Effects of relevant parameters on the bandgaps of acoustic metamaterials with multi-resonators

Locally resonant acoustic metamaterials with multi-resonators are generally regarded as a fine trend for managing the bandgaps, the different effects of relevant structural parameters on the bandgaps, which will be numerically investigated in this paper. A two-step homogenization method is extended to achieve the effective mass of multi-resonators metamaterial in the lattice system. As comparison, the dispersive wave propagation in lattice system and continuum model is studied. Then, the different effects of relevant parameters on the center frequencies and bandwidth of bandgaps are perfectly revealed, and the steady-state responses in the continuum models with purposed relevant parameters are additionally clarified. The related results can well confirm that the bandgaps exist around the undamped natural frequencies of internal resonators, and also their bandwidth can be efficiently controlled with the ensured center frequencies. Moreover, the design of purposed multi-resonators acoustic metamaterial in vibration control is presented and discussed by an example.