Dynamics of the Ring Micromechanical Gyroscope Taking into Account the Nonlinear Stiffness of the Suspension

A micromechanical gyroscope with a ring resonator and magnetoelectric control sensors is considered. By using Hamilton variational principle, the dynamics equations of the ring are obtained, taking into account dissipation, nonlinear stiffness of torsions, and applied Ampere forces. By using the Bubnov-Galerkin method, a system of nonlinear differential equations that describes the resonator dynamics in the single-mode approximation is obtained. The mathematical model of the gyroscope in the mode of forced oscillations taking into account the nonlinear stiffness of torsion bars is derived. It is shown that torsion bars of elastic suspension cause cubic nonlinearity as well as a shift of the oscillation frequency and gyroscope drift.