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Symmetry breaking bifurcations of a parametrically excited pendulum

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Abstract

This paper examines the bifurcation behavior of a planar pendulum subjected to high-frequency parametric excitation along a tilted angle. Parametric nonlinear identification is performed on the experimental system via an optimization approach that utilizes a developed approximate analytical solution. Experimental and theoretical efforts then consider the influence of a subtle tilt angle in the applied parametric excitation by contrasting the predicted and observed mean angle bifurcations with the bifurcations due to excitation applied in either the vertical or horizontal direction. Results show that small deviations from either a perfectly vertical or horizontal excitation will result in symmetry breaking bifurcations as opposed to pitchfork bifurcations.

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Authors and Affiliations

  1. Nonlinear Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia, Missouri-Columbia, MO, 65211, USA

    B. P. Mann

  2. Nonlinear Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, University of Florida-Gainesville, Florida-Gainesville, FL, 32611, USA

    M. A. Koplow

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  1. B. P. Mann
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  2. M. A. Koplow
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Mann, B.P., Koplow, M.A. Symmetry breaking bifurcations of a parametrically excited pendulum. Nonlinear Dyn 46, 427–437 (2006). https://doi.org/10.1007/s11071-006-9033-0

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  • DOI: https://doi.org/10.1007/s11071-006-9033-0

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