Low-frequency band gaps in quasi-zero stiffness locally resonant metamaterial shaft

The suppression of low-frequency torsional vibration has always been a difficult problem in the field of vibration control. Recently, metamaterials have attracted considerable attention due to their superior vibration insulation properties, at least in some targeted and tunable band gaps ranges. In particular, the position of the local resonance band gaps is related to the resonance frequency of the local resonator (LR). In this paper, a novel quasi-zero-stiffness torsional LR is proposed and a metamaterial shaft is devised by periodically attaching this LR onto a uniform shaft. The statics analysis for the torsional LR is conducted, and the propagation characteristics of the torsional vibration in the metamaterial shaft is studied with the transfer matrix theory and the Galerkin method. The analytical dispersion relation and the band gap structure indicate the existence of low frequency band gaps. And the location of the band gaps and the attenuation ability of torsional vibration can be effectively controlled by tuning the structural parameters of LR and the material of shaft, which provide a theoretical basis and guidance for addressing the challenge of low-frequency torsional vibration suppression.