Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics

A. D. Shaw*, A. R. Champneys, M. I. Friswell

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)
297 Downloads (Pure)


Sudden onset of violent chattering or whirling rotor-stator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronization condition previously reported for a single disc system. The synchronization formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the damping is sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further, secondary bifurcations can also occur within each family, altering the nature of the response and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice.

Original languageEnglish
Article number20160303
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2192
Publication statusPublished - 1 Aug 2016

Structured keywords

  • Engineering Mathematics Research Group


  • Bifurcation
  • Internal resonance
  • Rotating machines
  • Stator contact
  • Whirl


Dive into the research topics of 'Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics'. Together they form a unique fingerprint.

Cite this