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

Joseph Paez Chavez; Marian Wiercigroch

doi:10.1016/j.cnsns.2012.12.007

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

Joseph Paez Chavez^*, Marian Wiercigroch

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

74 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 language	English
Pages (from-to)	2571-2580
Number of pages	10
Journal	Communications in Nonlinear Science & Numerical Simulation
Volume	18
Issue number	9
Early online date	2 Jan 2013
DOIs	https://doi.org/10.1016/j.cnsns.2012.12.007
Publication status	Published - Sept 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

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10.1016/j.cnsns.2012.12.007

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title = "Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model",

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.",

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

author = "{Paez Chavez}, Joseph and Marian Wiercigroch",

year = "2013",

month = sep,

doi = "10.1016/j.cnsns.2012.12.007",

language = "English",

volume = "18",

pages = "2571--2580",

journal = "Communications in Nonlinear Science & Numerical Simulation",

issn = "1007-5704",

publisher = "ELSEVIER SCIENCE BV",

number = "9",

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TY - JOUR

T1 - Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model

AU - Paez Chavez, Joseph

AU - Wiercigroch, Marian

PY - 2013/9

Y1 - 2013/9

N2 - 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.

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.

KW - Jeffcott rotor

KW - non-smooth dynamical system

KW - TC-HAT

KW - numerical continuation

KW - grazing

KW - hysteresis

KW - grazing bifurcation

KW - stability analysis

KW - dynamical-systems

KW - stator systems

KW - chaos

KW - continuation

KW - rubs

U2 - 10.1016/j.cnsns.2012.12.007

DO - 10.1016/j.cnsns.2012.12.007

M3 - Article

SN - 1007-5704

VL - 18

SP - 2571

EP - 2580

JO - Communications in Nonlinear Science & Numerical Simulation

JF - Communications in Nonlinear Science & Numerical Simulation

IS - 9

ER -

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

Abstract

Keywords

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