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Harmonic and Sub-Harmonic Periodic Solutions (1/2; 1/3) Mathieu- of Generalized Van der Pol-Duffing Equations

Journal of Scientific Research & Reports • 2017
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Publication Information
Authors A. M. Elnaggar; K. M. Khalil and A. M. Omran
Keywords Not Available
Journal Journal of Scientific Research & Reports
Publisher Not Available
Volume 13
Issue 6
Pages 1-15
publication.type International
Paper Link Not Available
Supplementary Materials Not Available
Abstract
The frequency-locking area of harmonic and subharmonic (1/2, 1/3) solutions in a fast harmonic excitation Mathieu-Van der- Pol Duffing equation is studied. A perturbation technique is then performed on the slow dynamic near the harmonic and subharmonic (1/2, 1/3) solutions, to obtain reduced slow flow equations governing the modulation of amplitude and phase of the corresponding slow dynamics. Results show that fast harmonic excitation can change the nonlinear characteristic spring behavior from softening to hardening and causes the entertainment regions to shift. Numerical solutions are represented the analytical results.