Acoustic metamaterials are artificially engineered materials composed of subwavelength structural units, whose effective acoustic properties are primarily determined by structural design rather than intrinsic material composition. By introducing local resonances, these materials can exhibit unconventional acoustic behavior, enabling enhanced sound insulation beyond the limitations of conventional structures. In this study, a thin plate (thin sheet) refers to a structural element whose thickness is much smaller than its in-plane dimensions and can be accurately described using classical thin-plate vibration theory. When resonant mass blocks are attached to a thin plate, a thin-plate acoustic metamaterial is formed through the coupling between plate bending vibrations and local resonances. Thin-plate acoustic metamaterials exhibit excellent sound insulation performance in the low- and mid-frequency ranges. Multilayer configurations and the combination with porous materials can effectively broaden the insulation bandwidth and improve overall performance. However, the large number of structural parameters in multilayer composite thin-plate acoustic metamaterials significantly increases design complexity, making conventional trial-and-error approaches inefficient. To address this challenge, a neural-network-based inverse design framework is proposed for multilayer composite thin-plate acoustic metamaterials. An analytical model of thin-plate metamaterials with multiple attached cylindrical masses is established using the point matching and modal superposition methods and validated by finite element simulations. A multilayer composite unit cell is then constructed, and a dataset of 30,000 samples is generated through numerical simulations. Based on this dataset, a forward prediction network achieves a test error of 1.06%, while the inverse design network converges to an error of 2.27%. The inverse-designed structure is finally validated through impedance tube experiments. The objective of this study is to establish a systematic theoretical and neural-network-assisted inverse design framework for multilayer thin-plate acoustic metamaterials. The main novelties include the development of an accurate analytical model for thin-plate metamaterials with multiple attached masses, the construction of a large-scale simulation dataset, and the proposal of a neural-network-assisted inverse design strategy to address non-uniqueness in inverse design. The proposed approach provides an efficient and practical solution for low-frequency sound insulation design.

This study proposes a composite acoustic porous duct metamaterial muffler composed of a perforated tortuous channel and an externally wrapped porous layer, integrating both structural resonance and material damping effects. Theoretical models for the perforated plate, tortuous channel, and porous material were established, and analytical formulas for the total acoustic impedance and transmission loss of the composite structure were derived. Finite element simulations verified the accuracy of the models. A systematic parametric study was then performed on the effects of porous material type, thickness, and width on acoustic performance, showing that polyester fiber achieves the best results at a thickness of 30 mm and a width of 5 mm. Further analysis of periodic distribution modes revealed that axial periodic arrangement significantly enhances the peak noise attenuation, radial periodic arrangement broadens the effective bandwidth, and multi-frequency parallel configurations further expand the operating range. Considering practical duct conditions, a single-layer multi-cell array was constructed, and its modal excitation mechanism was clarified. By employing the Particle Swarm Optimization (PSO) algorithm for multi-parameter optimization, the average transmission loss was improved from 26.493 dB to 29.686 dB, corresponding to an increase of approximately 12.05%. Finally, physical samples were fabricated via 3D printing, and four-sensor impedance tube experiments confirmed good agreement among theoretical, numerical, and experimental results. The composite structure exhibited an average experimental transmission loss of 24.599 dB, outperforming the configuration without porous material. Overall, this work highlights substantial scientific and practical advances in sound energy dissipation mechanisms, structural optimization design, and engineering applicability, providing an effective approach for broadband and high-efficiency duct noise reduction.

With the continuous advancement of the automotive industry, users’ demands for vehicle ride comfort are constantly increasing. Low-frequency vibrations, characterized by their strong penetration and difficulty in attenuation, significantly impact ride comfort and represent a key challenge in current NVH research. Quasi-zero stiffness (QZS) structures demonstrate exceptional performance in low-frequency vibration isolation, making them widely adopted in automotive and industrial systems. However, traditional QZS structures predominantly rely on the parallel connection of positive and negative stiffness elements, presenting drawbacks such as stringent stiffness matching requirements and limited design freedom. This paper proposes a tandem-connected Oblique-Arch-Oblique (OAO) QZS structure based on a nonlinear deformation mechanism. By introducing symmetric nonlinear deformation, the structure effectively expands the operational range of conventional QZS systems and overcomes stiffness matching challenges. Firstly, the mechanical characteristics and key geometric parameters of the OAO structure were analyzed using the energy method. Secondly, finite element simulations validated the influence of critical parameters and demonstrated the design flexibility of the OAO structure in terms of load-bearing capacity. Finally, vibration isolation experiments were conducted to evaluate its low-frequency isolation performance. The results confirm that the proposed OAO structure achieves both a wide operational range and excellent low-frequency vibration isolation, validating it as an innovative structural solution for low-frequency vibration mitigation.

To address the broadband noise distribution, complex excitation sources, and insufficient low-frequency attenuation of conventional porous acoustic packages in commercial vehicle cabs, this study proposes a PU–six-cavity Helmholtz metamaterial composite acoustic package for broadband noise reduction. The proposed structure consists of a 30 mm PU porous layer for mid-to-high-frequency dissipation and a 30 mm six-cavity Helmholtz metamaterial layer for low-frequency absorption, forming a 60 mm composite acoustic package. A full-vehicle acoustic model of a commercial vehicle cab was established in VA One to identify the A-weighted sound pressure level (SPL) spectrum at the driver position. The results show that the PU porous acoustic package improves the mid- and high-frequency noise response, whereas pronounced peaks remain in the low- and low-to-mid-frequency ranges. To enhance these bands, the six sub-cavities of the Helmholtz metamaterial were tuned to 200, 250, 315, 400, 500, and 630 Hz through spatial partitioning and cavity grouping. COMSOL (version 6.1) simulations and particle velocity distributions confirmed the multi-peak absorption mechanism and the selective excitation of the corresponding sub-cavities. The composite structure was further validated through impedance-tube measurements, full-vehicle acoustic simulations, and in-vehicle tests. The VA One simulation shows that the total A-weighted SPL at the driver position decreases from 68.25 dB for the PU porous package to 66.01 dB after introducing the six-cavity Helmholtz metamaterial, corresponding to an additional reduction of 2.24 dB. A preliminary in-vehicle test under a stationary idling condition shows that the total A-weighted SPL near the driver’s ear decreases from 55.83 dB(A) to 54.56 dB(A). These results demonstrate that the proposed PU–six-cavity Helmholtz metamaterial composite acoustic package combines broadband porous dissipation with low-frequency resonant absorption, providing a feasible solution for broadband noise control in commercial vehicle cabs.