Nonlinear vibration and amplitude ratio output performance of a resonant micro-gyroscope based on bifurcation detection

Abstract

In this paper, we design a 3-degree-of-freedom (3-DOF) nonlinear resonant micro-gyroscope, which innovatively utilizes the bifurcation phenomenon of the nonlinear resonant beam as a detection method and uses the amplitude ratio before and after bifurcation as the sensitivity output of the system. The steady-state response of the driving equation is first solved by the complex exponential method. Coriolis force is amplified by the lever mechanism and transmitted to the axial direction of the resonant beam. The dimensions of the resonant beam are designed so that the frequency of Coriolis force is in a 2:1 relationship with the natural frequency of the resonant beam to enhance the parametric excitation effect. Subsequently, Hamilton principle and Galerkin method are used to derive and discretize the dynamical equations of the resonant beam containing axial force, respectively. The multi-scale method is used to perturbation analysis of discrete equations. Finally, the bifurcation characteristics and the amplitude-frequency response with different input angular velocities are studied. The results show that the comprehensive performance of the micro-gyroscope system using backward frequency sweep (BFS) is better than forward frequency sweep (FFS). Furthermore, by using the BFS, the relative sensitivity of the nonlinear resonant micro-gyroscope based on the amplitude ratio variation rises by about 168 times compared with that based on the frequency variation in the linear case. In addition, when considering the input angular velocity with the same magnitude but different directions, the bifurcation frequency of resonant beam is closely related to the direction of the input angular velocity, and the direction of the input angular velocity can be further identified by utilizing this phenomenon.