TIME-DELAYED SEMI-ACTIVE CONTROL OF DAMPING SYSTEM WITH FRACTIONAL-ORDER BINGHAM MODEL

On the issues of time delay in the semi-active control system with magnetorheological fluid damper, the controllable time-delay variable is introduced into the switching conditions of semi-active control strategy. The influences of time delay in the switching conditions of sky-hook damping control system are studied. The vibration characteristics of a linear stiffness system under foundation excitation, with magnetorheological fluid damper based on fractional-order Bingham model, are analyzed by the approximate analytical method. The analytical solutions of the primary resonance of the semi-active control system with time delay are obtained through the averaging method, and the stability conditions of the steady-state solution of the system are demonstrated according to Lyapunov theory. The amplitude-frequency responses of analytical solutions show a good correlation with the numerical solutions close-by the resonance frequency, which validates the accuracy and efficiency of the analytical solutions. Furthermore, the influences of time delay on the amplitude-frequency responses of the system at fixed excitation frequency, the primary resonance amplitude responses and the corresponding resonance frequencies changed with different time-delay values are investigated by using the approximate analytical solution. The results suggest that the amplitude responses of the semi-active control system in a small time-delay range is lower than the control system without time delay near the excitation frequency corresponding to the resonance peak, and there is an optimal time delay making a significant reduction of the amplitude of the primary resonance peak. However, the vibration of the control system would be worsened with larger time delays, leading to the flutter of the control system at high frequencies. The principles of time delay introducing to linear stiffness system with fractional-order Bingham model under semi-active control of sky-hook damping are determined. It provides a reference of selecting a feasible time delay in semi-active damping control vibration system.