Oscillatory Behavior of an Electrostatically Actuated Microcantilever Gyroscope

This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input angular rate of the beam along its axis. The input angular rotation can be measured by sensing the oscillation tuned to another DC voltage of the proof mass. First, a system of nonlinear equations governing the flexural–flexural motion of electrostatically actuated microbeam gyroscopes subjected to input rotations is derived by the extended Hamilton principle. The oscillatory behavior of the microgyroscopes subjected to DC voltages in both directions is then analytically investigated. Finally, the effects of the geometric parameters, base rotation and fringing field on the natural frequencies of the system are assessed.