Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence

modelling and experimental verification

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Experimental studies and mathematical modelling have been carried out for a nearly symmetrical piecewise linear oscillator to examine the bifurcation scenarios close to grazing. Higher period responses are found after grazing, although the period adding windows predicted as a generic feature of one-sided impacting systems are not observed. It appears that the presence of the second high stiffness spring stabilises additional periodic orbits. The global solution for a piecewise smooth model is developed by stitching locally valid maps. For the symmetrical case the highest period of response is three, if asymmetry in the gap and/or stiffness is introduced then higher periodic orbits are observed. Only small asymmetries are required to achieve a good correspondence with experiments. Further examination shows that many attractors are not stable to even small changes in the symmetry of the system.

Original languageEnglish
Pages (from-to)225-238
Number of pages13
JournalNonlinear Dynamics
Volume46
Issue number3
DOIs
Publication statusPublished - Nov 2006

Keywords

  • piecewise linear oscillator
  • experimental studies
  • clearance
  • asymmetry
  • excited oscillator
  • impact oscillator
  • restoring force
  • bifurcation
  • chaos
  • driven
  • system
  • rotor

Cite this

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title = "Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: modelling and experimental verification",
abstract = "Experimental studies and mathematical modelling have been carried out for a nearly symmetrical piecewise linear oscillator to examine the bifurcation scenarios close to grazing. Higher period responses are found after grazing, although the period adding windows predicted as a generic feature of one-sided impacting systems are not observed. It appears that the presence of the second high stiffness spring stabilises additional periodic orbits. The global solution for a piecewise smooth model is developed by stitching locally valid maps. For the symmetrical case the highest period of response is three, if asymmetry in the gap and/or stiffness is introduced then higher periodic orbits are observed. Only small asymmetries are required to achieve a good correspondence with experiments. Further examination shows that many attractors are not stable to even small changes in the symmetry of the system.",
keywords = "piecewise linear oscillator, experimental studies, clearance, asymmetry, excited oscillator, impact oscillator, restoring force, bifurcation, chaos, driven, system, rotor",
author = "James Ing and Ekaterina Pavlovskaia and Marian Wiercigroch",
year = "2006",
month = "11",
doi = "10.1007/s11071-006-9045-9",
language = "English",
volume = "46",
pages = "225--238",
journal = "Nonlinear Dynamics",
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publisher = "Springer",
number = "3",

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TY - JOUR

T1 - Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence

T2 - modelling and experimental verification

AU - Ing, James

AU - Pavlovskaia, Ekaterina

AU - Wiercigroch, Marian

PY - 2006/11

Y1 - 2006/11

N2 - Experimental studies and mathematical modelling have been carried out for a nearly symmetrical piecewise linear oscillator to examine the bifurcation scenarios close to grazing. Higher period responses are found after grazing, although the period adding windows predicted as a generic feature of one-sided impacting systems are not observed. It appears that the presence of the second high stiffness spring stabilises additional periodic orbits. The global solution for a piecewise smooth model is developed by stitching locally valid maps. For the symmetrical case the highest period of response is three, if asymmetry in the gap and/or stiffness is introduced then higher periodic orbits are observed. Only small asymmetries are required to achieve a good correspondence with experiments. Further examination shows that many attractors are not stable to even small changes in the symmetry of the system.

AB - Experimental studies and mathematical modelling have been carried out for a nearly symmetrical piecewise linear oscillator to examine the bifurcation scenarios close to grazing. Higher period responses are found after grazing, although the period adding windows predicted as a generic feature of one-sided impacting systems are not observed. It appears that the presence of the second high stiffness spring stabilises additional periodic orbits. The global solution for a piecewise smooth model is developed by stitching locally valid maps. For the symmetrical case the highest period of response is three, if asymmetry in the gap and/or stiffness is introduced then higher periodic orbits are observed. Only small asymmetries are required to achieve a good correspondence with experiments. Further examination shows that many attractors are not stable to even small changes in the symmetry of the system.

KW - piecewise linear oscillator

KW - experimental studies

KW - clearance

KW - asymmetry

KW - excited oscillator

KW - impact oscillator

KW - restoring force

KW - bifurcation

KW - chaos

KW - driven

KW - system

KW - rotor

U2 - 10.1007/s11071-006-9045-9

DO - 10.1007/s11071-006-9045-9

M3 - Article

VL - 46

SP - 225

EP - 238

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

ER -