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Bifurcation analysis of a piecewise-linear impact oscillator with drift

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An Erratum to this article was published on 02 April 2014

Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. Facultad de Ciencias Naturales y Matemáticas, Escuela Superior Politécnica del Litoral, P.O. Box 09-01-5863, Guayaquil, Ecuador

    Joseph Páez Chávez

  2. Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Joseph Páez Chávez, Ekaterina Pavlovskaia & Marian Wiercigroch

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  1. Joseph Páez Chávez
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  2. Ekaterina Pavlovskaia
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  3. Marian Wiercigroch
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Correspondence to Joseph Páez Chávez.

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Páez Chávez, J., Pavlovskaia, E. & Wiercigroch, M. Bifurcation analysis of a piecewise-linear impact oscillator with drift. Nonlinear Dyn 77, 213–227 (2014). https://doi.org/10.1007/s11071-014-1285-5

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