Nonlinear transition dynamics in a time-delayed vibration isolator under combined harmonic and stochastic excitations

Abstract

Based on the quasi-zero stiffness vibration isolation (QZS-VI) system, nonlinear transition dynamics have been investigated coupled with both time-delayed displacement and velocity feedbacks. Using a delayed nonlinear Langevin approach, we discuss a new mechanism for the transition of a vibration isolator in which the energy originates from harmonic and noise excitations. For this stochastic process, the effective displacement potential, stationary probability density function and the escape ratio are obtained. We investigate a variety of noise-induced behaviors affecting the transitions between system equilibria states. The results indicate that the phenomena of transition, resonant activation and delay-enhanced stability may emerge in the QZS-VI system. Moreover, we also show that the time delay, delay feedback intensities, and harmonic excitation play significant roles in the resonant activation and delay-enhanced stability phenomena. Finally, a quantitative measure for amplitude response has been carried out to evaluate the isolation performance of the controlled QZS-VI system. The results show that with properly designed feedback parameters, time delay and displacement feedback intensity can play the role of a damping force. This research provides instructive ideas on the application of the time-delayed control in practical engineering.