Bifurcation techniques for stiffness identification of an impact oscillator

Maolin Liao, James Ing*, Joseph Paez Chavez, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


In this paper, a change in stability (bifurcation) of a harmonically excited impact oscillator interacting with an elastic constraint is used to determine the stiffness of constraint. For this purpose, detailed one-and two-parameter bifurcation analyzes of the impacting system are carried out by means of experiments and numerical methods. This study reveals the presence of codimension-one bifurcations of limit cycles, such as grazing, period-doubling and fold bifurcations, as well as a cusp singularity and hysteretic effects. Particularly, the two-parameter continuation of the obtained codimension-one bifurcations (including both period-doubling and fold bifurcations) indicates a strong correlation between the stiffness of the impacted constraint and the frequency at which a certain bifurcation appear. The undertaken approach may prove to be useful for condition monitoring of dynamical systems by identifying mechanical properties through bifurcation analysis. The theoretical predictions for the impact oscillator are verified by a number of experimental observations. (C) 2016 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)19-31
Number of pages13
JournalCommunications in Nonlinear Science & Numerical Simulation
Early online date13 Feb 2016
Publication statusPublished - Dec 2016


  • impact oscillator
  • bifurcation analysis
  • stiffness identification
  • numerical continuation
  • piecewise-linear-oscillator
  • sided elastic constraint
  • dynamical-systems
  • grazing-incidence


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