On the analysis of a high-static-low-dynamic stiffness vibration isolator with time-delayed cubic displacement feedback

• The cubic displacement feedback with time delay is proposed.
• The effects of feedback gain and time delay on the frequency response are analysed.
• The cubic displacement feedback can improve the vibration isolation performance.

The cubic displacement feedback with time delay is proposed in this paper to improve the isolation performance of the high-static-low-dynamic stiffness (HSLDS) vibration isolator. First of all, the frequency response of the controlled HSLDS vibration isolator is obtained by using the multiple scales method and further verified by numerical simulation. Multi-valued responses, jump phenomenon and frequency island could coexist and their stabilities are analysed. Then, the effects of feedback gain and time delay on the frequency response are studied. The jump avoidance condition is obtained with the purpose of eliminating the adverse effects of excitation frequency fluctuation. Finally, the force transmissibility is defined to evaluate the isolation performance of the controlled HSLDS vibration isolator. The results show that with feedback parameters properly designed, such feedback control can play the role of damping force and the controlled HSLDS vibration isolator outperforms the passive counterpart.