Band-Gap Properties of Elastic Metamaterials With Inerter-Based Dynamic Vibration Absorbers

Abstract

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.