Dynamics and Realization of a Feedback-Controlled Nonlinear Isolator With Variable Time Delay

In this paper, time-delayed feedback (TD-FB) control is introduced for a nonlinear vibration isolator (NL-VI), and the isolation effectiveness features are investigated theoretically and experimentally. In the feedback control loop, compound control with constant and variable time delays is considered. First, a stability analysis is conducted to determine the range of control parameters for stable zero equilibrium without excitation. Next, the nonlinear resonance frequency and the nonlinear vibration attenuation are studied by the method of multiple scales (MMS) to demonstrate the mechanism of TD-FB control. The results of the nonlinear vibration performances show that large variable time delays can improve the vibration suppression. Additionally, the mechanism for the time delay is not only to tune the equivalent stiffness and damping but also to induce effective isolation bandgap at high frequency. Therefore, the variable time delay is assumed as the function of frequency to meet different requirements at different frequency bands. The relevant experiment verifies the improvement of designed variable time delay on isolation performances in different frequency bands. Due to the improvement of isolation performances by compound time delay feedback control on nonlinear systems, it can be applied in the fields of ships, flexible structure in aerospace and aviation.