Development of Adjustable Parallel Helmholtz Acoustic Metamaterial for Broad Low-Frequency Sound Absorption Band

An Investigation of Modular Composable Acoustic Metamaterials with Multiple Nonunique Chambers

To make the sound absorber easy to fabricate and convenient for practical application, a modular composable acoustic metamaterial with multiple nonunique chambers (MCAM-MNCs) was proposed and investigated, which was divided into a front panel with the same perforated apertures and a rear chamber with a nonunique grouped cavity. Through the acoustic finite element simulation, the parametric studies of the diameter of aperture d, depth of chamber T0, and thickness of panel t0 were conducted, which could tune the sound absorption performances of MCAM-MNCs-1 and MCAM-MNCs-2 for the expected noise reduction effect. The effective sound absorption band of MCAM-MNCs-1 was 556 Hz (773-1329 Hz), 456 Hz (646-1102 Hz), and 387 Hz (564-951 Hz) for T = 30 mm, T = 40 mm, and T = 50 mm, respectively, and the corresponding average sound absorption coefficient was 0.8696, 0.8854, and 0.8916, accordingly, which exhibited excellent noise attenuation performance. The sound absorption mechanism of MCAM-MNCs was investigated by the distributions of the total sound energy density (TSED). The components used to assemble the MCAM-MNCs sample were fabricated by additive manufacturing, and its actual sound absorption coefficients were tested according to the transfer matrix method, which demonstrated its feasibility and promoted its actual application.

Study on a Hexagonal Acoustic Metamaterial Cell of Multiple Parallel-Connection Resonators with Tunable Perforating Rate

The limited occupied space and various noise spectrum requires an adjustable sound absorber with a smart structure and tunable sound absorption performance. The hexagonal acoustic metamaterial cell of the multiple parallel-connection resonators with tunable perforating rate was proposed in this research, which consisted of six triangular cavities and six trapezium cavities, and the perforation rate of each cavity was adjustable by moving the sliding block along the slideway. The optimal geometric parameters were obtained by the joint optimization of the acoustic finite element simulation and cuckoo search algorithm, and the average sound absorption coefficients in the target frequency ranges of 650-1150 Hz, 700-1200 Hz and 700-1000 Hz were up to 0.8565, 0.8615 and 0.8807, respectively. The experimental sample was fabricated by the fused filament fabrication method, and its sound absorption coefficients were further detected by impedance tube detector. The consistency between simulation data and experimental data proved the accuracy of the acoustic finite element simulation model and the effectiveness of the joint optimization method. The tunable sound absorption performance, outstanding low-frequency noise reduction property, extensible outline structure and efficient space utilization were favorable to promote its practical applications in noise reduction.

Study on Sound-Insulation Performance of an Acoustic Metamaterial of Air-Permeable Multiple-Parallel-Connection Folding Chambers by Acoustic Finite Element Simulation

In order to achieve a balance between sound insulation and ventilation, a novel acoustic metamaterial of air-permeable multiple-parallel-connection folding chambers was proposed in this study that was based on Fano-like interference, and its sound-insulation performance was investigated through acoustic finite element simulation. Each layer of the multiple-parallel-connection folding chambers consisted of a square front panel with many apertures and a corresponding chamber with many cavities, which were able to extend both in the thickness direction and in the plane direction. Parametric analysis was conducted for the number of layers n_l and turns n_t, the thickness of each layer L₂, the inner side lengths of the helical chamber a₁, and the interval s among the various cavities. With the parameters of n_l = 10, n_t = 1, L₂ = 10 mm, a₁ = 28 mm, and s = 1 mm, there were 21 sound-transmission-loss peaks in the frequency range 200-1600 Hz, and the sound-transmission loss reached 26.05 dB, 26.85 dB, 27.03 dB, and 33.6 dB at the low frequencies 468 Hz, 525 Hz, 560 Hz, and 580 Hz, respectively. Meanwhile, the corresponding open area for air passage reached 55.18%, which yielded a capacity for both efficient ventilation and high selective-sound-insulation performance.

Effects of Aperture Shape on Absorption Property of Acoustic Metamaterial of Parallel-Connection Helmholtz Resonator

A Helmholtz resonator (HR) with an embedded aperture is an effective acoustic metamaterial for noise reduction in the low-frequency range. Its sound absorption property is significantly affected by the aperture shape. Sound absorption properties of HRs with the embedded aperture for various tangent sectional shapes were studied by a two-dimensional acoustic finite element simulation. The sequence of resonance frequency from low to high was olive, common trapeziform, reverse trapeziform, dumbbell and rectangle. Meanwhile, those HRs for various cross-sectional shapes were investigated by a three-dimensional acoustic finite element simulation. The sequence of resonance frequency from low to high were round, regular hexagon, square, regular triangle and regular pentagon. Moreover, the reason for these phenomena was analyzed by the distributions of sound pressure, acoustic velocity and temperature. Furthermore, on the basement of the optimum tangent and cross-sectional shape, the sound absorption property of parallel-connection Helmholtz resonators was optimized. The experimental sample with optimal parameters was fabricated, and its average sound absorption coefficient reached 0.7821 in 500-820 Hz with a limited thickness of 30 mm. The research achievements proved the significance of aperture shape, which provided guidance for the development of sound absorbers in the low-frequency range.

Mathematical Model for Estimating the Sound Absorption Coefficient in Grid Network Structures

Although grid network structures are often not necessarily intended to absorb sound, the gaps between the rods that make up the grid network are expected to have a sound absorption effect. In this study, the one-dimensional transfer matrix method was used to develop a simple mathematical model for accurately estimating the sound absorption coefficient of a grid network structure. The gaps in the grid network structure were approximated as the clearance between two parallel planes, and analysis units were derived to consider the exact geometry of the layers. The characteristic impedance and propagation constant were determined for the approximated gaps and treated as a one-dimensional transfer matrix. The transfer matrix obtained for each layer was used to calculate the sound absorption coefficient. The samples were fabricated from light-curing resin by using a Form2 3D printer from Formlabs. The measurement results showed that a sound absorption coefficient of 0.81 was obtained at the peak when seven layers were stacked. A sensitivity analysis was carried out to investigate the influence of the rod diameter and pitch. The simulated values tended to be close to the experimental values. The above results indicate that the mathematical model used to calculate the sound absorption coefficient is sufficiently accurate to predict the sound absorption coefficient for practical application.

Research on the Sound Insulation Performance of Composite Rubber Reinforced with Hollow Glass Microsphere Based on Acoustic Finite Element Simulation

The composite rubber reinforced with hollow glass microsphere (HGM) was a promising composite material for noise reduction, and its sound insulation mechanism was studied based on an acoustic finite element simulation to gain the appropriate parameter with certain constraint conditions. The built simulation model included the air domain, polymer domain and inorganic particles domain. The sound insulation mechanism of the composite material was investigated through distributions of the sound pressure and sound pressure level. The influences of the parameters on the sound transmission loss (STL) were researched one by one, such as the densities of the composite rubber and HGM, the acoustic velocities in the polymer and inorganic particle, the frequency of the incident wave, the thickness of the sound insulator, and the diameter, volume ratio and hollow ratio of the HGM. The weighted STL with the 1/3 octave band was treated as the evaluation criterion to compare the sound insulation property with the various parameters. For the limited thicknesses of 1 mm, 2 mm, 3 mm and 4 mm, the corresponding optimal weighted STL of the composite material reached 14.02 dB, 19.88 dB, 22.838 dB and 25.27 dB with the selected parameters, which exhibited an excellent sound insulation performance and could promote the practical applications of the proposed composite rubber reinforced with HGM.

Adjustable Sound Absorber of Multiple Parallel-Connection Helmholtz Resonators with Tunable Apertures Prepared by Low-Force Stereolithography of Photopolymer Resin

The variable noise spectrum for many actual application scenarios requires a sound absorber to adapt to this variation. An adjustable sound absorber of multiple parallel-connection Helmholtz resonators with tunable apertures (TA-MPCHRs) is prepared by the low-force stereolithography of photopolymer resin, which aims to improve the applicability of the proposed sound absorber for noise with various frequency ranges. The proposed TA-MPCHR metamaterial contains five metamaterial cells. Each metamaterial cell contains nine single Helmholtz resonators. It is treated as a basic structural unit for an array arrangement. The tunable aperture is realized by utilizing four segments of extendable cylindrical chambers with length l₀, which indicates that the length of the aperture l is in the range of [l₀, 4l₀], and that it is tunable. With a certain group of specific parameters for the proposed TA-MPCHR, the influence of the tunable aperture with a variable length is investigated by acoustic finite element simulation with a two-dimensional rotational symmetric model. For the given noise spectrum of certain actual equipment with four operating modes, the TA-MPCHR sample with a limited total thickness of 40 mm is optimized, which is made of photopolymer resin by the low-force stereolithography, and its actual average sound absorption coefficients for the frequency ranges of 500-800 Hz, 550-900 Hz, 600-1000 Hz and 700-1150 Hz reach 0.9203, 0.9202, 0.9436 and 0.9561, respectively. Relative to common non-adjustable metamaterials, the TA-MPCHR made of photopolymer resin can reduce occupied space and improve absorption efficiency, which is favorable in promoting its practical applications in the noise pollution prevention.

Optimal Design of Acoustic Metamaterial of Multiple Parallel Hexagonal Helmholtz Resonators by Combination of Finite Element Simulation and Cuckoo Search Algorithm

To achieve the broadband sound absorption at low frequencies within a limited space, an optimal design of joint simulation method incorporating the finite element simulation and cuckoo search algorithm was proposed. An acoustic metamaterial of multiple parallel hexagonal Helmholtz resonators with sub-wavelength dimensions was designed and optimized in this research. First, the initial geometric parameters of the investigated acoustic metamaterials were confirmed according to the actual noise reduction requirements to reduce the optimization burden and improve the optimization efficiency. Then, the acoustic metamaterial with the various depths of the necks was optimized by the joint simulation method, which combined the finite element simulation and the cuckoo search algorithm. The experimental sample was prepared using the 3D printer according to the obtained optimal parameters. The simulation results and experimental results exhibited excellent consistency. Compared with the derived sound absorption coefficients by theoretical modeling, those achieved in the finite element simulation were closer to the experimental results, which also verified the accuracy of this optimal design method. The results proved that the optimal design method was applicable to the achievement of broadband sound absorption with different low frequency ranges, which provided a novel method for the development and application of acoustic metamaterials.