Ultralow-frequency band gap in a quasi-zero-stiffness multi-resonator periodic hybrid structure

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.