Rigid-elastic combined metamaterial beam with tunable band gaps for broadband vibration suppression

Abstract

Extensive research efforts have been dedicated to exploring the application of metamaterial beams for vibration suppression. However, most existing designs primarily focused on utilizing the translational motion of local resonators to create band gaps. To address this limitation of employing solo motion to induce a relatively narrow band gap, this study proposes a novel design: a rigid-elastic combined metamaterial beam utilizing both translational and rotational motions of local resonators. Theoretical framework development involves extending the transfer matrix method to incorporate rigid bodies, with analytical results validated through finite element simulations and experimental data. Compared to conventional metamaterial beams, the proposed design exhibits an additional wide band gap in the low-frequency region that can be utilized for broadband vibration suppression. A parametric study elucidates the influences of geometric parameters on band gap formation, followed by an exploration of the tunability of the proposed meta-beam through a graded scheme and optimization strategy. In particular, a multiple-objective optimization approach is employed to enlarge the vibration suppression region and enhance vibration suppression ability. The optimized meta-beam demonstrates a remarkable 45% wider dominant suppression region and a 14% lower average transmittance compared to a uniform model.