文章基本信息

标题：Harmonic and Sub-Harmonic Periodic Solutions (1/2, 1/3) of Generalized Mathieu-Van der Pol-Duffing Equations
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作者：A. M. El-Naggar ; K. M. Khalil ; A. M. Omran 等
期刊名称：Journal of Scientific Research and Reports
电子版ISSN：2320-0227
出版年度：2017
卷号：13
期号：6
页码：1-15
DOI：10.9734/JSRR/2017/32122
出版社：Sciencedomain International
摘要：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.
关键词：MEMS; multiple scales method; fast excitation; slow motion and parametric forcing.