For the sake of lowering the locally resonant bandgap without additional mass or softer springs, a multi-resonator periodic hybrid structure with an ultralow-frequency band gap is proposed. The hybrid structure is composed of quasi-zero-stiffness (QZS) mechanical systems and multiple mass-in-mass (MIM) lattice systems. A theoretical model is established to investigate the dispersion relation of the structure. The effects of the stiffness ratio and mass ratio on the dispersion relation are studied. It can be seen that, thanks to the introduction of the QZS system, the band gaps of the hybrid structure can be flexibly shifted to lower frequency. In theory, a reasonable parameter setting can produce an ultra-low frequency first band gap. Furthermore, both the effective stiffness and effective mass of the unit of the hybrid structure are derived for further explanation of the attenuation mechanism. And the hybrid structure presents negative stiffness and negative mass properties in certain frequency ranges. Finally, the propagation of elastic waves in the hybrid structure is calculated, which further verifies the structure’s suppression ability of ultralow-frequency elastic waves.

为了在不增加质量或更软弹簧的情况下降低局部谐振带隙，提出了一种具有超低频带隙的多谐振器周期混合结构。混合结构由准零刚度 (QZS) 机械系统和多个质量质量 (MIM) 晶格系统组成。建立了理论模型来研究结构的色散关系。研究了刚度比和质量比对色散关系的影响。可以看出，由于QZS系统的引入，混合结构的带隙可以灵活地转移到较低的频率。理论上，合理的参数设置可以产生超低频的第一带隙。此外，推导出混合结构单元的有效刚度和有效质量，以进一步解释衰减机制。并且混合结构在某些频率范围内呈现负刚度和负质量特性。最后计算了弹性波在混合结构中的传播情况，进一步验证了该结构对超低频弹性波的抑制能力。