Chinese Journal of Theoretical and Applied Mechani ›› 2013, Vol. 45 ›› Issue (5): 755-762.DOI: 10.6052/0459-1879-13-017

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Shen Yongjun1, Zhao Yongxiang1,2, Tian Jiayu1, Yang Shaopu1   

  1. 1. Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
    2. China Railway 24th Bureau Group Anhui Engineering Company Limited, Hefei 230011, China
  • Received:2013-01-21 Revised:2013-02-28 Online:2013-09-23 Published:2013-10-23
  • Supported by:

    The project was supported by the National Natural Science Foundation of China (11072158, 10932006), the Science Fund for Distinguished Young Scholars of Hebei Province, China (E2010002047), the Program for New Century Excellent Talents (NCET-11-0936) and Innovative Research Team in University of Ministry of Education of China (IRT0971).


The dynamical analysis on a single degree-of-freedom semi-active suspension system with time delay is completed in this paper, where the limited relative displacement control is adopted in this system. The first-order approximately analytical solution is obtained by the averaging method, and the stability condition is set up based on Lyapunov theory. The results show that the steady-state amplitude of the approximate solution and the stability conditions are all periodic functions of time delay, and have the same period as the excitation one. Through the comparison of the amplitude-frequency curves obtained by the approximate solution and the numerical method, the correctness and satisfactory precision of the approximate solution are verified. The chattering phenomenon of semi-active control existing in high frequency is also explained. Moreover, the passive suspension is also researched analytically and compared with the semi-active one, and the results confirm the superiority of semi-active suspension. Finally, the effects of some key system parameters on control performance, including the control clearance, time delay and minimum damping ratio, are discussed.

Key words:

semi-active suspension|time delay|averaging method|vibration control

CLC Number: