For the common difficulties of noise control in a low frequency region, an adjustable parallel Helmholtz acoustic metamaterial (APH-AM) was developed to gain broad sound absorption band by introducing multiple resonant chambers to enlarge the absorption bandwidth and tuning length of rear cavity for each chamber. Based on the coupling analysis of double resonators, the generation mechanism of broad sound absorption by adjusting the structural parameters was analyzed, which provided a foundation for the development of APH-AM with tunable chambers. Different from other optimization designs by theoretical modeling or finite element simulation, the adjustment of sound absorption performance for the proposed APH-AM could be directly conducted in transfer function tube measurement by changing the length of rear cavity for each chamber. According to optimization process of APH-AM, The target for all sound absorption coefficients above 0.9 was achieved in 602–1287 Hz with normal incidence and that for all sound absorption coefficients above 0.85 was obtained in 618–1482 Hz. The distributions of sound pressure for peak absorption frequency points were obtained in the finite element simulation, which could exhibit its sound absorption mechanism. Meanwhile, the sound absorption performance of the APH-AM with larger length of the aperture and that with smaller diameter of the aperture were discussed by finite element simulation, which could further show the potential of APH-AM in the low-frequency sound absorption. The proposed APH-AM could improve efficiency and accuracy in adjusting sound absorption performance purposefully, which would promote its practical application in low-frequency noise control.

Acoustic metamaterials based on Helmholtz resonance have perfect sound absorption characteristics with the subwavelength size, but the absorption bandwidth is narrow, which limits the practical applications for noise control with broadband. On the basis of the Fabry–Perot resonance principle, a novel sound absorber of the acoustic metamaterial by parallel connection of the multiple spiral chambers (abbreviated as MSC-AM) is proposed and investigated in this research. Through the theoretical modeling, finite element simulation, sample preparation and experimental validation, the effectiveness and practicability of the MSC-AM are verified. Actual sound absorption coefficients of the MSC-AM in the frequency range of 360–680 Hz (with the bandwidth Δf₁ = 320 Hz) are larger than 0.8, which exhibit the extraordinarily low-frequency sound absorption performance. Moreover, actual sound absorption coefficients are above 0.5 in the 350–1600 Hz range (with a bandwidth Δf₂ = 1250 Hz), which achieve broadband sound absorption in the low–middle frequency range. According to various actual demands, the structural parameters can be adjusted flexibly to realize the customization of sound absorption bandwidth, which provides a novel way to design and improve acoustic metamaterials to reduce the noise with various frequency bands and has promising prospects of application in low-frequency sound absorption.

An acoustic metamaterial absorber of parallel–connection square Helmholtz resonators is proposed in this study, and its sound absorption coefficients are optimized to reduce the noise for the given conditions in the factory. A two–dimensional equivalent simulation model is built to obtain the initial value of parameters and a three–dimensional finite element model is constructed to simulate the sound absorption performance of the metamaterial cell, which aims to improve the research efficiency. The optimal parameters of metamaterial cells are obtained through the particle swarm optimization algorithm, and its effectiveness and accuracy are validated through preparing the experimental sample using 3D printing and measuring the sound absorption coefficient by the standing wave tube detection. The consistency between the experimental data and simulation data verifies feasibility of the proposed optimization method and usefulness of the developed acoustic metamaterial absorber, and the desired sound absorption performances for given conditions are achieved. The experimental results prove that parallel–connection square Helmholtz resonators can achieve an adjustable frequency spectrum for the low frequency noise control by parameter optimization, which is propitious to promote its application in reducing the noise in the factory.

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.

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.

The mechanical properties of resin samples in low-force stereolithography additive manufacturing were affected by the printing orientation, and were investigated and optimized to achieve excellent single or comprehensive tensile strength, compressive strength, and flexural modulus. The resin samples were fabricated using a Form3 3D printer based on light curing technology according to the corresponding national standards, and they were detected using a universal testing machine to test their mechanical properties. The influence of the printing orientation was represented by the rotation angle of the resin samples relative to the x–axis, y–axis and z–axis, and the parameters was selected in the range 0°–90° with an interval of 30°. The multiple regression models for the mechanical properties of the prepared resin samples were obtained based on least square estimation, which offered a foundation from which to optimize the parameters of the printing orientation by cuckoo search algorithm. The optimal parameters for the tensile strength, compressive strength and flexural modulus were ‘α = 45°, β = 25°, γ = 90°’, ‘β = 0°, β = 51°, γ = 85°’ and ‘α = 26°, β = 0°, γ = 90°’, respectively, which obtained the improvements of 80.52%, 15.94%, and 48.85%, respectively, relative to the worst conditions. The mechanism was qualitatively discussed based on the force analysis. The achievements obtained in this study proved that optimization of the printing orientation could improve the mechanical properties of the fabricated sample, which provided a reference for all additive manufacturing methods.