Subharmonic response suppression of a quasi-zero stiffness system

Quasi-zero stiffness (QZS) isolators can effectively suppress low-frequency vibration due to high-static-low-dynamic stiffness (HSLDS) characteristics. The existence of nonlinearity induces intricate nonlinear phenomena in QZS isolators, particularly under conditions of small damping and large excitation. These nonlinear characteristics can seriously affect the vibration isolation performance, which has rarely been focused on in existing studies. This study examines a typical QZS isolator with nonlinear damping. The modified incremental harmonic balance (IHB) method is applied to directly analyze its dynamic characteristics and investigate the suppression of the subharmonic response. The dynamic analysis results indicate multiple subharmonic vibration intervals, including the 1/2, the 1/3, and the 1/9 subharmonic vibration. The basin of attraction at different excitation frequencies shows that subharmonic vibration is highly likely to occur. The effect of different damping on the transmissibility proves to be different. Simultaneously, rational parameter matching can guarantee the absence of subharmonic vibration while maintaining the primary resonance frequency and amplitude unchanged. The research results of this study provide theoretical support for the parameter selection of QZS isolators. In addition, the higher-order approximations of most isolators have the same form, so these results can guide other QZS isolators in suppressing subharmonic vibrations and improving their operating range.