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Chaotic Behavior in the Double Pendulum Under Parametric Resonance

[+] Author Affiliations
Rafael H. Avanço, Helio A. Navarro

University of São Paulo, São Carlos, Brazil

Airton Nabarrete, José M. Balthazar

Technological Institute of Aeronautics, São José dos Campos, Brazil

Angelo Marcelo Tusset

UTFPR, Ponta Grossa, Brazil

Paper No. IMECE2016-65711, pp. V04BT05A013; 9 pages
doi:10.1115/IMECE2016-65711
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 literature, the classic parametrically excited pendulum is vastly studied. It consists of a pendulum vertically displaced with a harmonic motion in the support while it oscillates. The chaos in this mechanism may appear depending on the frequency and amplitude of excitation in superharmonic and subharmonic resonance. The double pendulum is also well analyzed in literature, but not under parametric excitation. Therefore, this is the novelty in the present paper. The present analysis considers a double pendulum under a harmonic excitation following the same idea performed previously for a single pendulum. The results are obtained based on methods, such as, phase portraits, Poincaré sections and bifurcation diagrams. The 0–1 tests analyze the presence of chaos while the parameters are varied. The dimensionless parameters take into account the excitation frequency and amplitude as mentioned for the classic parametric pendulum. In this case, we have the particular characteristic that the two pendulums have the same length, the same mass and the same friction coefficient in the joints. The types of motion observed include fixed points, oscillations, rotations and chaos. Results also demonstrated that there was a self-synchronization between these pendulums in ideal excitation.

Copyright © 2016 by ASME
Topics: Resonance , Pendulums

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