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.
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ASME 2016 International Mechanical Engineering Congress and Exposition
November 11–17, 2016
Phoenix, Arizona, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-5055-8
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Chaotic Behavior in the Double Pendulum Under Parametric Resonance Available to Purchase
Rafael H. Avanço,
Rafael H. Avanço
University of São Paulo, São Carlos, Brazil
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Helio A. Navarro,
Helio A. Navarro
University of São Paulo, São Carlos, Brazil
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Airton Nabarrete,
Airton Nabarrete
Technological Institute of Aeronautics, São José dos Campos, Brazil
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José M. Balthazar,
José M. Balthazar
Technological Institute of Aeronautics, São José dos Campos, Brazil
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Angelo Marcelo Tusset
Angelo Marcelo Tusset
UTFPR, Ponta Grossa, Brazil
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Rafael H. Avanço
University of São Paulo, São Carlos, Brazil
Helio A. Navarro
University of São Paulo, São Carlos, Brazil
Airton Nabarrete
Technological Institute of Aeronautics, São José dos Campos, Brazil
José M. Balthazar
Technological Institute of Aeronautics, São José dos Campos, Brazil
Angelo Marcelo Tusset
UTFPR, Ponta Grossa, Brazil
Paper No:
IMECE2016-65711, V04BT05A013; 9 pages
Published Online:
February 8, 2017
Citation
Avanço, RH, Navarro, HA, Nabarrete, A, Balthazar, JM, & Tusset, AM. "Chaotic Behavior in the Double Pendulum Under Parametric Resonance." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition. Volume 4B: Dynamics, Vibration, and Control. Phoenix, Arizona, USA. November 11–17, 2016. V04BT05A013. ASME. https://doi.org/10.1115/IMECE2016-65711
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