Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (5): 1466-1475.DOI: 10.6052/0459-1879-19-154

• Dynamics, Vibration and Control • Previous Articles     Next Articles


Xing Zikang*,Shen Yongjun*2)(),Li Xianghong**   

  1. * Department of Mechanical Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
    ? State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University, Shijiazhuang 050043,China
    ** Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China
  • Received:2019-06-17 Online:2019-09-18 Published:2019-09-30
  • Contact: Shen Yongjun


In grounded dynamic vibration absorbers (DVA), the changing tendencies of the fixed-point amplitude with the natural frequency ratio are not monotonous. Thus, the results obtained by optimizing this type DVA based on classical fixed-point theory may be the local optimum parameters. The primary system can obtain smaller amplitudes when selecting other parameters. The optimization of grounded type DVAs are worthy to further study. In addition, the damper of the DVA inevitably has some elasticity. Accordingly, a grounded three-element DVA is studied by analyzing the influence of system parameters on fixed-point positions and maximum amplitude in this paper. The local optimum parameters of the DVA are obtained and the performance is investigated. Firstly, the motion differential equation of the system is established, and the amplitude amplification factor of the primary system is obtained. It is found that there are three fixed-points independent of damping on the amplitude-frequency response curve. In most cases, by optimizing the damping ratio, the tendency of the larger of the fixed point changing with the system parameters can represent the tendency of the maximum amplitude changing with the system parameters. Therefore, the expressions of the fixed-point are obtained by using the Shengjin's formula. For more accuracy, the numerical algorithm is used to obtain the relationship between the maximum amplitude and the system parameters, and it is found that there are local optimum parameters in the system. Finally, in order to obtain the local optimum parameters the grounded three-element DVA is compared with the grounded DVA. The study shows that the local optimum parameters of the two DVAs are the same except the stiffness ratio. When the natural frequency is smaller than local optimum frequency ratio, the maximum amplitude of the primary system of the grounded three-element DVA model is much smaller than that of the grounded DVA.

Key words: vibration control, dynamic vibration absorber, fixed-point theory, parameters optimization

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