Homoclinic bifurcation and chaos control in MEMS resonators. (English) Zbl 1228.70015

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 Poincaré maps are applied to analyze the periodic and chaotic motions.


70Q05 Control of mechanical systems
34C23 Bifurcation theory for ordinary differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
37N35 Dynamical systems in control
70K44 Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
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