Plate-type Acoustic Metamaterials Research Articles

Improving low-frequency sound transmission loss of double panels with a plate-type acoustic metamaterial

The sound insulation performance of double-leaf partitions is crucially affected by the mass-air-mass resonance phenomenon, whose frequency reduction can shift the high sound insulation to lower frequencies. In this work, an alternative strategy for exceeding the low limit of the mass-air-mass resonance frequency of conventional double panels is proposed in terms of the effective surface mass density. An equivalent spring-mass model based on the effective medium theory is implemented to intuitively understand the characteristics. A simple double-panel metamaterial is designed by replacing one of the panels with a single-plate metamaterial attached strip masses to decrease the structural complexity. The extended semi-analytical method is applied to predict efficiently the sound transmission loss in the low-frequency range, which is verified by the coupled vibro-acoustic finite element method with excellent agreement. The results demonstrate that the proposed double-panel metamaterial can reduce the minimum of the resonant frequency without changing the areal mass density and panel spacing. The sound insulation can be significantly improved between the reduced mass-air-mass resonance and the anti-resonance frequencies. To provide a better understanding of the sound transmission loss improvement, parametric studies are conducted. The design strategy is validated through experiments conducted in an impedance tube, and the results corroborate the findings. This study is instrumental in designing double-panel partitions that require sound insulation in specific low-frequency regions.

Inverse design of laminated plate-type acoustic metamaterials for sound insulation based on deep learning

The laminated plate-type acoustic metamaterial (LPAM) has designable low-frequency sound insulation performance and ultrathin and ultralight characteristics. However, the complexity of LPAM design increases significantly as the number of layers increases. An inverse design method is proposed to determine the topology and design parameters of LPAM based on deep learning. To train the deep learning model, the finite element and analytic models are combined to generate sufficient training data. The experimental validation of the finite element model and the acoustic impedance model are carried out to reduce the deviation between the experiments and simulations. The LPAM design system contains the pre-processing, inverse design and post-processing modules. The pre-processing module can produce candidate targets based on the required sound-insulation design target. For each candidate target, the inverse design module utilizes convolutional neural networks to autonomously design topology and parameters of LPAM. Finally, the pre-processing and post-processing modules are combined to choose the optional LPAMs meeting the sound-insulation target. To verify effectiveness of the LPAM design system, typical cases, involving the sound insulation targets of one and two sound insulation peaks, and uniform sound insulation in a broadband from 50 Hz to 600 Hz, are designed successfully and efficiently.

On the validity of periodic boundary conditions for modelling finite plate-type acoustic metamaterials.

Plate-type acoustic metamaterials (PAMs) are thin structures that exhibit antiresonances with high sound transmission loss (STL) values, making PAMs a promising new technology for controlling tonal noise in the challenging low-frequency regime. A PAM consists of rigid masses periodically attached to a thin baseplate. The periodicity of PAM can be exploited in simulations, allowing to model only a single unit cell using periodic boundary conditions. This approach essentially represents the PAM as an infinite structure, but real PAM implementations will always be finite and influenced by boundary conditions. In this paper, extensive numerical simulations of different PAM configurations have been performed to study the performance of finite PAM compared to infinite PAM. The results indicate that as the number of unit cells in a finite PAM increase, the STL converges toward that of an infinite PAM. The impact of the finite PAM edge boundary conditions becomes negligible at some point. Based on the numerical results, a simple criterion is proposed to determine a priori how many unit cells are required in a finite PAM design to consider it quasi-infinite. This criterion aids in justifying unit cell models with periodic boundary conditions for efficient design optimizations in practical PAM applications.

A study of low frequency sound insulation mechanism of a perforated plate-type acoustic metamaterial

This paper presents a new design of a perforated plate-type acoustic metamaterial (PAM) to evade the influence of membrane pre-tension on the acoustic performance of metamaterials and to enable air ventilation while achieving the designated sound insulation. The study embarks on the analysis of sound insulation mechanism of a typical perforated membrane-type acoustic metamaterial (MAM) from the acoustic context, and discloses that sound transmission loss (STL) peaks of a perforated MAM are due to the strong wave interference between sound sources transmitted through the orifice(s) and the membrane(s). The sound insulation mechanism is explored further in the study by an acoustic impedance analysis of a perforated metamaterial using an electro-acoustic analogy in the latter part of the paper, and the result confirms that the STL peaks of a perforated PAM (or MAM) are indeed the outcome of a strong sound interference. The study also compares an experiment test and a finite element simulation on the sound transmission of a perforated PAM based on the new design. The result confirms that the new perforated PAM can yield a good broadband STL at relatively low frequencies. A practical application using the perforated PAM design is applied to reduce the noise propagation from the compressor compartment of a commercial refrigerator. The test result verifies the effectiveness of the design in terms of both sound reduction and air ventilation.

Multilayer coupled plate-type acoustic metamaterials for low-frequency broadband sound insulation

Acoustic metamaterials have been becoming a popular topic for the better sound insulation at low frequency than traditional materials. However, due to the local resonance mechanism, this excellent performance can only be demonstrated in narrow frequency bands. Therefore, multilayer coupled plate-type acoustic metamaterials (MPAM) are proposed in this paper. The structure consists of a large plate-type acoustic metamaterial (PAM) with periodic square metamaterial units and double-layer fibers with different densities. According to finite element study on the insertion loss (IL) of the MPAM, the governing physical mechanism of the MPAM was analyzed according to the sound pressure level distributions and the vibration modes of the PAM layer. In addition, large-scale MPAM samples with a size of 506 mm*506 mm were manufactured, the reverberation and anechoic chamber was employed to verify the sound insulation performance. It can be concluded from the test results that the IL peak originate from the anti-resonance of the PAM layer rather than the weight of the materials. Compared to the structures without PAM layer, in the range of 360 Hz−950 Hz, the IL is increased by 5 dB at least and up to 17 dB at most. The influences of the incident angles, the frame density and the coverage rate of the PAM layer on the IL are disscussed. The proposed MPAM structure, analytical techniques and test results may be helpful for the engineering application of acoustic metamaterials.

Plate-type acoustic metamaterials with integrated Helmholtz resonators

Plate-type acoustic metamaterials (PAM) consist of a thin film with periodically added masses. These metamaterials can be designed to be very lightweight and exhibit narrow bands at low frequencies with high sound transmission loss values that can exceed the corresponding mass-law considerably. In this paper, a new approach for improving the bandwidth of PAM by using Helmholtz resonators which represent the added masses is investigated. The key principle of this design is that the Helmholtz resonance gives rise to an additional peak in the transmission loss spectrum which can be tuned to increase the bandwidth of the PAM. Sound transmission loss measurements of a large-scale test sample with 270 resonators are used to demonstrate the performance of the proposed metamaterial under diffuse field excitation. Then, numerical simulations based on the finite element method are used to further investigate the physical mechanisms of the PAM with Helmholtz resonators. It is shown that when the baseplates of the Helmholtz resonators are stiff enough, the Helmholtz resonance is decoupled from the vibro-acoustics of the PAM. This can be exploited to effectively increase the bandwidth of PAM without any significant reductions of the sound transmission loss due to coupling resonances.

Laminated plate-type acoustic metamaterials with Willis coupling effects for broadband low-frequency sound insulation

Acoustic metamaterials provide a powerful tool for designing effective noise-reducing means at subwavelength scales. This paper is concerned with the sound insulation characteristics of plate-type acoustic metamaterials under some pragmatic conditions, including the effect of structure scale on the sound insulation performance, the Willis coupling effect in multilayer plate-type acoustic metamaterials, and the acoustic coupling between plate-type acoustic metamaterials and existing structures. Herein, laminated plate-type acoustic metamaterials (LPAM) composed of multilayer plate-type acoustic metamaterials sandwiched with porous materials are constructed to effectively insulate broadband low-frequency noise. By a numerical study on the normal, oblique, and diffuse-field incident sound transmission loss (STL) of the proposed LPAM and its constituent layers, the presence of superior sound insulation performance and the governing physical mechanism are discussed. The effectiveness of numerical study is validated by the STL experiments performed in a sound impedance tube for small-scale samples and in a reverberation and anechoic chamber for large-scale samples. The proposed LPAM construction, analysis technique, and reported findings may contribute to the design and application of plate-type acoustic metamaterials for broadband low-frequency noise control.

Multilevel plate-type acoustic metamaterials with level-to-level modal antiresonance for sound insulation

With the goal of engineering applications, the scalability of plate-type acoustic metamaterials (PAMs) is significant. However, most of the designed large-scale PAMs are formed by extending a single PAM cell to an array of cells, which will inevitably introduce vibroacoustic behavior to the entire array structure, resulting in a decay of sound transmission loss (STL) performance in certain frequency bands. To overcome this weakness, we present a new conceptual design of a multilevel PAM to enhance STL performance again by considering level-to-level modal antiresonance. The modal antiresonance of the second-level PAM, which manifests itself as the coupling through out-of-plane vibration of the first- and second-level PAMs, is analyzed to reveal the physical mechanisms. In addition, we also find that the STL profile of the second-level PAM has different dependence on the masses placed on the PAM cell and PAM array. We theoretically design and experimentally demonstrate the sound insulation properties of the proposed second-level PAM. Since the configuration of the multilevel PAM can be easily and flexibly designed in accordance with actual application requirements, it has broad application prospects including but not limited to submarine shells, aircraft cabins, and transformer rooms.

Plate-type acoustic metamaterials with strip masses.

Plate-type acoustic metamaterials (PAM) consist of a thin plate with periodically added masses. Similar to membrane-type acoustic metamaterials, PAM exhibit anti-resonances at low frequencies at which the transmission loss can be much higher than the mass-law without requiring a pretension. Most PAM designs previously investigated in literature require the addition of up to thousands of masses per square meter. This makes manufacturing of such PAM prohibitively expensive for most applications. In this contribution, a much simpler PAM design with strip masses is investigated. An analytical model is derived which can be used to estimate the modal properties, effective mass, and oblique incidence sound transmission loss of PAM with strip masses. For high strip masses (compared to the baseplate), this analytical model can be simplified to yield explicit expressions to directly calculate the resonance and anti-resonance frequencies of such PAM. The analytical model is verified using numerical simulations and laboratory measurement results are presented to demonstrate the performance of PAM with strip masses under diffuse field excitation and finite sample size conditions.

Experimental evidence of a hiding zone in a density-near-zero acoustic metamaterial

This paper examines the feasibility of cloaking an obstacle using Plate-type Acoustic Metamaterials (PAMs). We present two distinct strategies to cloak this obstacle, using either the near-zero-density regime of a periodic arrangement of plates or the acoustic doping phenomenon to achieve simultaneous zero-phase propagation and impedance matching. The strong limitations induced by viscothermal and viscoelastic losses that cannot be avoided in such a system are studied. A hiding zone is reported analytically, numerically, and experimentally. In contrast to cloaking, where zero-phase propagation must be accompanied by total transmission and zero reflection, the hiding configuration requires that the scattering properties of the hiding device must not be affected by the presence of the obstacle embedded in it. Contrary to cloaking, the hiding phenomenon is achievable even with a realistic PAM possessing unavoidable losses.

Optimizing the bandwidth of plate-type acoustic metamaterials

Plate-type acoustic metamaterials (PAM) consist of a thin film with multiple periodically attached masses. Although these metamaterials can be very lightweight and thin, the resulting sound transmission loss at low frequencies can be much larger than the corresponding mass-law. This is a result of anti-resonances at which the sound transmission through the PAM is strongly reduced. One general challenge, however, is that the anti-resonances are only very narrowband. This makes the application of PAM to noise control problems with broadband noise sources or changing tonal sources difficult. In this contribution, different design strategies to improve the bandwidth of PAM for low-frequency noise control applications (multiple masses per unit cell or stacking multiple PAM layers) are evaluated using optimizations. An efficient modal based model is employed to represent the PAM using their eigenfrequencies and modal masses. The model is validated using simulations and experimental measurements. The optimization results show that it is possible to significantly improve the bandwidth of PAM using the investigated design strategies. In fact, it is shown that the same bandwidths can be achieved either using multiple masses or multiple PAM layers. This allows for some flexibility in the design of suitable noise control treatments with PAM.

Doping of a plate-type acoustic metamaterial

We theoretically, numerically, and experimentally investigate the feasibility of acoustic doping, i.e., changing one of the effective properties of a medium by adding an impurity, to achieve supersqueezing. This effect, characterized by perfect and zero-phase transmission, can be obtained with zero index media. In acoustics, zero-phase propagation can be achieved with a plate-type acoustic metamaterial (PAM) acting as a density-near- zero metamaterial (DNZ). We point out the possibility of modifying the compressibility of a DNZ medium by mounting a Helmholtz resonator in parallel with the PAM. We are then able to dope the system and to turn it into a density-and-compressibility-near-zero medium, thus allowing supersqueezing.

Improving sound insulation in low frequencies by multiple band-gaps in plate-type acoustic metamaterials

According to the mass law, low-frequency sound attenuation is very difficult in engineering because the mass and space of structures are usually limited. In this paper, we propose a plate-type acoustic metamaterial with good sound insulation in low-frequency ranges. By attaching multilayered rubber and metal cylinders on a thin plate, multiple flexural wave band-gaps at low-frequency ranges are obtained. The band structures and eigenmodes are elucidated by finite element calculations. Both the flexural wave transmission spectra and the sound transmission loss are investigated. The results show that the obtained multiple band-gaps lead to more than one sound insulation peak at low frequencies. The geometrical parameter effects on the band-gap frequencies are discussed. By combining cells with different geometrical parameters, the formed supercell can improve the low-frequency sound insulation efficiency and introduce much more variety. The results in this paper will be useful for sound and vibration control in engineering applications.

Multi-mass synergetic coupling perforated bi-layer plate-type acoustic metamaterials for sound insulation

Thin plate-type acoustic metamaterials have the advantages of lightweight, high rigidity and adjustable parameters, showing great practical application values in sound wave control. In this paper, a type of perforated bi-layer plate-type acoustic metamaterials (PBPAM) is designed for low-frequency noise control. The sound insulation peaks can be increased by combining the perforated plate and synergetic masses, making the sound insulation performance close to the mass law at the resonant frequency. Compared to the results predicted by the mass law, a better performance of sound insulation is achieved based on the PBPAM. The effects of the structural parameters are investigated in this study. Based on the impedance tube experiments, the measured results have a good agreement with the simulated ones. This work can provide a reference for low-frequency and broadband sound insulation based on plate-type acoustic metamaterials in practical engineering.

Zero-phase propagation in realistic plate-type acoustic metamaterials

We theoretically, numerically, and experimentally analyze the Density-Near-Zero (DNZ) regime of a one-dimensional acoustic metamaterial. This acoustic metamaterial is composed of thin elastic plates periodically clamped in an air-filled waveguide, and the effective dynamic zero mass density is obtained from the strong dispersion around the bandgaps associated with the resonances of the plates. We emphasize the importance of the impedance mismatch between the acoustic metamaterial and the surrounding waveguide at the frequency of the zero effective density in addition to the consequences of the inherent losses. As a result, the frequency of the zero phase propagation, i.e., the acoustic propagation with zero phase delay, is not exactly the frequency of the zero density and lies in the frequency bandgap where the effective density is negative. Considering these limitations, the zero phase propagation is still experimentally observed and a subwavelength acoustic dipole is numerically designed, thus demonstrating the possible realistic implementations of DNZ acoustic metamaterials.

Synergetic coupling large-scale plate-type acoustic metamaterial panel for broadband sound insulation

In the field of low-frequency noise control, the locally resonant membrane and plate-type acoustic metamaterials (PAMMs) have received extensive attention from researchers due to its sub-wavelength thickness and low surface density properties. However, the existing research works mainly focus on the sound transmission loss (STL) of small-sized unit cells with the fixed boundary, resulting in that the sound insulation performances are great different from those of the large-scale structures used in engineering applications. For this reason, a square large-scale PAMM panel with side length of 0.704 m, which consists of a periodic array of square unit cells, is numerically studied under the normal incidence condition. The results show that the large-scale PAMM panels appear the obvious STL peak (~38 dB) in the low-frequency range. Moreover, the goal of broadband sound insulation based on the multi-cells synergetic coupling is realized by reasonably arranging the masses on the metamaterial panels. Numerical results indicate that a broadband insulation with average STL higher than 20 dB is obtained in the range of 300–900 Hz. Finally, a simplified experimental setup based on the box and semi-anechoic chamber is designed to verify the sound insulation performance, and the experiment under standard reverberation chamber and semi-anechoic chamber is performed in order to evaluate the sound insulation capability in the actual reverberation noise environment. The ideal periodic boundary is used in the numerical calculations, which is obviously different from the boundary condition in experiments. Therefore, the influence of the boundary condition on the STL is discussed and analyzed by calculating the STL of the metamaterial panels with different number of cells. The proposed design methods and results can provide some guidance for the application of the PAMM panels in practical engineering.

Modal displacement method for extracting the bending wave bandgap of plate-type acoustic metamaterials

To directly extract the bending wave bandgap of plate-type acoustic metamaterials, a modal displacement method is proposed. This method could replace the qualitative mode analysis with a quantitative statistical averaged mode displacement of the frame, in order to quantitatively extract the bandgap. Most importantly, the modal displacement method can reveal the mechanism behind a behavior wherein the mode evolution leads to the shifting of the upper edge of the bandgap—identifying this mechanism could correct misjudgment of the upper edge of the bending bandgap in the vibration mode analysis.

Shell-type acoustic metasurface and arc-shape carpet cloak

We systematically propose a thin shell-type acoustic metasurface, which could be used to design a carpet cloak that closely covers an arc-shaped object, therefore providing the necessary support for hiding an object with any arbitrary shape. To facilitate the experimental measurement, however, the work here starts with some rotary spherical shell-type and ellipsoidal shell-type cell structures. The measured and calculated sound transmission loss (STL) results of these structures suggest that the sound insulation performances of the shell-type structure are quite different from those of the plate-type structure, indicating a possible break in the shape of the classical sound insulation curve. Considering also that cylindrical shell structures are more widely used in practice than the rotary shell structures, a number of two-dimensional bilayer cylindrical and elliptic cylindrical shell structures were, therefore, designed in this assay. Due to the asymmetry of the structure, the shell-type cells could exhibit bianisotropic sound absorption, reflection and effective parameters. Furthermore, the stiffness of the thin shell structure changed nonlinearly with the changing of the radius of curvature, with a wing shape tendency. In addition, a bilayer cylindrical shell-type acoustic metasurface and an arc-shaped carpet acoustic cloak were successively designed, wherein the phased compensation of differently shaped cell structures could be adjusted by means of a new engineering iso-phase design method. This work could provide the necessary guidance to extend existing results in the field of membrane- and plate-type acoustic metamaterials for shell-type structures, and the realization of the arc-shaped cloak could provide support for the design of a carpet acoustical cloak for use with arbitrary shapes.

Membrane- and plate-type acoustic metamaterials with elastic unit cell edges

Membrane- and plate-type acoustic metamaterials are thin membranes or plates consisting of periodic unit cells with small added masses. It has been shown in numerous studies, that these metamaterials exhibit tunable anti-resonances with transmission loss values much higher than the corresponding mass-law. However, in most studies it is assumed that the unit cell edges (or grid) of the metamaterial are fixed. This idealised boundary condition is not applicable to real world applications in noise control. Therefore, the acoustic performance of these metamaterials under more realistic circumstances, where the grid structure cannot be perfectly rigid, can be expected to be different. In this contribution, the vibro-acoustic behavior of membrane- and plate-type acoustic metamaterials with a non-rigid grid is investigated. For this purpose, an efficient analytical model is developed to predict the eigenmodes and sound transmission loss of such metamaterials. In this model, elastic unit cell edges are modelled using a grid of Euler-Bernoulli beams and the sound transmission loss can be calculated for oblique incidence. A comparison to FEM simulations shows that the proposed model yields the same results but with a considerably reduced computational effort. The analytical model is then used to discuss the vibro-acoustic properties of the metamaterial, with particular focus on the influence of the mass and stiffness of the grid beams. It is shown that even when a non-rigid grid and diffuse incident sound fields are considered, the transmission loss of the metamaterial exhibits anti-resonances with remarkably high noise reduction values. These anti-resonances can be tuned by choosing appropriate values of the grid parameters. Furthermore, the formation of band gaps in the propagation of bending waves is discussed by investigating the dispersion curves of the metamaterial. The results in this contribution show that membrane- and plate-type acoustic metamaterials can still efficiently reduce low-frequency noise, even when the unit cell edges are not assumed to be fixed. This important finding and the proposed analytical modal can support the utilization of these metamaterials in practical noise control applications.

Plate-Type Acoustic Metamaterials: Experimental Evaluation of a Modular Large-Scale Design for Low-Frequency Noise Control

For industrial applications, the scalability of a finalised design is an important factor to consider. The scaling process of typical membrane-type acoustic metamaterials may pose manufacturing challenges such as stress uniformity of the membrane and spatial consistency of the platelet. These challenges could be addressed by plate-type acoustic metamaterials with an internal tonraum resonator. By adopting the concept of modularity in a large-scale design (or meta-panel), the acoustical performance of different specimen configurations could be scaled and modularly combined. This study justifies the viability of two meta-panel configurations for low-frequency (80–500 Hz) noise control. The meta-panels were shown to be superior to two commercially available noise barriers at 80–500 Hz. This superiority was substantiated when the sound transmission class (STC) and the outdoor-indoor transmission class (OITC) were compared. The meta-panels were also shown to provide an average noise reduction of 22.7–27.4 dB at 80–400 Hz when evaluated in different noise environments—traffic noise, aircraft flyby noise, and construction noise. Consequently, the meta-panel may be further developed and optimised to obtain a design that is lightweight and yet has good acoustical performance at below 500 Hz, which is the frequency content of most problematic noises.