Vol. 325 No. 4 (2014): Техника и технологии в энергетике

Influence of initial conditions on the behavior of two-electrode microelectromechanical systems

The authors have analyzed the areas of functioning of two-electrode microelectromechanical systems taking into account the electromechanical interactions between system elements. As an example, the paper considers the systems with a plane-parallel and interdigitated electrode structure and the influence of the initial conditions. For the dynamic systems described by ordinary differential equations, three types of solution are illustrated: equilibrium state, stable periodic and quasiperiodic solutions. The analysis was carried out by examining the phase trajectories. It is shown that the allowable values of power supply voltage, where the pull-in-effect has not manifested for two-electrode for microelectromechanical systems with plane-parallel electrodes design, are higher than the corresponding values for microelectromechanical systems with comb electrodes. It was found out that at the initial stage of operation the pull-in-effect in microelectromechanical systems data can be observed in the power supply voltage, significantly lower values of V0,кр, which are determined only by the conditions of static equilibrium. The authors obtained the expressions which allow defining the field of initial conditions (displacement and velocity), where the electrode pull-in-effect does not occur. It is shown that when decreasing voltages of the applied power source, the initial conditions domain, under which the pull-in-effect does not occur, is expanded. In some cases such an approach allows predicting potential emergencies, revealing new, previously unknown, modes and elaborating the effective algorithms to control the system. The authors found out the analytical expressions which allow determining the allowable values of power source voltage, where the pull-in-effect of the electrodes does not occur with zero initial conditions. It is shown that the weight of the movable electrode can significantly influence the manifestation and the lack of the pull-in-effect.

Keywords:

initial conditions, micromechanical system, phase portrait, critical values, electromechanical interaction, pull-in-effect, phase trajectories, electrostatic forces

Authors:

Ludmila Dragunova

Valeryi Dragunov