Low-frequency Sound Insulation Research Articles

Low-Frequency Sound-Insulation Performance of Labyrinth-Type Helmholtz and Thin-Film Compound Acoustic Metamaterial

This paper presents a type of acoustic metamaterial that combines a labyrinth channel with a Helmholtz cavity and a thin film. The labyrinth-opening design and thin-film combination contribute to the metamaterial’s exceptional sound-insulation performance. After comprehensive research, it is observed that in the frequency range of 20–1200 Hz, this acoustic metamaterial exhibits multiple sound-insulation peaks, showing a high overall sound-insulation quality. Specifically, the first sound-insulation peak is 26.3 Hz, with a bandwidth of 13 Hz and giving a transmission loss of 56.5 dB, showing excellent low-frequency sound-insulation performance. To further understand the low-frequency sound-insulation mechanism, this paper uses the equivalent model method to conduct an acoustic–electrical analogy, construct an equivalent model of the acoustic metamaterial, and delve into the sound-insulation mechanism at the first sound-insulation peak. To confirm the validity of the theoretical calculations, physical experiments are carried out by 3D printing experimental samples. The analysis of the experimental data has yielded results that are consistent with the simulation data, providing empirical evidence for the accuracy of the theoretical model. The material has significant practical application value. Finally, various factors are studied in depth based on the established equivalent model, which can provide valuable insights for the design and practical engineering application of acoustic metamaterials.

Sound transmission of truss-based X-shaped inertial amplification metamaterial double panels

To enhance the low-frequency sound insulation performance of conventional double panels, this work proposes a truss-based X-shape inertial amplification (TXIA) metamaterial double panel. A semi-analytical method is developed for computing the sound transmission loss (STL) of the TXIA metamaterial double panel, with numerical and experimental validations confirming the convergence and accuracy of this method. To further investigate the low-frequency acoustic wave attenuation of the proposed structure, four configurations are analyzed and discussed. Numerical results indicate that, compared to conventional and equivalent mass double panels, the TXIA metamaterial double panel effectively shifts the STL peaks to lower frequencies, exhibiting higher STL amplitudes and a reduced low-STL region. Configurations incorporating different springs enhance the STL performance without altering mass or other parameters. The STL dips of the metamaterial double panel coincide with odd-odd modes of the double panel, which have higher radiation efficiencies. Parametric studies reveal that changes in the IA angle shift the dips induced by in-phase modes to lower frequencies, while increased stiffness shifts these in-phase dips to higher frequencies. The depth of the cavity between the two panels only affects the first-order anti-phase dip. Additionally, increased stiffness enhances the STL performance and introduces a new peak in the stiffness-controlled region. Due to its flexibility, the TXIA metamaterial double panel holds significant potential for industrial applications.

Low-frequency noise attenuation through hybrid perforated hemispherical shells and membrane-type acoustic metamaterial

We propose a novel hybrid acoustic metamaterial that can achieve broadband sound insulation below 452 Hz and almost perfect sound absorption at 864 Hz. The metastructure was fabricated using additive manufacturing. Finite element method simulations were used to study the acoustic properties of the fabricated metamaterials. An equivalent electrical circuit was built using an electro-acoustic analogy to evaluate the sound absorption coefficient. The unique design of this meta-structure possesses two resonant frequencies. Low-frequency sound insulation is found due to the effective negative density at frequencies lower than the cutoff frequency of the elastic membrane. In contrast, a negative effective bulk modulus is the reason behind the broadband sound absorption. The theoretical and simulation results were validated through experiments. Experiments carried out showed an overall average sound transmission loss of 26.31 dB between 50 and 1600 Hz and 24.72 dB in the low-frequency zone (<400 Hz). Furthermore, over 69% of the sound intensity is absorbed in the 500–1000 Hz frequency range. The designed meta-structure exhibits broadband effective negative density below 452 Hz and effective negative bulk modulus from 864 to 1220 Hz. The design specifies a sample thickness of 3.8 cm, corresponding to a subwavelength thickness of approximately λ/10. As a result, the developed meta-structure can potentially be employed for sound insulation and absorption at low frequencies in the aerospace and automotive industries and in-room acoustic applications.

Improvement of broadband low-frequency sound insulation of sandwich plates with negative Poisson's ratio butterfly-shaped auxetic cellular

The novel cellular cores auxetic metamaterials with negative Poisson's ratio (NPR) exhibit unique mechanical deformation characteristics compared to conventional cellular cores, which can be further exploited in modeling lightweight sandwich structures. The butterfly-shaped auxetic cellular is not only an improvement upon the traditional re-entrant auxetic cellular with NPR, but also a kind of bionic design, which possesses higher stiffness and thus offers greater potential for sound insulation. Based on this, the present article explores a study of the sound transmission characteristics exhibited by sandwich plates with butterfly-shaped auxetic cellular core layers. Firstly, the motion equation is derived based on the first-order shear deformation theory and Hamilton's principle, which is further solved analytically based on fluid-structure coupling conditions and combined with Navier method. Then, the sound transmission loss (STL) is analytically described. The correctness of the theoretical model is verified by comparing the theoretical solution with the calculation results of the commercial software COMSOL and the experimental results of impedance tube sound insulation tests. Based on the theoretical model, it is calculated that the sound insulation effect of butterfly-shaped auxetic cellular core is better than that of traditional re-entrant cellular with NPR. An analysis is subsequently conducted to explore the impact of key parameters on the STL of the butterfly-shaped cellular sandwich plates.

Plate-type metastructure with low-frequency sound insulation and high stiffness properties

According to the mass law, it is impossible to increase sound transmission loss (STL) of conventional structures at low frequencies without increasing their weight. Metastructures are capable to break the limits of the mass law at low frequencies. However, many existing sound insulation metastructures need to be constructed using a host structure with low-stiffness properties, such as a thin plate and a thin membrane. As a result, the metastructures normally have large exposed areas with low-stiffness characteristics and are unable to bear heavy loads, which limits their practical applications. In this work, we propose a high-stiffness plate-type metastructure (HSPM) with both low-frequency sound insulation performance and high stiffness properties. The STL performance of the HSPM is demonstrated analytically, numerically and experimentally, indicating that the HSPM can deeply break the mass law at low frequencies. Owing to the simple construction, high stiffness properties, and high sound insulation performance at low frequencies, the proposed HSPM has promising applications in practical noise control engineering.

Improving Sound Insulation in Low Frequencies by a Three-Component Cladding Acoustic Metamaterial Panel

In this paper, a three-component cladding acoustic metamaterial panel with good sound insulation effect in the low-frequency range is proposed. The sound transmission loss of metamaterial panels under different structural configurations and different material parameters is investigated by combining finite element simulation calculations with experimental research. The results show that the closer the center of gravity of the scatterer is to the substrate, the better the stability of the resonance unit, the wider the range of effective sound isolation frequencies, and the higher the degree of normalization. The filling rate of the scatterer is maintained at about 0.5 to obtain a better sound insulation effect. At the same time, choosing lower density materials for the substrate and metal materials with high density and high modulus of elasticity for the scatterer can maximally widen the bandgap and allows for low-frequency sound insulation below 600 Hz. This approach improves the low-frequency sound insulation efficiency of acoustic metamaterials. The results provide important explanations and references for a deeper understanding of the sound insulation mechanism and the effects of different parameters on sound insulation.

Enhancing sound insulation performance with active constrained layer damping plates at low frequencies

In this paper, the normal incident sound transmission loss characteristics of active constrained layer damping (ACLD) plates are investigated numerically and experimentally. The sound insulation performance of the ACLD plate configuration with a centrally positioned 30 mm × 30 mm patch is initially examined in both passive and active control states. The analog feedback control strategy is employed to physically demonstrate that the ACLD treatment can effectively improve airborne sound insulation performance at low frequencies. To enhance control efficiency and mitigate control spillover effects, an edge-enhanced ACLD (EACLD) plate configuration is proposed, which enables a direct electrical connection between the PZT layer and base plate. Control mechanism is further analyzed from the perspectives of mean quadratic normal velocity and deformed modal shapes. Results show that, in the passive state, the formation of sound insulation peaks of the ACLD and EACLD plate configurations are attributed to structural anti-resonance effects. By applying active control, the shear deformation degree of the viscoelastic layer can be further increased, and the advantages of active and passive hybrid damping are formed. Therefore, the sound insulation performance of the EACLD plate configuration in the first-order resonance region around 190 Hz can be enhanced by approximately 20 dB. The proposed EACLD plate configuration demonstrates a broad low-frequency sound insulation bandwidth and holds strong potential for engineering applications.

A novel arc-type auxetic cellular doubly-curved shells with negative Poisson's ratio for broadband low-frequency sound insulation

The novel cellular cores auxetic metamaterials with negative Poisson's ratio (NPR) have unique mechanical deformation characteristics compared to conventional cellular cores, which can be further applied to modeling lightweight sandwich structures. The Arc-type cellular core is based on the traditional re-entrant cellular core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. Based on that, the sound transmission characteristics of sandwich doubly-curved shells with NPR arc-type auxetic cellular core layer is studied in this article. The Hamilton's principle is applied to derive the governing equations and considers fluid-structure coupling by applying normal velocities continuity conditions at the fluid-structure interface, which is further analytically solved using Navier's method, and the sound transmission loss (STL) is described analytically. The correctness of the proposed formula is verified by comparing the theoretical solution with the calculation results of the commercial software COMSOL and the experimental results of impedance tube sound insulation. Based on the theoretical model, it is calculated that the average STL of the arc-type cellular is 6.61% higher than that of the traditional re-entrant cellular within the broad low-frequency range of 100–2448Hz. Then the effect of key parameters on the STL of sandwich structure is systematically analyzed, and the results show that the first frequency of the sandwich shell decreases with the increase of the rib thickness, but increases with the increase of the arc radius. Notably, a smaller arc radius and a larger rib thickness exhibit superior sound insulation properties across a broad frequency range. In addition, when the core layer thickness increases from 0.007m to 0.009m, the average STL of sandwich structures is reduced by 7.38% in a broad low-frequency range of 100–2448Hz.

An investigation on synergistic resonances of membrane-type acoustic metamaterial with multiple masses

Membrane-type acoustic metamaterials (MAM) represent a class of materials that are lightweight, compact, structurally simple, and simultaneously offer flexibility and moldability, all while demonstrating exceptional sound attenuation properties in the low-frequency range. As a continuation, this study focuses on membrane-based acoustic metamaterials with synergistic resonance of multiple loaded mass blocks. By varying the unit shape, arrangement method, radius and material of the loaded mass blocks, the low-frequency sound insulation performance of membrane-based acoustic metamaterials with synergistic resonance of multiple loaded mass blocks was calculated using a numerical model that are experimentally validated. The results indicate that the peak transmiss loss (TL) frequencies can be tuned to specific values. The optimized membrane-type acoustic metamaterial could achieve a TL bandwidth up to 844 Hz (>5dB) and a TL bandwidth up to 376 Hz (>10 dB) within the low-frequency range. Acoustic-membrane analysis further revealed the vibration patterns of the structure under different frequency excitations, providing profound physical insights into the mechanisms of low-frequency sound insulation. Moreover, by altering the relative angles between the loaded mass blocks could further broaden the effective noise reduction bandwidth which can benefit the understanding on the optimized membrane-acoustic interactions.

Broadband low-frequency sound insulation of stiffened sandwich PFGM doubly-curved shells with positive, negative and zero Poisson's ratio cellular cores

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative and zero Poisson's ratios have unique mechanical deformation characteristics, which can be further applied to modeling lightweight sandwich structures. Based on that, the sound transmission characteristics of a novel stiffened sandwich porous functionally graded materials (PFGM) doubly-curved shells with full Poisson's ratio characteristic range cellular cores are investigated in this study. The adjustment of material properties of PFGM face sheets in the thickness direction is achieved through power law based on component volume fraction, and the core layer consists of cellular cores with positive, negative, and zero Poisson's ratios (PPR, NPR, and ZPR). Two common types of stiffened sandwich shell types, namely, the shell with PFGM face sheets and metal-rich cellular cores (type-A), and the ceramic-rich cellular cores (type-B), are discussed, and the Hamilton's principle is used to derive the governing equations. By applying normal velocities continuity conditions at the fluid-structure interface to consider fluid-structure coupling, which is further analytically solved using Navier's technology, and the average sound transmission loss (STL) with broadband low-frequency is described. The effectiveness of the established theoretical model is confirmed by comparing it with previously published results, experimental and simulated results obtained by impedance tube and COMSOL commercial software. A systematic comparison is conducted on the performance of stiffened sandwich PFGM doubly-curved shells with full Poisson's ratio characteristic range cellular cores, and the results show superior performance in the sound insulation for the sandwich shell with ZPR cellular cores, considerably at a broad low-frequency range of 220–2040 Hz, in comparison with the sandwich shell with NPR cellular cores and conventional PPR cellular cores types. This work's findings can serve as a benchmark for future studies and help to design and create engineering sandwich structures with improved sound insulation properties.

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.

Sustainable Solutions in Sound Shielding: Harnessing Metamaterials for Acoustic Cloaking

The development of metamaterials promises to enable smallscale, worldwide industry-wide acoustic, electromagnetic, mechanical, and solar energy harvesting. Engineered structures surpass natural material limitations, offering capabilities unattainable in traditional counterparts. This paper explores metamaterials' manipulation of acoustic, electromagnetic, mechanical, and solar energy. Mechanical metamaterials convert strain into electrical energy, applicable from interstellar travel to terrestrial infrastructure. Precision-configured acoustic metamaterials efficiently harness dispersed acoustic energy, improving renewable energy methodologies. Integration into photovoltaic cells showcases metamaterials' solar potential, with innovative designs enhancing solar energy conversion efficiency. “Metamaterials” is a word used to describe artificial structures whose properties are based on the aggregate expression of individual components. Acoustic metamaterials are the term used for such constructions intended for the manipulation of acoustic waves. Controlled wave propagation is made possible by acoustic metamaterials, which is frequently not possible with bulk materials created chemically. This indicates that the wave propagation in acoustic metamaterials is directed and produces desired acoustic effects, independent of the mass-density properties of the material. The distinct properties of acoustic metamaterials have paved the way for the creation of practical solutions for a variety of uses, such as passive destructive interference, acoustic cloaking, sound focusing, low-frequency sound insulation, and biomedical acoustics. The kind of sound modification determines the general properties of an acoustic metamaterial. The properties of several of the most promising acoustic metamaterials from passive to active are introduced in this work. In order to achieve a sustainable future, it is necessary to combine environmentally friendly technologies with renewable energy sources for their final application. This is demonstrated by highlighting both the fundamental concepts and the physical models that were assessed.

Band gap tunability and wave propagation of a novel fully symmetric single-phase metamaterial

In this paper, a new type of fully symmetric single-phase metamaterial structure is proposed. Based on the finite element method, the band gap characteristics of different forms of the structure and the generation principle of the band gap are discussed. The analysis of the formation mechanism of the band gap shows that the proposed structure can achieve the purpose of expanding the band gap in the low frequency range by changing the structure and adding inclusions. Then, the variation trend of the band gap frequency range in the case of small deformation of the proposed structure is discussed. In addition, the propagation characteristics of elastic waves in the proposed structure are analyzed according to the variation characteristics of frequency contours, phase velocities and group velocities. Finally, the frequency response spectrum obtained from the propagation of elastic waves in a finite lattice composed of Model No. 3 elements further confirms the role of the proposed structure in suppressing wave propagation. The results show that the proposed structure has good band gap characteristics in a certain frequency range, which can provide ideological guidance for the design of metamaterials for achieve low-frequency sound insulation and vibration reduction.

Improvement of the low-frequency sound insulation performance of hollow double-leaf panels by inserting a bending panel

Air-borne sound transmission loss of building materials generally follows the mass law. Transmission loss decreases at lower frequencies and is minimal at the fundamental natural frequency f0. On the other hand, transmission loss increases below f0, and is controlled by stiffness. Moreover, the stiffer the materials, the higher the f0. In the other words, even without increasing the mass, increasing the stiffness can improve low-frequency transmission loss. We focus on the fact that flexible lightweight panels are easily stiffened by bending deformation. We conduct a basic study on the effect of inserting a bending panel into hollow double-leaf panels. Experimental results on single panels showed a correspondence between the increase of f0 by bending deformation and the improvement of low-frequency sound insulation performance. In the case of the double-leaf panels with the lightweight bending panel inserted inside, the stronger the bending, the more low-frequency sound insulation performance tended to be improved.

A low-frequency sound insulation metastructure with relatively high ventilation

Noise pollution is growing nowadays and there is always a conflict between ventilation and noise insulation. The advances in acoustic metamaterials provide an effective solution for this conflict. In this paper, we propose a metastructure with protruded necks based on Helmholtz resonance. Sound transmission loss (STL) of 13 dB at low-frequency of 488[Formula: see text]Hz is obtained in experiment with the ventilation of 20%, which is in good agreement with the simulation. It is revealed that introduction of protruded neck can reduce the resonant frequency. Sound absorption is the main mechanism for noise insulation at low frequency. Next, the effects of geometric parameters on sound insulation are discussed. A reduction in cross-sectional area of neck, an increase in neck length, and an increase in ventilation all lead to a decrease in both resonant frequencies and STL amplitudes. Finally, a two-layer structure is constructed by the proposed metastructure with different neck length in each unit. Both the amplitude and frequency range of STL are enlarged. These results exhibit a practical application for ventilated metastructure in sound insulation at low frequency.

Lightweight sound insulation optimization of simply supported locally resonant plate

A theoretical model of the normal sound insulation of a rectangular locally resonant (LR) plate with simply supported boundary conditions is established. The accuracy of the model is verified through comparison with finite element simulation results. Considering a 1-m2 aluminum plate as the research object, a non-dominated genetic algorithm is introduced. The algorithm optimizes the lightweight sound insulation of an LR finite plate with a center frequency band of 20–800 Hz as the optimization objective of maximum average sound insulation and minimum mass. The optimization parameters are substrate thickness and local resonance parameters (including resonator target frequency (fobj), number of resonators, additional mass ratio, and resonator damping). Optimization results indicate that the average sound insulation fluctuates at approximately 2 dB due to changes in fobj. The results also provide an optimal solution to the algorithm. The optimal sound insulation value curve of LR plates corresponding to different surface densities of intermediate improved cases is fitted and compared with the sound insulation value of an equal-mass bare plate. Under lightweight optimization, the resonators are deemed capable of improving the local frequency band sound insulation. In contrast, the wideband average sound insulation can approximate but not surpass the insulation provided by the equal-mass bare plate. In practical applications, an LR plate that can improve the local frequency band sound insulation and ensure the overall lightweight sound insulation performance of the wide frequency band can be obtained. This can be achieved by analyzing the frequency spectrum of optimal points in the lightweight sound insulation optimization process. Relevant research can provide a basis for the evaluation and design of the low-frequency sound insulation of plates for transportation equipment, such as airplanes, high-speed trains, and cars.

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

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

Sound transmission across locally resonant honeycomb sandwich meta-structures with large spatial periodicity.

Honeycomb sandwich structures have been widely used in the field of engineering owing to their outstanding mechanical properties. However, for a honeycomb sandwich structure with large spatial periodicity, there is a low-frequency sound insulation valley. Here, the sound transmission across locally resonant honeycomb sandwich meta-structures was investigated to overcome this sound-insulation valley. An analytical model was developed based on the space-harmonic approach and the low-frequency sound insulation valley was determined analytically and numerically. The results indicate that the resonator distributed at the center of the face panel has a significant impact on the sound transmission performance of the honeycomb sandwich structure, whereas the resonator distributed on the wall of the honeycomb core does not contribute to overcoming this sound-insulation valley. Based on the research results, a design strategy for overcoming this sound-insulation valley was determined by tuning the damping parameter and constructing graded resonators. Moreover, sound transmission under the excitation of oblique incidence sound waves was also investigated. Compared with the method of filling porous materials, the proposed design method is more effective, and more importantly, the mass of the resonator is only 1.23% of that of the porous materials.

Broadband low-frequency sound insulation of a metamaterial plate with inertial amplification

The recent development of Inertia Amplification (IA) acoustic metamaterial (AMM) opens a new venue for insulating low-frequency sound waves. This differs from conventional approaches that rely excessively on the structural density of the insulator and, therefore, lead to prohibitively heavy structures. The IA-AMM acquires a large effective density and a broad flexural bandgap by amplifying the inertia of many small mass elements periodically distributed in its unit cells, thus holding great promise as an effective yet lightweight solution for low-frequency sound insulation. This paper explores this possibility through numerical and experimental investigations. A semi-analytical model of an IA-AMM plate is developed by combining analytical equations characterizing the kinematics of an IA mechanism and FEM equations governing the vibration of the host plate. Based on this model, sound transmission characteristics of the plate under various sound incidences are analyzed with different amplification angles. By comparing with a locally resonant AMM plate, we found that the IA-AMM plate's sound transmission losses (STLs) are significantly and systematically improved over a wide frequency range of 116–544 Hz. To understand the underlying physics, the band diagram of the IA-AMM plate is calculated, which indicates the formation of a flexural bandgap covering the frequencies of the improved STL. The velocity contour of the plate at the center frequency of this bandgap also reveals much-suppressed vibration velocity amplitudes and a dipole-like sound radiation directivity, further explaining the observed enhancement of the sound insulation ability. Numerically predicted improvement of sound insulation is finally confirmed by experiments.

Topological Design of Two-Dimensional Phononic Crystals Based on Genetic Algorithm.

Phononic crystals are a kind of artificial acoustic metamaterial whose mass density and elastic modulus are periodically arranged. The precise and efficient design of phononic crystals with specific bandgap characteristics has attracted increasing attention in past decades. In this paper, an improved adaptive genetic algorithm is proposed for the reverse customization of two-dimensional phononic crystals designed to maximize the relative bandwidth at low frequencies. The energy band dispersion relation and transmission loss of the optimal structure are calculated by the finite-element method, and the effective wave-attenuation effect in the bandgap range is verified. This provides a solution for the custom-made design of acoustic metamaterials with excellent low-frequency bandgap sound insulation or other engineering applications.