Research on the low-frequency band gap characteristics of longitudinal vibration of ship shafting based on bionic quasi-zero stiffness metamaterials

A novel one-dimensional quasi-zero-stiffness (QZS) metamaterial is proposed in this paper to acquire low-frequency band gaps to control the low-frequency longitudinal vibration of propulsion shaft using the bionic QZS as the local resonant oscillator. Firstly, the parameter design of the representative unit cell (RUC) for metamaterials using a bionic limb-shaped QZS structure is carried out and static analysis is conducted to verify its QZS property. Secondly, we model the QZS metamaterials as a lumped-mass-spring chain and derive the dispersion relationship through the Harmonic Balance method, then discuss the impact of damping, stiffness ratio, mass ratio, and excitation amplitude on this band gap. Finally, the resulting band gap is then confirmed through numerical simulations. Both the theoretical and numerical predictions show very low-frequency band gaps (about 7.5 Hz). Therefore, the proposed QZS metamaterials should be a promising solution for low-frequency wave filtering or attenuation for longitudinal vibration of ship shafting.