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The nonlinear effects of a vibrating micromechanical gyroscope with a ring resonator supported by a flexible torsion system are considered. A mathematical model of the thin elastic resonator forced oscillations is derived to account for the nonlinear properties of the resonator material. The resonator dynamics in slow variables measured by the device electronic circuit is investigated according to the Krylov-Bogolyubov averaging method. It is shown that the nonlinear elastic properties of the resonator material led to additional errors of the gyroscope, unstable branches of resonance curves, and quenching.
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Martynenko et al. (2010) studied this question.
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