Dynamic characteristics of axially moving slender structures with quasi-zero stiffness boundary conditions

Quasi zero stiffness (QZS) isolators are generally constructed by combining positive stiffness component and a negative stiffness component. In this research, a nonlinear vibration isolator with quasi zero stiffness characteristics is proposed, primarily consisting of air spring and permanent magnets. Force displacement relationship and the stiffness displacement relationship of the proposed isolator are established by analyzing the force feature of the air spring and the magnet. The harmonic balance method (HBM) is employed to analyze the force transfer characteristic of isolator. The effect of isolator parameters on the system’s stiffness characteristics and force transmissibility is examined. The performance of quasi zero stiffness isolator is verified by experiments. Then, the proposed nonlinear isolator is employed as the boundary support at both ends of the slender structure. On the basis of Euler-Bernoulli beam theory, the governing equation of a slender beam with quasi zero stiffness support and axial motion is established. Then, natural frequencies and mode functions of the beam are determined using the assumed mode method. The HBM is utilized to simplify the equations to solve the amplitude-frequency response and transfer characteristics of the beam. Furthermore, the impact of system parameters and axial velocity on the vibration isolation performance of the system is investigated.