Tuning The Primary Resonance of Vibrating Beam Micro-Gyroscopes Based On Piezoelectric Actuation and Multiple Nonlinearities

Abstract In this paper, the nonlinear dynamic characteristics of statically piezoelectric actuated vibrating beam micro-gyroscopes are studied. The comprehensive nonlinear model including curvature, inertia and electrostatic force nonlinearities is considered. In the research of electrostatic micro-gyroscopes, it’s a novel way to tune the primary resonance by piezoelectric actuation and multiple nonlinearities. The multiple scales method and numerical continuation technique are used to characterize the frequency-amplitude and force-amplitude responses of the micro-gyroscopes. The effect of varying the size-dependent, fringing field, statically piezoelectric voltage and nonlinear curvature and inertia on the dynamic response of the micro-gyroscope is investigated in detail. The frequency-response results show that small vibrations produce a symmetrical frequency response curve in sense direction while the system actually has a significant softening characteristic in drive direction. The nonlinear multi-value problem effectively reduces in sense direction under the size-dependent effect, which plays an important role in the design of detection instruments for micro-gyroscopes. Choosing a positive piezoelectric actuation voltage will obtain a higher sensitivity. Increasing the curvature nonlinearity and reducing the inertial nonlinearity of the gyroscopic system will help the micro-gyroscope obtain better sensitivity, and may eliminate multi-valued responses as much as possible.