The oscillatory behavior, static and dynamic analyses of a micro/nano gyroscope considering geometric nonlinearities and intermolecular forces

The nonlinear dynamic and static deflection of a micro/nano gyroscope under DC voltages and base rotation are investigated. The gyroscope undertakes two coupled bending motions along the drive and sense directions and subjected to electrostatic actuations and intermolecular forces. The nonlinear governing equations of motion for the system with the effect of electrostatic force, intermolecular tractions and base rotation are derived using extended Hamilton principle. Under constant voltage, the gyroscope finds the preformed shape. First, the deflection of the micro/nano gyroscope under electrostatic forces is obtained by static and dynamic analyses. Furthermore, the static and dynamic instability of the system are investigated. Afterward the oscillatory behavior of the pre-deformed micro/nano gyroscope around equilibrium is studied. The effects of intermolecular and nonlinear parameters on the static and dynamic deflection, natural frequencies and instability of the micro/nano gyroscope are studied. The presented model can be used to exactly determine static and the dynamic behavior of vibratory micro/nano gyroscopes.