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Experimental study of regular and chaotic transients in a non-smooth system

Publication ,  Journal Article
George, C; Virgin, LN; Witelski, T
Published in: International Journal of Non-Linear Mechanics
May 1, 2016

This paper focuses on thoroughly exploring the finite-time transient behaviors occurring in a periodically driven non-smooth dynamical system. Prior to settling down into a long-term behavior, such as a periodic forced oscillation, or a chaotic attractor, responses may exhibit a variety of transient behaviors involving regular dynamics, co-existing attractors, and super-persistent chaotic transients. A simple and fundamental impacting mechanical system is used to demonstrate generic transient behavior in an experimental setting for a single degree of freedom non-smooth mechanical oscillator. Specifically, we consider a horizontally driven rigid-arm pendulum system that impacts an inclined rigid barrier. The forcing frequency of the horizontal oscillations is used as a bifurcation parameter. An important feature of this study is the systematic generation of generic experimental initial conditions, allowing a more thorough investigation of basins of attraction when multiple attractors are present. This approach also yields a perspective on some sensitive features associated with grazing bifurcations. In particular, super-persistent chaotic transients lasting much longer than the conventional settling time (associated with linear viscous damping) are characterized and distinguished from regular dynamics for the first time in an experimental mechanical system.

Duke Scholars

Published In

International Journal of Non-Linear Mechanics

DOI

ISSN

0020-7462

Publication Date

May 1, 2016

Volume

81

Start / End Page

55 / 64

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

Citation

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George, C., Virgin, L. N., & Witelski, T. (2016). Experimental study of regular and chaotic transients in a non-smooth system. International Journal of Non-Linear Mechanics, 81, 55–64. https://doi.org/10.1016/j.ijnonlinmec.2015.12.006
George, C., L. N. Virgin, and T. Witelski. “Experimental study of regular and chaotic transients in a non-smooth system.” International Journal of Non-Linear Mechanics 81 (May 1, 2016): 55–64. https://doi.org/10.1016/j.ijnonlinmec.2015.12.006.
George C, Virgin LN, Witelski T. Experimental study of regular and chaotic transients in a non-smooth system. International Journal of Non-Linear Mechanics. 2016 May 1;81:55–64.
George, C., et al. “Experimental study of regular and chaotic transients in a non-smooth system.” International Journal of Non-Linear Mechanics, vol. 81, May 2016, pp. 55–64. Scopus, doi:10.1016/j.ijnonlinmec.2015.12.006.
George C, Virgin LN, Witelski T. Experimental study of regular and chaotic transients in a non-smooth system. International Journal of Non-Linear Mechanics. 2016 May 1;81:55–64.
Journal cover image

Published In

International Journal of Non-Linear Mechanics

DOI

ISSN

0020-7462

Publication Date

May 1, 2016

Volume

81

Start / End Page

55 / 64

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4901 Applied mathematics
  • 4017 Mechanical engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics