Low-frequency band gap mechanism of torsional vibration of lightweight elastic metamaterial shafts

In this paper, the low-frequency band gap mechanism of torsional vibration is investigated for a kind of light elastic metamaterial (EM) shafts architecture comprised of a radial double-period element periodically as locally resonant oscillators with low frequency property. The dispersion relations are calculated by a method combining the transfer matrix and a lumped-mass method. The theoretical results agree well with finite method simulations, independent of the density of the hard material ring. The effects of the material parameters on the band gaps are further explored numerically. Our results show that in contrast to the traditional EM shaft, the weight of our proposed EM shaft can be reduced by 27% in the same band gap range while the vibration attenuation is kept unchanged, which is very convenient to instruct the potential engineering applications. Finally, the band edge frequencies of the lower band gaps for this light EM shaft are expressed analytically using physical heuristic models.