Chinese Journal of Theoretical and Applied Mechanics ›› 2019, Vol. 51 ›› Issue (3): 894-903.DOI: 10.6052/0459-1879-18-375

• Dynamics, Vibration and Control • Previous Articles     Next Articles

PARAMETERS OPTIMIZATION OF A DYNAMIC VIBRATION ABSORBER WITH AMPLIFYING MECHANISM AND NEGATIVE STIFFNESS1)

Zhaoyang Xing, Yongjun Shen2)(), Haijun Xing, Shaopu Yang   

  1. Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
  • Received:2018-11-09 Online:2019-05-18 Published:2019-05-28
  • Contact: Yongjun Shen

Abstract:

Mechanical vibration is detrimental in most engineering situations, and it may not only generate noise but also reduce the operational accuracy and working life of the equipment. It is generally difficult for vibration absorption and isolation systems with positive stiffness characteristics to achieve satisfactory performance, which becomes noticeable especially in low-frequency vibration control systems. Amplifying mechanism and negative stiffness element both show good performance in the field of vibration control, but the dynamic vibration absorber with both amplifying mechanism and negative stiffness element is rarely studied. Based on the Voigt type dynamic vibration absorber, a dynamic vibration absorber with negative stiffness element using amplifying mechanism is presented, and the optimal system parameters are studied in detail. Firstly, the differential equation of motion is established and the analytic solution of the system is obtained, and it is found that there are two fixed points independent of damping ratio in the amplitude-frequency curves of the primary system. The optimal frequency ratio of the dynamic vibration absorber is obtained based on the fixed-point theory. According to the characteristics of negative stiffness, the optimal negative stiffness ratio is founded under the premise of ensuring the system stability. A simple method is used to derive the approximate optimal damping ratio of the system. The correctness of the analytical results is verified by the comparison with the results by numerical simulation. Compared with other dynamic vibration absorbers under harmonic and random excitations, it could be found that the model with optimal parameters in this paper can greatly reduce the resonance amplitude, broaden the vibration band, and lower the resonance frequency of the primary system. These results may provide theoretical basis for the optimal design of similar dynamic vibration absorbers.

Key words: vibration control, dynamic vibration absorber, amplifying mechanism, negative stiffness, fixed-point theory, parameter optimization

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