Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model

Joseph Paez Chavez, Marian Wiercigroch

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived. (C) 2012 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)2571-2580
Number of pages10
JournalCommunications in Nonlinear Science & Numerical Simulation
Volume18
Issue number9
Early online date2 Jan 2013
DOIs
Publication statusPublished - Sep 2013

Keywords

  • Jeffcott rotor
  • non-smooth dynamical system
  • TC-HAT
  • numerical continuation
  • grazing
  • hysteresis
  • grazing bifurcation
  • stability analysis
  • dynamical-systems
  • stator systems
  • chaos
  • continuation
  • rubs

Cite this

Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model. / Paez Chavez, Joseph; Wiercigroch, Marian.

In: Communications in Nonlinear Science & Numerical Simulation, Vol. 18, No. 9, 09.2013, p. 2571-2580.

Research output: Contribution to journalArticle

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AB - We investigate complex dynamics occurring in a non-smooth model of a Jeffcott rotor with a bearing clearance. A bifurcation analysis of the rotor system is carried out by means of the software TC-HAT [25], a toolbox of AUTO 97 [6] allowing path-following and detection of bifurcations of periodic trajectories of non-smooth dynamical systems. The study reveals a rich variety of dynamics, which includes grazing-induced fold and period-doubling bifurcations, as well as hysteresis loops produced by a cusp singularity. Furthermore, an analytical expression predicting grazing incidences is derived. (C) 2012 Elsevier B.V. All rights reserved.

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KW - numerical continuation

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KW - hysteresis

KW - grazing bifurcation

KW - stability analysis

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KW - stator systems

KW - chaos

KW - continuation

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