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publication name Harmonic and Sub-Harmonic Periodic Solutions (1/2,1/3) of Generalized Mathieu-Van der Pol-Duffing Equations 3) o
Authors A. M. Elnaggar , K. M. Khalil and A. M. Omran and A. M. Omran
year 2017
keywords MEMS; multiple scales method; fast excitation; slow motion and parametric forcing
journal Journal of Scientific Research & Reports
volume 6
issue 13
pages 1-15
publisher Not Available
Local/International International
Paper Link Not Available
Full paper download
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 PolDuffing 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 entrainment regions to shift. Numerical solutions are represented the analytical results.

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