eng Science and Education Publishing Journal of Mathematical Sciences and Applications 2333-8792 2016-08-16 3 1 22 31 10.12691/jmsa-3-1-4 JMSA2015314 article Usama H. Hegazy u.hejazy@alazhar.edu.ps, uhijazy@yahoo.com 1 Helmy F. Alsultan 1 Department of Mathematics, Faculty of Science, Al-Azhar University, P.O. Box 1277, Gaza, Palestine 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. http://pubs.sciepub.com/jmsa/3/1/4/jmsa-3-1-4.pdf oscillations analytical solution numerical solution combination resonances