Global dynamics of a harmonically excited oscillator with a play: Numerical studies

Antonio S. E. Chong, Yue Yuan, Ekaterina Pavlovskaia, Marian Wiercigroch

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27 Citations (Scopus)
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In this paper a harmonically excited linear oscillator with a play is investigated. Direct numerical simulation and numerical continuation techniques were employed to study the system behaviour. To conduct the numerical analysis, the system differential equations were transformed into the autonomous form
and were then solved using our newly developed in-house Matlab-based computational suite ABESPOL [1]. The results are presented in form of trajectories and Poincaré maps on the phase plane, bifurcation diagrams and basins of attraction. The bifurcation analysis was supported by a path following method. The influence of each system parameter (except gap) on the system dynamics was studied in detail. The bifurcations known as interior crisis and boundary crisis were observed and discussed in this work. Notably, the parameter regions where various types of grazing induced bifurcations occurred were detected and investigated.
Original languageEnglish
Pages (from-to)98-108
Number of pages11
JournalInternational Journal of Non-Linear Mechanics
Early online date19 Mar 2017
Publication statusPublished - Sept 2017

Bibliographical note

This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Politécnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.


  • Non-smooth systems
  • Backlash
  • Clearance
  • Impacts
  • Numerical simulation
  • Path following
  • Bifurcation analysis


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