Abstract
In this paper, a coupled mismatched time-lag controlled quasi-zero static stiffness vibration isolator (QZS-VI) system is investigated to enhance its vibration isolation performance. Firstly, a mathematical model of the controlled QZS-VI system is established, and the steady state response is solved analytically using the averaging method and further verified by the Runge-Kutta numerical method. Subsequently, the stability of the system is analysed in depth, and the effects of Hopf bifurcation and saddle-node bifurcation on the dynamic characteristics of the system are explored. The modulation effects of the dual time-lag parameters on the amplitude-frequency characteristics, peak amplitude and resonant frequency are further investigated, and it is found that the proper selection of the time-lag parameters can effectively control the emergence and evolution of the frequency islands. In addition, the effect of double time-lag control on the force transfer rate of the system is analysed, and the results demonstrate that an appropriately mismatched time-lag control can attenuate the resonance peak and broaden the vibration isolation frequency band. Finally, the equivalent damping effect of displacement-velocity feedback control is discussed, and it is indicated that different time-lag parameters can optimise the vibration isolation performance of the system. The results show that mismatched time-lag control can significantly improve the vibration isolation effect of the QZS-VI system, which provides theoretical guidance for the optimal design of nonlinear vibration systems.