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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 546364, 18 pages
http://dx.doi.org/10.1155/2012/546364
Research Article

Chaos in a Magnetic Pendulum Subjected to Tilted Excitation and Parametric Damping

1Center for Nonlinear Dynamics and Control, Department of Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, PA 19085, USA
2Laboratory of Mechanics, University Hassan II, Casablanca, Morocco

Received 18 May 2012; Revised 3 August 2012; Accepted 3 August 2012

Academic Editor: Stefano Lenci

Copyright © 2012 C. A. Kitio Kwuimy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate the Melnikov predictions. In the absence of parametric damping, the results show that an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly.