Nonlinear Vibration Reduction of Resonant Accelerometers Based on the Equivalent Nonlinear Circuit Model

By establishing the nonlinear vibration model of a resonant accelerometer, this article analyzes the effects of mechanical nonlinearity and electrostatic nonlinearity on the output frequency offset of the resonant accelerometer. It is found that these two types of nonlinearities affect the nonlinear coefficient oppositely. Thereby, a nonlinearity compensation model is proposed and built by using electrostatic nonlinearity to counteract mechanical nonlinearity. Subsequently, the polarization voltage conditions aiming for zero nonlinear coefficient are investigated, so that to decrease the output frequency offset of the resonant accelerometer, improving the stability of the output frequency. Finally, through theoretical calculations and numerical simulations, it is figured out that under the compensation voltage, the output frequency offset is less than 0.001%. According to the principles of electromechanical equivalence, the nonlinear vibration compensation model is equivalently represented by an electrical circuit model. The output frequencies of the equivalent circuit turned out to be consistent with that obtained by numerical analysis of the nonlinear vibration compensation model. The linearity of the accelerometer output curve before and after compensation is compared, and the results certify the feasibility of the proposed nonlinear vibration compensation method.