Nonlinear Dynamics

, Volume 77, Issue 1–2, pp 213–227 | Cite as

Bifurcation analysis of a piecewise-linear impact oscillator with drift

  • Joseph Páez Chávez
  • Ekaterina Pavlovskaia
  • Marian Wiercigroch
Original Paper


We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation analysis, we use the computational package TC-HAT, a toolbox of AUTO 97 for numerical continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems (Thota and Dankowicz, SIAM J Appl Dyn Syst 7(4):1283–322, 2008) The study reveals the presence of co-dimension-1 and -2 bifurcations, including fold, period-doubling, grazing, flip-grazing, fold-grazing and double grazing bifurcations of limit cycles, as well as hysteretic effects and chaotic behaviour. Special attention is given to the study of the rate of drift, and how it is affected by the control parameters.


Drifting impact oscillator Non-smooth dynamical system Bifurcation analysis Numerical continuation TC-HAT Resonance enhanced drilling 



The authors wish to thank Scottish Enterprise for the financial support to this research.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Joseph Páez Chávez
    • 1
    • 2
  • Ekaterina Pavlovskaia
    • 2
  • Marian Wiercigroch
    • 2
  1. 1.Facultad de Ciencias Naturales y MatemáticasEscuela Superior Politécnica del LitoralGuayaquilEcuador
  2. 2.Centre for Applied Dynamics Research, School of EngineeringUniversity of AberdeenAberdeenUK

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