Experimental study of impact oscillator with one-sided elastic constraint

James Ing, Ekaterina Pavlovskaia, Marian Wiercigroch, Soumitro Banerjee

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89 Citations (Scopus)

Abstract

In this paper, extensive experimental investigations of an impact oscillator with a one-sided elastic constraint are presented. Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excitation amplitude. The mass acceleration signal is used to effectively detect contacts with the secondary spring. The most typical recorded scenario is when a non-impacting periodic orbit bifurcates into an impacting one via grazing mechanism. The resulting orbit can be stable, but in many cases it loses stability through grazing. Following such an event, the evolution of the attractor is governed by a complex interplay between smooth and non-smooth bifurcations. In some cases, the occurrence of coexisting attractors is manifested through discontinuous transition from one orbit to another through boundary crisis. The stability of non-impacting and impacting period-1 orbits is then studied using a newly proposed experimental procedure. The results are compared with the predictions obtained from standard theoretical stability analysis and a good correspondence between them is shown for different stiffness ratios. A mathematical model of a damped impact oscillator with one-sided elastic constraint is used in the theoretical studies.

Original languageEnglish
Pages (from-to)679-705
Number of pages26
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume366
Issue number1866
Early online date18 Oct 2007
DOIs
Publication statusPublished - 13 Mar 2008

Keywords

  • impact oscillator
  • experimental chaos
  • grazing
  • stability of limit cycles
  • piecewise-linear-oscillator
  • grazing-incidence
  • border-collision
  • dynamics
  • bifurcations
  • systems
  • motions
  • chaos
  • verification
  • behavior

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