Controllably ultrawide bandgap of a metamaterial beam based on inertial amplification and magnetorheological elastomer

This paper presents the design of a metamaterial beam for controllably ultrawide bandgap (36.3Hz–218.6Hz) and low-frequency vibration attenuation, achieved by a lever-based inertial amplification and a variable stiffness of a magnetorheological elastomer (MRE) modulated by an external magnetic field. The metamaterial is formed by periodical mass-lever inertial amplifier and spring-MRE resonators connected to a base beam. The Galerkin method is employed to theoretically investigate the controllably ultrawide tunability of a low-frequency bandgap in terms of the MRE properties, the mass-lever inertial amplification and the geometric nonlinearity conditions. The results obtained are validated through numerical simulations. The study further extends to lightweight design of metamaterials, where the target frequency that depends on controllably ultrawide bandgap is introduced. With the same target frequency of bandgap, the proposed system exhibits a lighter resonator mass than the traditional metamaterials. Finally, a target frequency-based bandgap control strategy is developed, enabling real-time tunability of the bandgap within a low-frequency wideband range without changing the mass of the resonator or reconstructing the structure. Compared to typical "mass-spring" metamaterials, the proposed system shows superiority in achieving ultrawide bandgaps. This metamaterial offers a promising solution for creating controllably ultrawide vibration-attenuating structures, making it highly suitable for practical applications.