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.

本文提出了具有多自由度 (MDOF) 混合谐振器的弹性超材料，以在不增加质量以减少振动的情况下实现更低和更宽的带隙。首次分析了多谐振器弹性超材料（EMs）带隙中心频率的显式表达式，以探索宽的低频带隙。主动解析获得带隙的边界频率以寻找更宽的带隙，该带隙符合具有自由端或固定端的晶胞的固有频率。通过色散曲线和质量的相对运动探索了带隙形成机制。此外，为宽带隙生成获得了带隙合并的条件。最后，将具有相同总质量的混合谐振器的三类所提出模型的能带结构与经典电磁模型（MODEL T）进行比较，揭示所提出模型的带隙中心频率变低，或带隙的总宽度显着扩大。Hybrid Series MODEL Ⅱ的带隙比具有相同质量和刚度的经典局部共振EM（MODEL T）低14.5%，宽81%，而Hybrid Parallel MODEL Ⅱ的带隙宽163%。