Chaotic Dynamics of the Partially Follower-Loaded Elastic Double Pendulum

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    Abstract

    The non-linear dynamics of the elastically restrained double pendulum, with non-conservative follower-type loading and linear damping, is re-examined with specific reference to the occurrence of chaotic motion. A local non-linear perturbation analysis is performed, showing that in three distinct regions of loading parameter space, small initial disturbances will result in, respectively, (1) static equilibrium solutions, (2) stable periodic motion, and (3) initially large changes in amplitude due to a destabilizing effect of both linear and non-linear forces. A global numerical analysis confirms the theoretical findings for regions (1) and (2), and shows that in region (3) almost all solutions are chaotic. It is suggested that chaos is triggered by a bifurcating cascade of large amplitude stable and unstable equilibrium points, which may be explored by orbits only when the zero-solution is destabilized by both linear and non-linear forces. Although heuristically based, this may be used as a practical and rather accurate predictive criterion for chaos to appear in the specific system.
    Copyright © 1995 Academic Press. All rights reserved.
    Original languageEnglish
    JournalJournal of Sound and Vibration
    Volume188
    Issue number3
    Pages (from-to)385-405
    ISSN0022-460X
    DOIs
    Publication statusPublished - 1995

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