Multi-scale optimization method for metamaterial plates with compression-torsion coupling inertial amplification

Inertial-amplified resonators are commonly used for vibration control in plates due to their favorable low-frequency properties. However, metamaterial plates incorporating such resonators in periodic arrangements can have a significant amount of added mass. To address this challenge, this paper proposes a multi-scale integrated optimization method for a compression-torsion coupling inertial amplification metamaterial plate, aiming to simultaneously optimize both the added mass and vibration attenuation capabilities. The proposed optimization method integrated two stages: the optimization of resonator structural parameters using the grid search method and the optimization of resonator distribution using the NSGA-Ⅱ algorithm. Through two-stage optimization, the optimal structural parameters of the resonator were first determined; subsequently, an efficient distribution scheme was established to minimize the resonator count, thereby further reducing the added mass. Optimization results demonstrate that even with a substantially reduced number of resonators, the metamaterial plate can still achieve significant vibration attenuation within the bandgap range. Specifically, with only 8% of the original number of resonators, a maximum vibration attenuation exceeding 30 dB within the bandgap can be achieved. Prototypes for experimental purposes were fabricated via a combination of machining and 3D printing. The experimental results demonstrate satisfactory agreement with the numerical predictions, confirming the reliability of the optimization approach. The method in this work may offer an efficient design solution for lightweight, broadband metamaterial plates.