Modeling of Nonlinear Stiffness of Micro-Resonator in Silicon Resonant Accelerometer

Abstract

Nonlinearities of the resonator in silicon resonant accelerometer (SRA) limit the ultimate short term frequency stability. In SRA, this stability is a measure of the achievable resolution. This paper discusses the nonlinear vibration phenomenon of micro-resonator considering the impact of the entire structure of SRA and builds a model to calculate the micro-resonator nonlinear stiffness K3,eff of the SRA prototype. The dies of SRA were fabricated by Silicon on Insulator (SOI) process. The equivalent model of the micro-resonator is built and the analytical value of the elastic constraint stiffness Ka of micro-resonator is derived as 8.91×104 N/m. It is calculated that K3,eff is equal to 5×1011 N/m3,and as a comparison, the simulation result is 5.026×1011 N/m3. The error between them is 0.52%. The nonlinear vibration experiments show that the maximum error between the theoretical and experimental value of resonance frequency is 2.1%. The prediction for the nonlinear stiffness contributes to further research on nonlinear vibration of the resonant beam. The model in this paper could also provide guidance and reference for optimal design of SRA.