Investigation on the free vibration characteristics of vertical quasi-zero stiffness isolation system considering the disc spring's loading position

This study investigates a quasi-zero stiffness (QZS) isolation system designed for vertical vibration control in isolation structures. The QZS characteristics are achieved by connecting a negative stiffness disc spring in parallel with the linear positive stiffness spiral spring. Initially, the force-displacement relationship of the disc spring is established, taking into account the loading position, and validated through static experiments. Subsequently, the free vibration equations of the QZS system are derived. The Jacobi elliptic functions and the Newton-harmonic balance (NHB) method are then employed to study its free vibration characteristics without considering damping. The results demonstrate that the natural vibration period of the QZS system is related to the nondimensional amplitude and the height of the loaded inner cone. Furthermore, the second-order analytical approximate solution obtained via the NHB method exhibits remarkable accuracy. Finally, the critical damping ratio of the damped QZS isolation system is investigated using a numerical approach. The findings indicate that the critical damping ratio is only correlated with the nondimensional amplitude. This study addresses the gaps in existing research and provide recommendations for the parametric design of vertical QZS isolation system.