Chinese Journal of Theoretical and Applied Mechani ›› 2008, Vol. 40 ›› Issue (1): 98-106.DOI: 10.6052/0459-1879-2008-1-2007-078

• Research paper • Previous Articles     Next Articles

Mechanism analysis of delayed nonlinear vibration absorber

Yanying Zhao Jian Xu   

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
  • Received:2007-02-06 Revised:2007-09-26 Online:2008-01-25 Published:2007-12-25

Abstract: In a two-degree-of-freedom system with delayed nonlinear dynamical vibration absorber, the method of multiple scales is employed to study its performance of vibration suppression. The amplitude-delay response curves of the primary system are obtained. The results show that for the delayed nonlinear dynamical vibration absorber, the gain and the delay may be tuned to control the vibration of the primary system. With the delay varying for a fixed gain, it is easy to see that the vibration can be suppressed at some values of the delay under the conditions of the system is stable. The ``maximum vibration suppression point'' may be predicted at which the amplitude of the primary system is the minimum for a fixed gain. For different values of the gain, the amplitudes of the primary system are different at their ``maximum vibration suppression point''. Correspondingly, the optimum values of the gain and the delay may be obtained to suppress the amplitude of the primary system to a minimum. The results of this paper show that the vibration of the primary system can be suppressed about 90{\%} when the optimum values of the gain and the delay are obtained by comparing with the nonlinear dynamical vibration absorber. All the analytical predictions of this paper are in good agreement with the numerical simulation.

Key words: nonlinear, feedback, delayed nonlinear dynamical vibration absorber, delayed linear dynamical vibration absorber