Beneficial performance of a quasi-zero-stiffness vibration isolator with time-delayed active control

• The model of quasi-zero-stiffness vibration isolator with active control is established.
• Existence and stability of equilibria of the system are analyzed for engineering application.
• Time delay induces beneficial on isolation for impact load and force excitation.
• Time delay has significant effect on vibration isolation in the resonant region for base excitation.

The potential beneficial performance of a quasi-zero-stiffness vibration isolator (QZS-VI) with a simple linear time-delayed active control strategy is investigated in this study. Stability and bifurcation analysis shows that an active control can basically improve the system robustness in stability at the equilibrium position. However, a time-delayed active control can not only further strengthen the robustness of the system in stability, but also noticeably improve system transmissibility performance both in force and base excitations and obviously decrease the settling time of system transient response subject to an impact load. Moreover, it is shown that the controlled stiffness and especially the introduced time delay could be designed deliberately so that undesirable bifurcation and chaotic behaviors can be avoided or greatly suppressed. The results provide a useful insight into the analysis and design of nonlinear vibration isolators by exploiting potential nonlinear benefits of the time delay in vibration control.