulting from engineering applications of AVMs.
Data availability
The data generated and/or analyzed during the current study are not publicly available for legal/ethical reasons but are available from the corresponding author on reasonable request.
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Acknowledgements
Financial supports by the National Natural Science Foundation of China (Grant Nos. 12021002 and 12102276) are gratefully acknowledged.
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Conceptualization, Y. S. Wang, Y. F. Wang and N. Zhen; investigation and resources, Y. F. Wang and R. R. Huang; data curation, R. R. Huang; writing—original draft, N. Zhen and R. R. Huang; writing—review and editing, N. Zhen and Y. F. Wang; formal analysis, S. W. Fan and R. R. Huang; methodology, Y. S. Wang; funding acquisition, Y. S. Wang, Y. F. Wang and S. W. Fan. All authors contributed to scientific discussions, reviewed the final manuscript, and approved the submitted version.
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Zhen, N., Huang, RR., Fan, SW. et al. Resonance-based acoustic ventilated metamaterials for sound insulation. npj Acoust. 1, 7 (2025). https://doi.org/10.1038/s44384-025-00011-y
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DOI: https://doi.org/10.1038/s44384-025-00011-y
