Dynamics of a nearly symmetrical piecewise linear oscillator close to grazing incidence: modelling and experimental verification

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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

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