Advertisement

Meccanica

, Volume 41, Issue 3, pp 269–282 | Cite as

Phase Shift Adjustment for Harmonic Balance Method Applied to Vibro-impact Systems

  • Ko-Choong Woo
  • Albert A. Rodger
  • Richard D. Neilson
  • Marian Wiercigroch
Article

Abstract

This work addresses the phase shift adjustment between the external forcing and the responses for strongly non-linear dynamic systems calculated by Harmonic Balance Method (HBM). The HBM offers fast and robust solutions for strongly non-linear systems operating in periodic regimes, however, the phase information when applying the harmonic balance method is lost. In this paper, a practical scheme for calculating the phase difference for a piecewise oscillator mimicking a vibro-impact system is proposed.

Keywords

Phase shift Vibro-impact system Harmonic balance method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Szemplinska-Stupnicka, W. 1978‘The generalised harmonic balance method for determining the combination resonance in the parametric systems’J. Sound Vib.58347361MATHADSGoogle Scholar
  2. 2.
    Lau, S.L., Zhang, W.S. 1992‘Nonlinear vibrations of piecewise-linear systems by incremental harmonic balance’J. Appl. Mech. Trans. ASME59153160MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Woo, K.-C., Rodger, A.A., Neilson, R.D., Wiercigroch, M. 2000‘Application of the harmonic balance method to ground moling machines operating in periodic regimes’Chaos Soliton. Fract.1125152525MATHCrossRefGoogle Scholar
  4. 4.
    Bishop, S.R. 1994Philos. Trans. Roy. Soc. Ser. A347345448ADSGoogle Scholar
  5. 5.
    Bishop, S.R., Impact Oscillators Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences 347 (1683): 347–351 May 16 1994.Google Scholar
  6. 6.
    Foale, S. 1683‘Analytical determination of bifurcations in an impact oscillator’Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347353364May 16 1994Google Scholar
  7. 7.
    Budd, C., Dux, F. 1683‘Chattering and related behaviour in impact oscillators’Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347365389May 16 1994Google Scholar
  8. 8.
    Cusumano, J.P., Sharkady, M.T., Kimble, B.W. 1683‘Experimental measurements of dimensionality and spatial coherence in the dynamics of a flexible-beam impact oscillator’Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347421438May 16 1994Google Scholar
  9. 9.
    Hogan, S.J. 1683‘Rigid block dynamics confined between side-walls’Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347411419May 16 1994Google Scholar
  10. 10.
    Shaw, S.W., Haddow, A.G., Hsieh, S.-R. 1683‘Properties of cross-well chaos in an impacting’ systemPhilosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347391410May 16 1994Google Scholar
  11. 11.
    Stensson, A., Nordmark, A.B. 1683‘Experimental investigation of some consequences of low-velocity impacts in the chaotic dynamics of a mechanical system’Philosophical transactions of the royal society of London series A-Mathematical physical and Engineering Sciences347439448May 16 1994Google Scholar
  12. 12.
    Bishop, S.R., Wagg, D.J., Xu, D. 1998‘Use of control to maintain period-1 motions during or wind-down operations of an impacting driven beam’Chaos Soliton. Fract.9261269CrossRefGoogle Scholar
  13. 13.
    Natsiavas, S. 1993‘Dynamics of multiple-degree-of-freedom oscillators with colliding components’J. Sound Vib.165439453MATHMathSciNetCrossRefADSGoogle Scholar
  14. 14.
    Peterka, F., Vacik, J. 1992‘Transition to chaotic motion in mechanical systems with impacts’J. Sound Vib.15495115MATHMathSciNetCrossRefADSGoogle Scholar
  15. 15.
    Hagedorn, P., Nonlinear Oscillations, Oxford University Press, 1978.Google Scholar
  16. 16.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P., Numerical Recipes in C++, Cambridge University Press, 2002.Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Ko-Choong Woo
    • 1
  • Albert A. Rodger
    • 2
  • Richard D. Neilson
    • 2
  • Marian Wiercigroch
    • 2
  1. 1.Division of EngineeringThe University of Nottingham Malaysia CampusKuala LumpurMalaysia
  2. 2.Centre for Applied Dynamics Research, School of Engineering and Physical SciencesUniversity of Aberdeen, King’s CollegeAberdeenUK

Personalised recommendations