Study of nonlinear vibration of resonant gyroscope based on uncertainty analysis method

To study the nonlinear vibration characteristics of resonant gyroscope, the vibration model of the resonant beam is established primarily, aiming for the analytical formulas of the nonlinear stiffness coefficients and linear intrinsic frequencies of the gyroscope. With that foundation, the influence of the structural parameters of the resonant beam on the frequency tracking error caused by nonlinear vibration is analyzed thoroughly at first. Secondly, by random sampling, an uncertainty analysis model is established to evaluate the impact of each structural parameter of the resonant beam on the critical performance indexes of the gyroscope such as linear intrinsic frequency, nonlinear frequency offset and scale factor of the resonant beam. Finally, an equivalent circuit is constructed corresponding to the nonlinear vibration equations of the resonant gyroscope based on the electromechanical analogy method. By studying the nonlinearity of the circuit for equivalence, it turns out that the vibration characteristics of the equivalent circuit are consistent with that of the resonant gyroscope obtained by using the uncertainty analysis method. It effectively verifies the feasibility of the nonlinear vibration research method for the resonant gyroscope based on uncertainty analysis method.