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W. A. El-Ganini, N. A. Saeed, and M. Eissa, 2013. Positive position feedback (PPF) controller for suppression on nonlinear system vibration. Nonlinear Dyn., 72, 517-537.

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Article

Nonlinear Dynamics of a Controlled Cantilever Beam with Varying Orientation under Primary Resonance

1Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 1277, Gaza, Palestine


American Journal of Mechanical Engineering. 2014, Vol. 2 No. 7, 316-327
DOI: 10.12691/ajme-2-7-31
Copyright © 2016 Science and Education Publishing

Cite this paper:
Usama H. Hegazy. Nonlinear Dynamics of a Controlled Cantilever Beam with Varying Orientation under Primary Resonance. American Journal of Mechanical Engineering. 2014; 2(7):316-327. doi: 10.12691/ajme-2-7-31.

Correspondence to: Usama  H. Hegazy, Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 1277, Gaza, Palestine. Email: uhijazy@yahoo.com

Abstract

The problem of controlling the oscillations and chaotic behavior of a nonlinear cantilever beam with varying orientation under mixed excitations is tackled. Numerical integration of the second order nonlinear ordinary differential equation is performed with different control strategies to explore the chaotic dynamics of the first mode of the beam at the primary resonance case. The method of multiple scales perturbation technique is applied to obtain approximate solution and the stability of the response is studied. The effects of the various parameters are investigated by numerical simulations.

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