Static deflection and pull-in instability analysis of an electrostatically actuated mirocantilever gyroscope considering geometric nonlinearities

In this paper, a mathematical modeling of a microcantilever gyroscope is presented considering the nonlinearities of the system due to electrostatic forces, fringing field, geometry and the inertial terms. The microgyroscope is actuated and detected by electrostatic methods and subjected to coupled bending oscillations. First a system of two nonlinear integro-differential equations is derived which describes flexural-flexural motion of electrostatically actuated and detected microbeam gyroscopes. Afterward, static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (driving and sensing) directions are studied for different parameters. The model's predictions are in good agreement with the experimental data found in the literature and finite element simulation. Results show that the nonlinearities become important when pull-in happens.