Resonance frequency for a micro-gyroscope plays an extremely significant role since the driving frequency is accordingly tuned so that the best sensitivity and resolution can be achieved. In practice, the micro-gyroscope is usually driven into resonance to retain its superior angular rate detection capability. However, the embedded nonlinearity effect upon the micro-gyroscopic dynamics may not only deteriorate the stability around the vicinity of operation point, but also alter the initially-designed resonance frequencies so that the angular rate detection performance of the micro-gyroscope is dramatically degraded. Hence, the nonlinearities, mainly resulting from flexure springs and electrostatic force, are both taken into account to construct the nonlinear dynamic model of the micro-gyroscope in our work at first. Secondly, the instability region of the proposed micro-gyroscope under different driving frequency and natural frequencies, which tends to be drifted due to mechanical fatigue and temperature rise, is unveiled. In order to catch the insight of slight variation of system parameters, the nonlinear dynamic equation is analyzed by using multiple scales method to outstand the influence of the variation of driving moment. Thirdly, the external resonance and non-resonant hard excitation of the micro-gyroscope-totally five types-are both theoretically studied. It is interesting to find that the resonance frequencies and resonant magnitude are both changed accordingly if either the driving frequency or the magnitude of driving moment is tuned via control loop for the sake of considering more stability or better performance. Finally, the chaotic behavior of the micro-gyroscope is numerically inspected by bifurcation diagrams and verified that the sense mode and drive mode have the similar orbits for transitions across distinct patterns of dynamic motion of the presented micro-gyroscope.
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