a b s t r a c tThe 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.

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The dynamical behavior of a parametrically excited simple rigid disk-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The principal parametric resonance case is considered and studied. The motion of the rotor is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order ordinary differential equations are determined to describe the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions. The steady-state response and the stability of the solutions for various parameters are studied numerically, using the frequency response function method. The numerical results show that the system behavior includes multiple solutions, jump phenomenon, and sensitive dependence on initial conditions. It is also shown that the system parameters have different effects on the nonlinear response of the rotor. Results are compared to previously published work.

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