Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events

Karin Mora, Chris Budd

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

A new discontinuity-induced bifurcation, referred to as nonsmooth Hopftype bifurcation, observed in a nonautonomous impacting hybrid systems in ℝ4 is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmoothHopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient.

Original languageEnglish
Title of host publicationExtended Abstracts Spring 2016
Subtitle of host publicationNon Smooth Dynamics
EditorsA. Columbo, M. R. Jeffrey, J. T. Lazaro, J. M. Olm
PublisherBirkhäuser
Pages129-134
Number of pages6
ISBN (Electronic)978-3-319-55642-0
ISBN (Print)9783319556413
DOIs
Publication statusPublished - 2017

Publication series

NameTrends in Mathematics
Volume8

Fingerprint

Grazing Bifurcation
Friction
Bifurcation
Contact
Magnetic Bearing
Nonautonomous Systems
Friction Coefficient
Bifurcation Point
Hybrid Systems
Periodic Orbits
Instantaneous
Discontinuity
Damping
Rotating
Unstable
Scenarios
Motion
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Mora, K., & Budd, C. (2017). Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. In A. Columbo, M. R. Jeffrey, J. T. Lazaro, & J. M. Olm (Eds.), Extended Abstracts Spring 2016: Non Smooth Dynamics (pp. 129-134). (Trends in Mathematics; Vol. 8). Birkhäuser. https://doi.org/10.1007/978-3-319-55642-0_23

Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. / Mora, Karin; Budd, Chris.

Extended Abstracts Spring 2016: Non Smooth Dynamics. ed. / A. Columbo; M. R. Jeffrey; J. T. Lazaro; J. M. Olm. Birkhäuser, 2017. p. 129-134 (Trends in Mathematics; Vol. 8).

Research output: Chapter in Book/Report/Conference proceedingChapter

Mora, K & Budd, C 2017, Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. in A Columbo, MR Jeffrey, JT Lazaro & JM Olm (eds), Extended Abstracts Spring 2016: Non Smooth Dynamics. Trends in Mathematics, vol. 8, Birkhäuser, pp. 129-134. https://doi.org/10.1007/978-3-319-55642-0_23
Mora K, Budd C. Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. In Columbo A, Jeffrey MR, Lazaro JT, Olm JM, editors, Extended Abstracts Spring 2016: Non Smooth Dynamics. Birkhäuser. 2017. p. 129-134. (Trends in Mathematics). https://doi.org/10.1007/978-3-319-55642-0_23
Mora, Karin ; Budd, Chris. / Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events. Extended Abstracts Spring 2016: Non Smooth Dynamics. editor / A. Columbo ; M. R. Jeffrey ; J. T. Lazaro ; J. M. Olm. Birkhäuser, 2017. pp. 129-134 (Trends in Mathematics).
@inbook{b4113fb8075e4f978b6a295ab45e5806,
title = "Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events",
abstract = "A new discontinuity-induced bifurcation, referred to as nonsmooth Hopftype bifurcation, observed in a nonautonomous impacting hybrid systems in ℝ4 is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmoothHopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient.",
author = "Karin Mora and Chris Budd",
year = "2017",
doi = "10.1007/978-3-319-55642-0_23",
language = "English",
isbn = "9783319556413",
series = "Trends in Mathematics",
publisher = "Birkh{\"a}user",
pages = "129--134",
editor = "A. Columbo and Jeffrey, {M. R.} and Lazaro, {J. T.} and Olm, {J. M.}",
booktitle = "Extended Abstracts Spring 2016",
address = "Switzerland",

}

TY - CHAP

T1 - Non-smooth hopf-type and grazing bifurcations arising from impact/friction contact events

AU - Mora, Karin

AU - Budd, Chris

PY - 2017

Y1 - 2017

N2 - A new discontinuity-induced bifurcation, referred to as nonsmooth Hopftype bifurcation, observed in a nonautonomous impacting hybrid systems in ℝ4 is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmoothHopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient.

AB - A new discontinuity-induced bifurcation, referred to as nonsmooth Hopftype bifurcation, observed in a nonautonomous impacting hybrid systems in ℝ4 is presented. The system studied models the bouncing motion, repeated instantaneous impacts with friction, in rotating machines with magnetic bearing support. At the nonsmoothHopf-type bifurcation point a stable regular equilibrium and two unstable small amplitude 1-impact periodic orbits arise. The existence of this bifurcation scenario depends on a complex relationship between damping, the restitution, and the friction coefficient.

UR - http://www.scopus.com/inward/record.url?scp=85020249736&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1007/978-3-319-55642-0_23

U2 - 10.1007/978-3-319-55642-0_23

DO - 10.1007/978-3-319-55642-0_23

M3 - Chapter

SN - 9783319556413

T3 - Trends in Mathematics

SP - 129

EP - 134

BT - Extended Abstracts Spring 2016

A2 - Columbo, A.

A2 - Jeffrey, M. R.

A2 - Lazaro, J. T.

A2 - Olm, J. M.

PB - Birkhäuser

ER -