Parameter optimization of a two-stage quasi-zero-stiffness system with linear dynamic vibration absorber

Compared to the two-stage linear vibration isolator (TLVI), the two-stage quasi-zero stiffness (TQZS) system offers superior vibration isolation performance, making it a promising candidate for vibration isolation of precision instrument. However, the TQZS system exhibits a significant vibration amplitude due to its low dynamic stiffness. In this paper, a coupled (TQZS-UDVA) system consisting of a TQZS system and a dynamic vibration absorber (DVA) attached to the upper stage of the TQZS system is presented. The harmonic balance method is employed to obtain approximate analytical solution. The effects of system parameters on dynamic behavior and isolation performance are studied in detail. Five performance indexes are proposed, and based on these indexes, the damping and tuning stiffness of DVA are optimized. The results indicate that the integration of DVA effectively mitigates the vibration amplitude and extends the isolation frequency band, without compromising high-frequency performance.