This paper aims to develop a resonant accelerometer for high-sensitivity detection and to investigate the nonlinear vibration of the MEMS resonant accelerometer driven by electrostatic comb fingers. First, a nonlinear vibration model of the resonator with comb fingers in a MEMS resonant accelerometer is established. Then, the nonlinear and nonlinear stiffness coefficients are calculated and analyzed with the Galérkin principle. The linear natural frequency, tracking error, and nonlinear frequency offset are obtained by multi-scale method. Finally, to further analyze the nonlinear vibration, a sample-based stochastic model is established, and the uncertainty analysis method is applied. It is concluded from the results that nonlinear vibration can be reduced by reducing the resonant beam length and increasing the resonant beam width and thickness. In addition, the resonant beam length and thickness have more significant effects, while the resonant beam width and the single concentrated mass of comb fingers have little effect, which are verified by experiments. The results of this research have proved that uncertainty analysis is an effective approach in nonlinear vibration analysis and instructional in practical resonant accelerometer design.

A compensation method for nonlinear vibration of a silicon micro resonant sensor is proposed and evaluated to be effective through simulation and experimental analysis. Firstly, the parameter characterization model of the silicon micro resonant sensor is established, which presents significant nonlinearity because of the nonlinear vibration of the resonant beam. A verification circuit is devised to imitate the nonlinear behavior of the model by matching the simulation measurement error of the frequency offset produced by the circuit block with the theoretical counterparts obtained from the model. Secondly, the principle of measurement error compensation is studied, and the compensation method dealing with nonlinear characteristics of the resonant beam is proposed by introducing a compensation beam and corresponding differential operations. The measurement error, compensation rate, and measurement residual between the two scenarios that use single beam and double beams, respectively, are derived and are compared with their simulation and experimental counterparts. The results coincide with the predicted trend, which verifies the effectiveness of the compensation method.