Acoustic and mechanical metamaterials for various applications -A brief review

Fuyin Ma^*

• Xi'an Jiaotong University, Xi'an, China

Sound-absorbing metamaterials can be divided into three categories according to different structural design methods. The first type is the membrane-type sound-absorbing metamaterials.In 2012, Mei et al. proposed a membrane-type dark acoustic sound absorption metamaterial, which can achieve low-frequency broadband super sound absorption, and the thickness is about three orders of magnitude lower than the operating wavelength 3 . In 2014, Ma et al. proposed an impedance-matched membrane-type metamaterial, achieving adjustable perfect absorption by tuning the back cavity thickness. The second type is the cavity-type sound-absorbing metamaterials 4 . In 2014, Cai et al. bent and coileAcoustic and mechanical metamaterialsd the sound damping tube with a quarter wavelength so that the sound wave was forced to pass through the gyratory structure, thereby reducing the reflection, and finally achieved more than 90% of the sound absorption effect at 400 Hz 5 . In 2017, Yang et al. designed a folding broadband sound absorption metamaterial based on the Fabry-Pérot (F-P) cavity, with a thickness of 10.36 cm, which can achieve continuous and perfect sound absorption in the 400-3000 Hz range. The third type is the porous sound absorption metamaterial 6 . In 2015, Yang et al. divided porous materials into periodic arrangements with rigid partitions, enhancing low-frequency sound absorption performance 7 .Although the membrane-type metamaterial achieves good low-frequency sound absorption performance in the size of deep sub-wavelength, its surface tension is difficult to control, which is challenging to meet the actual engineering application. At the same time, the working frequency band of porous sound absorption metamaterial is high, which makes it challenging to solve the contradiction between metamaterial thickness and low-frequency sound absorption.Therefore, we often use cavity-type sound absorption metamaterial in practical engineering applications.The local resonance mechanism limits the unit's sound absorption bandwidth for the cavity-type sound-absorbing metamaterials. In 2019, Liu et al. proposed a low-frequency broadband ultra-thin sound absorption metamaterial with multi-order sound absorption characteristics, which can obtain multiple near-perfect absorption peaks at higher frequencies without changing the original absorption peaks and structure size. Its structural thickness is 60 mm, with a continuous near-perfect absorption spectrum in the 450-1360 Hz (Fig. 1a) 8 . On this basis, by accurately balancing the parameters of each unit, the absorption bandwidth of the subwavelength metamaterial is significantly expanded, which has great engineering application potential. At present, the first anechoic chamber has been constructed based on this study (Fig. 1b). In order to further improve the low-frequency broadband sound absorption capacity of cavity-type sound-absorbing metamaterials, in 2021 and 2022, Sheng 9 and Ma 10 proposed to improve their low-frequency sound absorption capability by opening small holes in the wall and using soft material to build a soft sound boundary, respectively. The method of using soft material to build a soft sound boundary does not need to increase the overall size of the original sound absorption unit. The preparation process is more straightforward and more suitable for rapid preparation. It is expected to improve the low-frequency sound absorption amplitude of cavity-type structures in practical engineering applications (Fig. 1c). Simultaneously, the thickness dimension of cavity-type sound-absorbing metamaterials determines the lower limit of sound absorption frequency. It is still difficult to apply if it absorbs low-frequency sound waves in a limited-sized space. For this reason, in 2023, Ma et al. introduced an ultra-thin metasurface design method based on phase-coherent cancellation. Reflection and scattering were suppressed by redistributing the thickness dimension to the planar layer and leveraging phase offsets between weakly absorbing units, thereby enhancing broadband absorption 11 . The impedance tube sample test results show that the average sound absorption coefficient in the 600-1300 Hz frequency band is 0.8, and the thickness is only 23 mm (Fig. 1d). A 1.5 m × 1.5 m large-scale sample was fabricated to validate sound absorption under irregular incidence.The reverberation chamber test results show that the sound absorption coefficient in the 600-1200 Hz range exceeds 0.85, which is conducive to engineering applications.On the other hand, its sound absorption performance can still be maintained under oblique or irregular incidence, indicating that the near-field effect can be ignored. In the same year, in order to make the proposed superstructure easy to realize engineering applications, Ma et al. used a ceramic-containing high-temperature resistant material, and a 3D printing process with a special preheating-preservation-cooling cyclic heat treatment was accordingly developed 12 .Through the joint development of materials and processes, the high-precision preparation of large-size and ultra-thin shell structures is realized (Fig. 1e). This absorber comprehensively utilizes the advantages of porous material, slit-type absorber, F-P resonant unit, and embedded Helmholtz resonant structure, and the average sound absorption coefficient above 50 Hz reaches 0.8, which has potential application value in engineering fields. In addition, shifting the sound absorption frequency band to a low frequency can be achieved by increasing the volume of the cavity, but this will increase the thickness of the sound absorption structure, which still needs to be weighed in practical engineering applications. At the same time, in practical engineering applications, sound absorption structures are often harmed by noise and impact energy, which requires them to have good mechanical characteristics to resist external loads and make them ineffective, so the multifunctional materials that integrate noise absorption, high stiffness are increasingly sought after for all-inone applications. From 2023 to 2025, Li et al. focused on multifunctional metamaterials' innovative design and performance optimization. They broke through the trade-off limit between acoustic absorption and mechanical properties of traditional materials through decoupling design 13 , bionic design 14 , and interwoven biphasic design 15 , respectively, providing a design paradigm for lightweight and multifunctional materials for transportation, aerospace, and other fields.A mature sound-absorbing metamaterial often undergoes multiple iterations of "modelingsimulation-experiment", which requires a lot of time, computing power and labor costs.Fortunately, the rapid development of machine learning techniques has provided completely new solutions for the on-demand design of sound-absorbing metamaterials. On the one hand, the trained neural network (Fig. 1f) can discover the complex and non-intuitive nonlinear relationship between structural geometric parameters and their performance response from the training samples, thus replacing the time-consuming numerical simulation process in the design process of traditional methods. Zheng et al. realized the on-demand design of sound-absorbing metamaterial based on Gauss-Bayesian model in machine learning. Specifically, the complex mapping relationship from structural parameters to sound absorption performance is constructed by training Gauss-Bayesian model instead of time-consuming simulation process.Finally, only 37 evaluations are used to achieve the goal of low frequency sound absorption coefficient ≥0.9 16 network structure to achieve accurate prediction of sound-absorbing metamaterial performance in milliseconds, which was 4 orders of magnitude faster than that of traditional simulation 18 .On the other hand, machine learning technology can also be used to achieve a direct mapping from the target performance to structural parameters, which further improves the design efficiency compared with the iterative optimization process. Peng et al. proposed a design method of low-frequency sound absorption metamaterial based on autoencoder-like neural network (ALNN) to solve the control problem of low-frequency noise. The ALNN model is composed of a forward network (decoder part in Fig. 1g) and a reverse network (encoder part in Fig. 1g), which can realize the accurate prediction of the sound absorption coefficient curve according to the structural parameters and the non-iterative customized design of the structural parameters according to the target sound absorption coefficient curve respectively. Experiments show that the proposed method can design near-perfect soundabsorbing metamaterials in the low frequency range of 50-100Hz. The sound absorption range of a single cavity is very limited, which is difficult to meet the practical needs of engineering applications 19 . Furthermore, Liang et al. proposed a 14-cavity coupled sound absorption metamaterial design method based on metaheuristic-enhanced autoencoder network (MEAN) for low-frequency and wideband noise control. A series of methods, such as serialization of structural parameters, staged training and heterogeneous loss functions, optimize the convergence effect of the neural network, and achieve a highly customized design for the sound absorption coefficient in the range of 500-1500Hz 20 .To sum up, the sound-absorbing metamaterial breaks through the thickness limit of a quarter wavelength of traditional porous materials. It achieves near-perfect sound absorption performance at low frequency under ultra-thin conditions, combines with machine learning techniques, the design efficiency can be greatly improved. In order to promote the application of acoustic metamaterials in the field of noise reduction, it is necessary to further develop the advanced manufacturing technology of acoustic metamaterials, solve the problems of largescale, batch, low-cost, and high-efficiency manufacturing, and strengthen the research on the design methods of multifunctional integrated acoustic metamaterials such as sound absorption, sound insulation, and load bearing, to better meet the everyday needs of the new generation of equipment development for advanced multifunctional material technology.At the beginning of this century, Liu et al. proposed a locally resonant phononic crystal whose lattice constant is smaller than the relevant wavelength by two orders of magnitude yet can exhibit spectral bandgaps, breaking the constraint of the mass law 21 . Since then, artificially designed acoustic metamaterials for sound insulation have attracted extensive attention in the academic community. Acoustic metamaterials can be classified into two categories based on their structural configurations. One category is the membrane/plate-type acoustic metamaterials composed of frame-membrane/plate-mass structures, and the other is the periodic thin-plate phononic crystals constructed by attaching multiple identical masses to a large thin plate substrate with specific periodicity. The former was initially proposed by Yang et al. in 2008. The specific structural configuration involves attaching a small mass to a membrane with fixed boundaries, which is referred to as membrane-type acoustic metamaterials. It can achieve total reflection of acoustic waves between two intrinsic modes, minimizing sound transmission and breaking the constraint of the mass law 22 .The operating bandwidth can be effectively broadened by employing a parallel coupling design with in-plane gradient parameters 23 and a series lamination design in the thickness direction 24 . In these two design methods, the parallel coupling design with in-plane gradient parameters will attenuate the sound insulation peak to a certain extent. In contrast, the series lamination design in the thickness direction will increase the thickness dimension of the structure. Although membrane-type acoustic metamaterials can achieve noise attenuation effects, their stability and durability are poor since membranes are prone to relaxation and aging, and membranes' tension is difficult to control precisely. To address this, Ma et al. developed membrane-type acoustic metamaterials into plate-type structures by increasing the thickness of the membrane to reduce dependence on tension, significantly improving their engineering applicability, and achieving low-frequency broadband sound insulation effect through the synergetic coupling effects of multiple units (Fig. 2a) 25 . Building on this, Li et al. achieved ultra-strong sound insulation across a broadband range with a thickness of 25 mm via the joint utilization of parallel coupling design with in-plane gradient parameters and series lamination design in the thickness direction (Fig. 2b) 26 . Tang et al. achieved broadband sound insulation and vibration reduction while maintaining light transmittance by adopting a parallel coupling design with in-plane gradient parameters and simultaneously compounding multiple pure transparent materials. The structure exhibits a thickness of less than 6 mm and a surface density of less than 6 kg/m² (Fig. 1c) 27 . Additionally, Ma et al. adopted flexible frames to overcome the issues of excessive structural stiffness and overly high operating frequencies in lowfrequency applications for thin-plate structures 28 . They transformed the lumped coupling resonance effect's negative impact into a positive one and achieved an excellent low-frequency broadband sound insulation effect (Fig. 2d). For periodic thin-plate phononic crystals, they can generate a high-amplitude sound insulation peak in the low-frequency range but exhibit poor sound insulation performance in mid-to-high frequency ranges 29 . Due to their inherent structural limitations, broadening the operating bandwidth cannot be achieved through parallel coupling of in-plane gradient parameters. To address this, the operating bandwidth can be broadened by series-stacking two or more layers of periodic thin-plate phononic crystals with different structural sizes. However, this method will lead to the problem of enormous thickness dimensions. Additionally, introducing porous materials between two layers of such phononic crystals can effectively improve sound insulation performance in diffuse fields 30 .It is worth mentioning that the introduction of machine learning techniques in the design process of sound insulation acoustic metamaterials can quickly and accurately design the required acoustic metamaterials. For example, Song et al. proposed a deep learning-based inverse design method for the topology and design parameters of laminated plate-type acoustic metamaterials, which can successfully and efficiently design laminated plate-type acoustic metamaterials meeting specific objectives 31 . The development of acoustic metamaterials for sound insulation still focuses on three aspects: lightweight and thin structure, low-frequency broadband performance, and engineering applications. In addition, integrating multiple functions is also a development direction that should be considered in the future, such as integrating sound insulation and load-bearing functions, sound insulation and ventilation functions, sound insulation and vibration reduction functions, etc.Based on their working mechanisms, vibration-absorbing metamaterials can be classified into Bragg-type and locally resonant-type. Among them, since the bandgap position and width of local resonance metamaterials are mainly determined by the local resonance characteristics of the scatterers and are independent of the arrangement of the scatterers, it dramatically enhances the potential of such structures for practical engineering applications. From the perspective of typical structural design, current technologies mainly fall into two categories: membrane/plate-type metamaterials and metamaterial inclusions. The earliest studies focused on membrane-type metamaterials, where membranes act as elastic elements to form vibrationabsorbing devices. By adding ultra-light thin-membrane local resonance units with a mass of less than 1%, low-frequency vibration absorption of the target object was achieved, which has practical significance for lightweight engineering applications. In 2015, Nouh et al. developed a finite element model to predict various membrane-type metamaterial configurations modal and frequency responses 32 . They employed the Floquet-Bloch method to demonstrate metamaterial plates' excellent low-frequency vibration attenuation performance. Considering that the resonant frequency in such structures is susceptible to membrane tension, Ma et al.increased the membrane thickness and proposed a rigid membrane-type metamaterial to eliminate the dependence on tension, thereby bridging the membrane-type and plate-type metamaterials 28 . Building on this concept, they further introduced the multi-unit cooperative weak coupling mechanism 33 and the multi-scale synergistic broadband coupling mechanism the efficiency of structural design, researchers have further introduced machine learning into metamaterial design. In 2024, Zhang et al. employed fully connected neural networks and convolutional neural networks to establish a mapping between the geometric parameters of metamaterials and their band structures, enabling the inverse design of high-performance metamaterials 37 . However, this approach remains essentially a forward prediction method and struggles to resolve the underdetermined problem where the input parameters number is smaller than that of the output parameters.Notably, the most significant advantage of vibration-absorbing metamaterials in solving engineering problems lies in their unique subwavelength characteristics, which can suppress the vibration capacity of large wavelengths and low frequencies under lightweight conditions. Therefore, the frequency bandwidth and frequency range are important technical indicators.Currently, three primary broadband metamaterial design methods are multi-frequency resonant locally resonant unit design, bandgap mechanism coupling structural design, and active tunable design. Regarding multi-frequency resonant locally resonant unit design, research mainly focuses on the mass components of the metamaterials. The number and width of bandgaps can be increased through multiple combinations of resonators and under strong coupling effects. In 2023, Althamer et al. generated multiple bandgap intervals by constructing a multi-degree-offreedom local resonant system 38 . The frequency response was accurately simulated based on the finite element calculation method of the Timoshenko beam theory. However, the difficulty of this method lies in the multi-layered structural design, which often results in complex composite structures, thereby increasing the design difficulty and fabrication complexity.Considering that locally resonant bandgaps gradually transform into Bragg bandgaps as they shift to higher frequencies, appropriate adjustment of metamaterial parameters can realize the coexistence or even coupling of the two types of bandgaps, generating ultra-broadband coupled bandgaps. In 2017, Krushynska et al. conducted a theoretical analysis of the coupling effect of two mechanism bandgaps in single-phase elastic metamaterials 39 . The research indicated that when bandgap coupling occurs, the Bragg bandgap coincides with the resonance mode of the metamaterial matrix, which can generate a broad and stable bandgap interval. The third broadband design approach is active tunable design, primarily focusing on using innovative materials, such as piezoelectric materials, electromagnetic materials, dielectric/electrorheological elastomers, shape memory alloys, and optical field tuning. By incorporating multi-field coupled media into the design of metamaterials, it is possible to dynamically adjust the bandgaps of the structures by applying external bias fields that modulate material properties. It enables functionalities such as bandgap switching 40 , tuning 41 , and elastic wave manipulation 42 ; alternatively, the geometric configuration can be changed through mechanical methods (prestress control or direct load application) to realize mechanically reconfigurable metamaterials. In 2016, Langfeldt et al. controlled the air volume between the membrane and the frame in the double-layer thin-membrane metamaterial to change the membrane's prestress and geometric stiffness, thereby adjusting the dissipation interval 43 . In addition, to ensure that the bandgap interval of vibration-absorbing metamaterials is as low as possible, extensive research has been conducted on the Inertial Amplification (IA) mechanism.In 2023, Sun et al. proposed a beam-shaped metamaterial with an X-shaped inertial amplification mechanism 44 . Meanwhile, the coupling effect of transverse and longitudinal waves exists in the structure, which induces the emergence of a new bandgap interval (Fig. 3d).In conclusion, for the design of metamaterials, it is essential to broaden the vibration absorption bandwidth further, and lower the operating frequency range, particularly in achieving complete bandgaps at low frequencies. In practical vibration isolation applications for equipment, isolation devices are required not only to suppress vibrations effectively but also to possess sufficient load-bearing capacity to support the weight of the equipment itself. However, existing vibration isolation technologies struggle to integrate load-bearing and isolation capabilities. First, traditional vibration isolation techniques rely on soft isolators to achieve low-frequency isolation.However, overly compliant structures can not often support heavy loads, limiting their applicability in high-load equipment 45 . Second, although vibration isolation metamaterials can enhance isolation performance to some extent, the bandgaps of Negative Poisson's Ratio (NPR) structures generally fall within the kilohertz to tens-of-kilohertz range, making them ineffective for attenuating low-frequency vibrations [46][47][48] . In addition, composite Quasi-Zero Stiffness (QZS) structures achieve quasi-zero stiffness by combining positive and negative stiffness elements. However, such configurations are usually bulky, space-consuming, and challenging to manufacture and assemble 49,50 . Existing compliant QZS structures are mostly single-layered and struggle to balance low-frequency isolation and load-bearing capacity [51][52][53] . Looking ahead to the future development of vibration isolation structures, it is difficult for single-mechanism designs to meet the practical demands of compact size, high load-bearing capacity, and strong isolation performance simultaneously. Composite structures based on multi-mechanism integration offer a promising solution by enabling the effective combination of distinct functional characteristics from different mechanisms. Meanwhile, the use of intelligent algorithms such as machine learning can significantly accelerate the design process of metamaterials, enabling optimal parameter selection over a broader design space with faster speed and higher efficiency. This includes, for example, the design of wider QZS platforms and flexible multi-stage platforms. Efficient and customized design driven by machine learning is also one of the key directions for the future development of vibration isolation metamaterials.Additionally, the widespread use of soft materials in current isolation systems significantly limits their durability and environmental adaptability. Future research should focus on exploring the large-deformation behavior of thin-walled metal structures, with the aim of replacing soft materials with metals. This transition must also account for the potential increase in isolation frequency caused by the use of stiffer materials. Ultimately, the goal is to realize a highly reliable, durable, and compact vibration isolation structure that provides low-frequency, broadband isolation along with robust load-bearing capacity-laying the foundation for practical and long-term engineering applications.The traditional ventilation noise reduction technology is limited by the contradiction between ventilation efficiency and noise reduction performance for a long time. However, the emergence of acoustic metamaterials provides a new path to break through this bottleneck. So proposed a design scheme for an arc-shaped conformal metasurface underwater sound absorption coating (Fig. 5b) 61 . Through the optimization of elastic wall materials, the design of micro-perforated cover plates, and the integration of multi-stage sound absorption structures, an average transmission loss of 4.2 dB was achieved in the 600-1040 Hz frequency band. The experimental value is better than the simulation by 3.3 dB. This scheme employs an integrated strategy utilizing multi-stage silencing units. Specifically, wide absorption units are designed to enhance low-frequency performance, whereas narrow units focus on expanding highfrequency capabilities. This approach preserves the integrity of the flow passage section and achieves a 37% extension in noise reduction bandwidth through the gradient combination of unit widths. Consequently, it successfully resolves the inherent contradiction between lowfrequency silencing in thin-layer structures and the minimization of the flow passage crosssectional area. In the same year, Wang et al. introduced an ultrathin spatially shifted metasurface element barrier (Fig. 5c) 62 . Leveraging the principle of acoustic siphon, this barrier achieved a harmonious integration of low thickness, broadband sound insulation, and high ventilation efficiency. The key to its success lies in an innovative design approach emphasizing sound absorption over traditional isolation methods, thereby revolutionizing the balance between acoustic performance and air permeability. The non-ventilated area of this structure is equipped with a folded labyrinth-type resonant sound absorption unit with a gradient length. By utilizing the Helmholtz resonance principle, the sound absorption unit can In sonar detection, underwater sensing and imaging are the core functions that are critical for establishing underwater wireless acoustic communication and exploring and developing marine resources. The space sampling law constrains traditional sonar, and the spatial resolution of acoustic imaging is limited by the number of sensors and the array size. To achieve long-distance and high-precision detection, the system requires higher precision, more sensors, a larger array structure, and more complex processing algorithms. However, this also brings Subsequently, in 2019, Jiang et al. proposed a space-coiling anisotropic metamaterial with stochastic structural parameters 69 . Through the encoding of structural units, they achieved the identification and localization of sound sources on the radial plane. Further, they realized the imaging of sound sources on another target plane by stacking the structure. However, this structure fails to achieve omnidirectional sound source perception and detection, and the spacecoiling structure does not possess a gain function. As a result, its resolution for nearby targets and weak sound sources is relatively poor. Meanwhile, considering that the existing acoustic detection systems are mainly used for underwater equipment and the wavelength of sound waves in water is relatively large, this also increases the structural size of the space-wound channels. Further consideration is needed to balance the structural size with the detection effect.Considering the interference of waves and viscous losses, the signal-to-noise ratio of spacewound metamaterials in underwater environments is worrying, and their application will be minimal. In 2020, Sun et al. designed a multi-layer metamaterial spherical shell with spatially disordered distribution and achieved spatial acoustic source perception and detection through compressive sensing 70 . Integrating multi-layer pores and cavities provides excellent gain amplification, enabling higher resolution in distinguishing nearby targets and weak sound sources. However, the disorderly encoding inevitably leads to a low space utilization rate, and the modulation effect of the structure lacks targetedness. Meanwhile, in the signal processing process, these researchers have not fully utilized the various characteristics of sound signals, which limits the perception accuracy of the system.Taking these into account, in 2023, Wang et al. proposed a multi-information fusion compressive sensing method 71 . Inspired by the structure of the nautilus shell, they designed the structural units in accordance with the equivalent medium theory, thereby constructing the Nautilus metamaterial (Fig. 6b). The multi-information fusion compressive sensing method comprehensively analyzed various features such as the phase and amplitude of the sound signal, thereby improving the accuracy of sound source identification and location of the system. The design of the cavity structure unit enhances the response level and achieves higher precision Although anisotropic metamaterials based on compressive sensing can achieve excellent sound source detection, their accuracy still needs to be improved. Firstly, the current detection of anisotropic structures only uses one or two sensors. Increasing the number of detection points appropriately can improve their accuracy without resulting in overly complex systems.Secondly, the accuracy of existing compressive sensing algorithms is limited by the richness of the observation matrix, and the detection range and resolution are also limited by the division of the grid. They have not yet achieved omnidirectional underwater detection. Therefore, it is imperative to balance their complexity and detection performance. Thirdly, the existing acoustic detection metamaterials have not been tested and applied in complex underwater environments. Considerations for underwater waves and static pressure are insufficient, and the selection of structural materials is also relatively limited. Last but not least, the structural forms of existing metamaterials are diverse but lack a systematic design system. The design goals for detection distance, resolution, and accuracy have not established standardized indicators, and the sonar systems and underwater equipment have insufficient correlation. In summary, future research directions and priorities will establish a standardized design scheme, adopt more reasonable structural forms and material compositions, match existing underwater equipment, and consider the actual complex underwater environment.From the introduction of different directions mentioned above, it can be seen that the research on acoustics and elastic metamaterials has shifted from basic theoretical research to research driven by application requirements. In basic theoretical research, more attention is paid to the establishment of theoretical models, the revelation of physical and mechanical mechanisms, and the analogy of physical phenomena between different physical fields. In the research of application traction, more emphasis is placed on the implementation of functions and the improvement of performance, focusing on the combination with practical application scenarios. In addition, with the development of artificial intelligence, using artificial intelligence to empower structural design and design more intelligent devices and components has become a very important direction of development. Limited by the fact that this paper is an editorial, it is difficult to provide a detailed introduction to the relevant research progress. The main focus is on providing a brief overview based on the research conducted by the author's group. For more related developments, readers are advised to pay attention to more professional review papers and textbooks.