A disordered composite metamaterial beam optimized using NSGA-Ⅱ:a structure with an adjustable hybrid bandgap

To address the limitations of conventional periodic metamaterials in regulation and optimization, this study introduces a novel staggered supercell beam configuration designed to enhance low-frequency vibration isolation. The proposed supercell beam is composed of single cells with varying staggered degrees and inductances. Initially, the transmission matrix method was employed to model both symmetrical and staggered structures, enabling the determination of their attenuation constant and transmission coefficient. Subsequently, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was implemented for multi-objective optimization to identify Pareto frontiers. Theoretical analysis demonstrated that the staggered beam exhibits a lower attenuation constant than its symmetrical counterpart and, critically, introduces a new coupling bandgap at low frequencies. Experimental transmission coefficient measurements confirmed that the optimized staggered beam achieves superior low-frequency vibration isolation performance compared to the symmetrical beam. This improvement is attributed to the successful application of NSGA-II, which effectively balances bandgap width and attenuation constant—a challenge previously unresolved in the field, as evidenced by studies that have explored the maximum limits of attenuation constants and the influence of parameters such as resistance, piezoelectric sheet thickness, and lattice constant length on bandgap characteristics. The findings of this study demonstrate that the proposed disordered staggered supercell beam configuration, optimized with NSGA-II, achieves superior bandgap attenuation, offering significant potential for advancements in low-frequency vibration isolation research.