Study on nonlinear dynamics and semi-active control of a quasi-zero-stiffness magnetorheological damping floating slab track system

Based on the traditional steel spring floating slab track, a quasi-zero-stiffness magnetorheological damping (MRD) track system is constructed by introducing the horizontal spring negative stiffness mechanism and MRD. First, the mechanical model of the system is established, the static analysis is done, and the effects of each parameter on the nonlinear behaviors of the system are numerically analyzed. Then, the dynamics equation of system is set up; subsequently, the amplitude–frequency response equation is obtained by means of the average method. The influences of different parameters on the dynamic response of the system are analyzed. Finally, three semi-active control methods, PID control, fuzzy-PID control and frequency + fuzzy-PID control, are designed, and then, the vibration reduction effect of each control method is simulated. The results present that the proposed system has good vibration isolation effect in low frequency region and a high bearing capacity. The larger nonlinear coefficient, vertical damping ratio, horizontal damping ratio, Coulomb damping force, viscous damping ratio and input current are beneficial to improve the low frequency vibration of the system. By adopting the frequency + fuzzy-PID control method, the peak of force transmissibility and the initial vibration isolation frequency are reduced by 61.9 and 14.2%, respectively, compared with that of the uncontrolled system. The proposed system presents good vibration isolation performance outside the frequency range of 1–3 Hz.