Elastic metamaterial shaft with a stack-like resonator for low-frequency vibration isolation

This paper presents an elastic metamaterial shaft with a new class of stack-like resonators consisting of bonded periodically annular rubber and lead rings that support the formation of ultra-low-frequency vibration band gaps because of reduced stiffness resulting from the discretized rubber rings. By using finite element method, the band structures and the transmission power spectra of the proposed metamaterial shaft are investigated. Subsequently, the mechanism of the band gaps is illustrated by analyzing the displacement fields of extracted mode shapes at the edge of band gaps. Lastly, finite element method is used to explore the effects of geometrical parameters on the band gaps. The related results confirm the very-low-frequency vibration mitigation performance of the proposed meta-shaft below 120 Hz and indicate there is a complete bandgap in which flexural, longitudinal and torsional vibration can be simultaneously attenuated. Moreover, multiple flexural band gaps are observed in the concerned region of frequencies in our design, and the mechanism behind this characteristic is analyzed by eigenmodes. The new structure presented here can thus be used to reduce vibrations of shaft-like structures at low frequencies in the practical environment.