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Dr. Khalil Mohamed Khalil Mohamed :: Publications: |
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| Title: | Harmonic and Sub-Harmonic Periodic Solutions (1/2; 1/3) Mathieu- of Generalized Van der Pol-Duffing Equations |
| Authors: | A. M. Elnaggar; K. M. Khalil and A. M. Omran |
| Year: | 2017 |
| Keywords: | Not Available |
| Journal: | Journal of Scientific Research & Reports |
| Volume: | 13 |
| Issue: | 6 |
| Pages: | 1-15 |
| Publisher: | Not Available |
| Local/International: | International |
| Paper Link: | Not Available |
| Full paper | 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. |
