Homoclinic bifurcation and chaos control in MEMS resonators

被引:83
作者
Siewe, M. Siewe [2 ]
Hegazy, Usama H. [1 ]
机构
[1] Al Azhar Univ, Dept Math, Gaza, Israel
[2] Univ Yaounde I, Fac Sci, Dept Phys, Lab Mecan, Yaounde, Cameroon
关键词
MEMS resonator; Melnikov method; Bifurcation; Time-varying stiffness; Control; MICROELECTROMECHANICAL SYSTEM; NONLINEAR DYNAMICS; OSCILLATOR;
D O I
10.1016/j.apm.2011.05.021
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The chaotic dynamics of a micromechanical resonator with electrostatic forces on both sides are investigated. Using the Melnikov function, an analytical criterion for homoclinic chaos in the form of an inequality is written in terms of the system parameters. Detailed numerical studies including basin of attraction, and bifurcation diagram confirm the analytical prediction and reveal the effect of parametric excitation amplitude on the system transition to chaos. The main result of this paper indicates that it is possible to reduce the electrostatically induced homoclinic and heteroclinic chaos for a range of values of the amplitude and the frequency of the parametric excitation. Different active controllers are applied to suppress the vibration of the micromechanical resonator system. Moreover, a time-varying stiffness is introduced to control the chaotic motion of the considered system. The techniques of phase portraits, time history, and Poincare maps are applied to analyze the periodic and chaotic motions. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:5533 / 5552
页数:20
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