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B. Pratiher and S. K. Dwivedy (2008) “Non-linear vibration of a single link viscoelastic Cartesiar manipulator” International Journal of Non-Linear Mechanics 43, 683-696.

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Article

Combination Resonances of a Beam with Two-Mode Interaction

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


Journal of Mathematical Sciences and Applications. 2015, Vol. 3 No. 1, 22-31
DOI: 10.12691/jmsa-3-1-4
Copyright © 2016 Science and Education Publishing

Cite this paper:
Usama H. Hegazy, Helmy F. Alsultan. Combination Resonances of a Beam with Two-Mode Interaction. Journal of Mathematical Sciences and Applications. 2015; 3(1):22-31. doi: 10.12691/jmsa-3-1-4.

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

Abstract

We present the perturbation and numerical solutions of two-dimensional nonlinear differential equations that describe the oscillations of two modes of the beam under axial forces. The multiple scales and Rung-Kutta fourth order methods are utilized to investigate the system behavior and its stability. All possible resonance cases are extracted and effects of different parameters on system behavior at resonant condition are studied.

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