Hybrid multi-resonators elastic metamaterials for broad low-frequency bandgaps

Elastic metamaterials with multi-degree-of-freedom (MDOF) hybrid resonators are proposed in order to achieve the lower and wider bandgaps without increase of mass for vibration attenuation in this paper. The explicit expressions for the central frequencies of the bandgaps of the multi-resonators elastic metamaterials (EMs) are analyzed for the first time to exploring broad low-frequency bandgap. The boundary frequencies of the bandgaps are initiatively obtained analytically to seek for the wider bandgap, which comply with the natural frequencies of the unit cell with its free or fixed ends. The bandgap forming mechanism is explored by dispersion curve and relative movement of the masses. Besides, the condition for bandgap merging is obtained for broad bandgap generation. Finally, the band structure of the three classes of proposed models with hybrid resonators with the same total mass are compared with the classical EMs model (MODEL T), revealing that the central frequencies of bandgap of proposed models become lower, or the total width of the bandgap is significantly widened. The Hybrid Series MODEL II achieves 14.5% lower and 81% wider bandgap while Hybrid Parallel MODEL II achieves 163% wider bandgap than that of classical local resonance EMs (MODEL T) with the same mass and stiffness.