Modelling of vibro-impact system driven by beat frequency

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A mathematical model of vibro-impact system accounting for oscillatory and progressive motion, and capable of transferring a high-frequency low-amplitude excitation into low-frequency high-amplitude response is developed. A special beat frequency kinematic excitation was used, which has two distinctive features:

(i) the low-frequency modulated excitation is tuned to the natural frequency of the oscillating system, and (ii) the excitation is asymmetric. The model considers also visco-elastic properties of the media.

It is demonstrated that this mechanism allows to overcome the resistance force of the media and to move forward. Several different ways to achieve a steady progression without supplying additional energy are explored, however, in all these cases progression rates are relatively low. A significant increase of progression rates is only possible by controlling the motion of the system. A simple control strategy enhancing progression rates substantially is proposed and implemented. (C) 2003 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)623-641
Number of pages18
JournalInternational Journal of Mechanical Sciences
Issue number4
Publication statusPublished - Apr 2003

Bibliographical note

The authors would like to acknowledge the financial support from EPSRC under the grant GR/N16341.


  • vibro-impact system
  • beat frequency excitation
  • drift
  • dry friction
  • control
  • nonlinear oscillator
  • dry friction model
  • rate prediction
  • oscillator
  • dynamics


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