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Bifurcation Tree of Period-1 Motion to Chaos in a Pendulum With Periodic Excitation

[+] Author Affiliations
Yu Guo

Midwestern State University, Wichita Falls, TX

Albert C. J. Luo

Southern Illinois University Edwardsville, Edwardsville, IL

Paper No. DETC2016-59331, pp. V006T09A067; 9 pages
doi:10.1115/DETC2016-59331
From:
  • ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Charlotte, North Carolina, USA, August 21–24, 2016
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5018-3
  • Copyright © 2016 by ASME

abstract

In this paper, the bifurcation trees of period-1 motions to chaos are presented in a periodically driven pendulum. Discrete implicit maps are obtained through a mid-time scheme. Using these discrete maps, mapping structures are developed to describe different types of motions. Analytical bifurcation trees of periodic motions to chaos are obtained through the nonlinear algebraic equations of such implicit maps. Eigenvalue analysis is carried out for stability and bifurcation analysis of the periodic motions. Finally, numerical simulation results of various periodic motions are illustrated in verification to the analytical prediction. Harmonic amplitude characteristics are also be presented.

Copyright © 2016 by ASME

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