Micro/nano gyroscopes which can measure angular rate or angle are types of merging gyroscope technology with MEMS/NEMS technology. They have extensively used in many fields of engineering, such as automotive, aerospace, robotics and consumer electronics. There are many studies of a variety of gyroscopes with various drive and detect methods and different resonator structures in last years. In case of electrostatically actuated and detected beam micro/nano-gyroscopes, DC voltages are applied in driving and sensing directions and AC voltage is utilized in driving direction in order to excite drive oscillation. The intermolecular surface forces are especially significant when the gyroscopes are working in vacuum without the effect of capillary forces and the separations between movable components are in the sub-micrometer range. In this paper, a new model is used to study the static and dynamic behavior and pull-in instability of the vibratory clamped-clamped beam micro/nano gyroscopes. The system is operated by electrostatic mechanisms and subjected to base rotation. In this model, the effects of the intermolecular attractions and fringing electrostatic fields are accounted. Nonlinear differential equations governing the dynamic motion of the system are obtained using extended Hamilton principle. The static and dynamic problems are solved for various values of nondimensional design parameters.

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