Abstract:In the present paper, the nonlinear vibration characteristics and delayed feedback control of vertical vibration are studied in the railway high-speed train suspension system. Firstly, a two-degree-of-freedom nonlinear suspension system model is established, and the controlling differential equations are obtained. The modal analysis is used to decouple the equations, then multi-scales method is applied to obtain the approximate analytical solution of the equations. Secondly, the 1:3 internal resonance and primary external resonance are analyzed by six cases under the conditions of different parameters of external excitation and time delay. The effects of external excitation frequencies and time-delay items orders on the vehicle vibration of the amplitude of the body are analyzed. Finally, the analytical results are verified by numerical simulation. The results show that in the nonlinear vibration systems with delayed feedback control, the amplitude of the body is the largest for multiple frequencies external excitation. The linear delayed feedback control system is more stable than nonlinear delayed feedback control system. By adjusting the reasonable time-delay term, the vehicle vibration of the body can be effectively suppressed. The amplitude of the body can suppressed about 68.87% compared with the passive system. However, the amplitude of the body may be enlarged when the parameters are chosen in the other range of parameters, the vibration of the body will become more severe. The results of present paper may contribute to research of suspension vibration of the railway high speed train. It will provide a new research direction for the design and development of time-delay vibration absorber.