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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
العودة
معلومات البحث
المؤلفون A. M. Elnaggar; K. M. Khalil and A. M. Omran
الكلمات المفتاحية Not Available
المجلة العلمية Journal of Scientific Research & Reports
الناشر Not Available
المجلد 13
العدد 6
الصفحات 1-15
publication.type International
رابط البحث Not Available
المواد المرفقة Not Available
الملخص
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.