Homoclinic bifurcation and chaos control in MEMS resonators

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 basi...

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Bibliographic Details
Published in:Applied mathematical modelling 2011-12, Vol.35 (12), p.5533-5552
Main Authors: Siewe, M. Siewe, Hegazy, Usama H.
Format: Article
Language:English
Subjects:
Amplitudes
Bifurcation
Bifurcations
Chaos theory
Control
Dynamics
Exact sciences and technology
Excitation
Fundamental areas of phenomenology (including applications)
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Mathematical analysis
Mathematical models
Mechanical instruments, equipment and techniques
Melnikov method
MEMS resonator
Micromechanical devices and systems
Physics
Resonators
Solid mechanics
Structural and continuum mechanics
Time-varying stiffness
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary: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.
ISSN:0307-904X
DOI:10.1016/j.apm.2011.05.021