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Journal of Scientific Research and Reports

Journal of Scientific Research and Reports, ISSN: 2320-0227,Vol.: 13, Issue.: 6

 

Original-research-article

 

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

 

 

A. M. El-Naggar1, K. M. Khalil1 and A. M. Omran1*
1Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt.

 

Abstracts

 

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.

 

Keywords :

MEMS; multiple scales method; fast excitation; slow motion and parametric forcing.

 

Full Article - PDF    Page 1-15    Article Metrics

 

DOI : 10.9734/JSRR/2017/32122

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