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Harmonic and Sub-Harmonic Periodic Solutions (1/2,1/3) of Generalized Mathieu-Van der Pol-Duffing Equations 3) o
Journal of Scientific Research & Reports • 2017
Publication Information
Authors
A. M. Elnaggar , K. M. Khalil and A. M. Omran
and A. M. Omran
Keywords
MEMS; multiple scales method; fast excitation; slow motion and parametric forcing
Journal
Journal of Scientific Research & Reports
Publisher
Not Available
Volume
6
Issue
13
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 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.
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.