Accurate nonlinear dynamic characteristics analysis of quasi-zero-stiffness vibration isolator via a modified incremental harmonic balance method

Quasi-zero-stiffness (QZS) vibration isolator is widely used in low-frequency vibration isolation due to its high-static-low-dynamic-stiffness (HSLDS) characteristics. The complex nonlinear force of the QZS vibration isolator increases the difficulty of solving it while realizing the HSLDS characteristics. The typical analysis method is to use Taylor expansion to simplify the nonlinear force and make it approximate to polynomial form, which leads to inaccurate analysis results in the case of large excitation and small damping. Therefore, the modified incremental harmonic balance (IHB) method is used to directly analyze the dynamic characteristics of the QZS vibration isolator without simplification in this paper. The classical three-spring QZS vibration isolation model is used as the calculation example. The results are different from the previous approximate equation analysis results in three aspects: (1) There is no unbounded response of the system under displacement excitation; (2) Even harmonics and constant terms also exist in the response of the system and can lead to multiple solution intervals; (3) In the case of small damping and large excitation, both displacement excitation and force excitation have subharmonic resonance, reducing the vibration isolation performance of the system. In addition, the accuracy of the solution obtained by the IHB method is verified by the Runge–Kutta method. The accurate analysis method in this paper provides favorable theoretical support for the design and optimization of vibration isolators.