Characterization of Static Behavior of a Nonlinear Doubly Clamped Microbeam Under Electrostatic Actuation and Detection

In this study, the static deflection and pull-in instability of the doubly clamped microbeam with a mass attached to its midpoint are investigated. Nonlinear electrostatic forces, fringing fields, base rotation and mid-plane stretching of the beam in this model are considered. First, a system of two nonlinear integro-differential equations are expressed in partial derivatives which describe coupled flexural-flexural motion of electrostatically actuated microbeam gyroscopes under rotation. Then static deflection and pull-in instability of the microgyroscopes acted upon by DC voltages in both (direction and sensing) directions are studied. The equations of static motion are reduced by Galerkin’s decomposition method. The static response of the microgyroscope to variations in the DC voltage across the drive and sense electrodes is obtained.