Surrogate-model-based design optimization of multiple locally resonant metamaterials for low-frequency vibration reduction

This study presents a surrogate-model-based optimal design framework to enhance low-frequency vibration attenuation of multiple locally resonant metamaterials (M-LRMs). The geometric parameters of the M-LRM unit cell are defined as design variables, enabling systematic tuning of resonator configurations. For each band gap, a performance index is defined to reflect the downward shift of the lower band-edge frequency and the increase in band-gap width, and these indices are integrated into a single objective function using a weighted-sum scalarization method. The relationship between the design variables and the performance indices is approximated by a surrogate model, and global optimization is performed in the surrogate design space using a hybrid metaheuristic algorithm (HMA) to identify an optimal unit cell configuration. Dispersion analysis confirms that, compared to the initial design, wider band gaps are formed with reduced lower band-edge frequencies. Frequency response function (FRF) analysis of a finite panel incorporating the optimized M-LRM demonstrates that the vibration response is attenuated within the band-gap frequency ranges predicted by dispersion analysis, validating the proposed framework for finite structures. The proposed approach streamlines the design of M-LRMs for low-frequency, broadband vibration reduction and offers extensibility to diverse unit cell configurations and lightweight panel applications.