Elnaggar, A., Khalil, K., Omran, A. (2018). Combination Solution of Additive Type for Two Coupled Weakly Nonlinear Second Order Differential Equations. test, 5(4), 268-281. doi: 10.21608/jbes.2018.370541
A. M. Elnaggar; K. M. Khalil; A. M. Omran. "Combination Solution of Additive Type for Two Coupled Weakly Nonlinear Second Order Differential Equations". test, 5, 4, 2018, 268-281. doi: 10.21608/jbes.2018.370541
Elnaggar, A., Khalil, K., Omran, A. (2018). 'Combination Solution of Additive Type for Two Coupled Weakly Nonlinear Second Order Differential Equations', test, 5(4), pp. 268-281. doi: 10.21608/jbes.2018.370541
Elnaggar, A., Khalil, K., Omran, A. Combination Solution of Additive Type for Two Coupled Weakly Nonlinear Second Order Differential Equations. test, 2018; 5(4): 268-281. doi: 10.21608/jbes.2018.370541

Combination Solution of Additive Type for Two Coupled Weakly Nonlinear Second Order Differential Equations

Journal of Basic and Environmental Sciences
Volume 5, Issue 4, October 2018, Pages 268-281    PDF (3.38 M)
Document Type: Original Article
DOI: 10.21608/jbes.2018.370541
Authors
A. M. Elnaggar; K. M. Khalil; A. M. Omran
Dept. of Math., Faculty of Science, Benha University, Egypt, B. O. 13518
Abstract
Combinations solution of additive type to a two coupled weakly nonlinear second order differential equations which governed the motion of a two coupled nonlinear
oscillator subjected to linear parametric excitation and external excitation. We determined the modulation equations in the amplitude and the phase, steady state solutions,
the frequency-response equation and stability analysis of the steady state solutions by
MSMS. Numerical study of the frequency-response equations and stability equations
are given for different values of the parameters. Results are plotted in group of Figures.
Finally discussion and conclusion are given. 
Keywords
MSM; combinations solution; external excitation
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