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Analytical Bifurcation Trees of a Periodically Excited Pendulum

[+] Author Affiliations
Yu Guo

Midwestern State University, Wichita Falls, TX

Albert C. J. Luo

Southern Illinois University Edwardsville, Edwardsville, IL

Paper No. IMECE2016-65916, pp. V04BT05A016; 9 pages
doi:10.1115/IMECE2016-65916
From:
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5055-8
  • Copyright © 2016 by ASME

abstract

In this paper, the bifurcation trees of a periodically excited pendulum are investigated. Implicit discrete maps for such a pendulum are developed to construct discrete mapping structures. Bifurcation trees of the corresponding periodic motions are predicted semi-analytically through the discrete mapping structure. The corresponding stability and bifurcation analysis are carried out through eigenvalue analysis. Finally, numerical illustrations of various periodic motions are given to verify the analytical prediction. The accurate periodic motions in the periodically forced pendulum are predicted for the first time through the implicit mapping systems, and the corresponding bifurcation trees of periodic motion to chaos are obtained.

Copyright © 2016 by ASME

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