Theoretical Analysis, Neural Network-Based Inverse Design, and Experimental Verification of Multilayer Thin-Plate Acoustic Metamaterial Unit Cells

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.