On the Analysis of Chatter in Mechanical Systems with Impacts

Harry Dankowicz, Erika Fotsch

Research output: Contribution to journalConference articlepeer-review


In rigid-body mechanics, models that capture collisional contact as an instantaneous exchange of momentum may exhibit dynamics that include infinite sequences of impacts accumulating in finite time to a state of persistent contact, often referred to as chatter. In this paper, we review theoretical tools for the analysis of transient and steady-state behavior in the vicinity of critical periodic orbits for which chatter terminates at a point corresponding to the imminent release from persistent contact, and illustrate the application of this theory to a simplified model of a mechanical pressure relief valve. A general theory for single-degree-of-freedom impact oscillators, previously described in an unpublished manuscript by Nordmark and Kisitu1, is shown to yield both qualitative and quantitative agreement with model simulation results. The predicted bifurcation structure shows that the border orbit unfolds supercritically into a universal cascade of local attractors with nontrivial scaling relationships.

Original languageEnglish (US)
Pages (from-to)18-25
Number of pages8
JournalProcedia IUTAM
StatePublished - 2017
Event24th International Congress of Theoretical and Applied Mechanics 2016 - Montreal, Canada
Duration: Aug 22 2016Aug 24 2016


  • Accumulation of impacts
  • Bifurcation analysis
  • One-dimensional map
  • Pressure relief valve
  • Universal cascade

ASJC Scopus subject areas

  • Mechanical Engineering


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