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Dr. Khalil Mohamed Khalil Mohamed :: Publications:

Title:
Periodic Solutions of a Modifi ed Duffing Equation Subjected to a Bi-Harmonic Parametric and External Excitations
Authors: A M Elnaggar; A F El-Bassiouny; K M Khalil; A M Omran
Year: 2016
Keywords: MEMS; weakly nonlinear di erential equation; multiple scales method; parametric excitation and external excitation
Journal: British Journal of Mathematics & Computer Science
Volume: 16
Issue: 4
Pages: 1-12
Publisher: Not Available
Local/International: International
Paper Link: Not Available
Full paper Khalil Mohamed Khalil Mohamed_Omran1642016BJMCS25684.pdf
Supplementary materials Not Available
Abstract:

In this paper, we investigated the periodic solutions of type superharmonic and subsuperharmonic of modified Duffing equation subjected to a bi-harmonic parametric and external excitations. The method of multiple scales is used to construct a first order uniform expansion of approximate solutions. Two first-order nonlinear ordinary differential equations(Modulation Equation) are derived from the evolution of the amplitude and the phase. Steady state solutions and their stability are given for selected values of the system parameters. The consequences of these (quadratic and cubic) nonlinearities on these the vibrations are particularly examined. With this research, it has been confirmed that the qualitative effects of these nonlinearities are different. Regions of the hard (soft) nonlinearity of the system exist for the case of subsuperharmonic oscillation. Numerical solutions are presented in a group of figures which demonstrate the actions of the steady-state reaction plenitude as the purpose of the detuning parameter.

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