Torsional bandgap characteristics in metamaterial rods with multiple internal multi-degree-of-freedom resonators

The elastic metamaterials have received widespread attention owing to their unique ability of manipulating elastic waves and thus the promising potential in vibration control. However, to obtain a wider and lower bandgap is still a challenge, especially within the space and mass constraints. This paper proposes a type of metamaterial rod with multiple internal multi-degree-of-freedom resonators, which is suitable for the case of limited space. The band structure is calculated by using the transfer matrix method and verified with the results in published work and finite element simulations. The merging effects of different bandgaps are observed, which largely broaden the bandgap. The novelty of this paper stems from two aspects: the discovery of minor bandgaps and the proposal of a design strategy to widen bandgaps within the space and mass constraints. The emergence of minor bandgaps is observed with the increase of non-dimensional lattice constant for the first time. And the reason for the emergence and some important characteristics of minor bandgaps are concluded through parameter studies. Furthermore, a design strategy based on the results of graded resonators is proposed to widen and lower the bandgap under the constraints of space and mass.