高速列车非线性减振系统联合时滞反馈控制

本文主要研究列车运行过程中垂直方向上的非线性振动特性,以及车体振动的时滞反馈主动控制。首先建立二自由度非线性悬挂系统模型，得到系统的运动微分方程，利用模态分析进行解耦，再结合多尺度法求解方程组的近似解析表达式。然后以1：3内共振为例，通过6组外激励和时滞的情况对比研究，分析不同共振频率的外激励项和不同阶数的时滞项对车体振幅的影响。最后通过数值模拟来验证解析结果。研究结果表明,对含有时滞项的非线性振动系统，多频的外激励使车体振幅最大。线性时滞项系统的稳定性比非线性时滞项系统稳定性高，通过调节合理的时滞项，对车体能起到很好的减振作用，车体的减振幅度同被动系统相比最高可以达到68.87%。与之相对的，如果其参数选择不当，车体的振幅将会增大，振动变得更加恶劣。本文的研究结果有助于列车悬挂系统的振动进一步完善，同时也为时滞减振器的设计和研发提供一个新的思考方向。

Combined Delayed Feedback Control Analysis of Railway High-speed Train in Nonlinear Vibration System

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.