Journal of Mathematical Sciences and Applications
ISSN (Print): 2333-8784 ISSN (Online): 2333-8792 Website: http://www.sciepub.com/journal/jmsa Editor-in-chief: Prof. (Dr.) Vishwa Nath Maurya, Cenap ozel
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Journal of Mathematical Sciences and Applications. 2015, 3(1), 22-31
DOI: 10.12691/jmsa-3-1-4
Open AccessArticle

Combination Resonances of a Beam with Two-Mode Interaction

Usama H. Hegazy1, and Helmy F. Alsultan1

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

Pub. Date: August 16, 2016

Cite this paper:
Usama H. Hegazy and 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

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.

Keywords:
oscillations analytical solution numerical solution combination resonances

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