Single-Crystal Silicon Micro-Ring Gyroscopes-Attitude Sensors

The aim of this paper is to analyze a single-crystal micro-ring gyroscope. It is found that Si(111) ring is in-plane isotropic but out-of-plane anisotropic, while Si(100) ring is fully anisotropic. Hamiltonian's principle is used to derive the equations of vibration, which is a set of partial differential equations with variable coefficients. The exact solutions for frequencies and mode shapes are found. It is also found that the degeneracy of frequencies for isotropic ring splits for anisotropic ring Then structure design and dynamic analysis of silicon resonant micro-ring gyroscope are presented. The perturbation method of multiple scales is used to find the explicit expression for the relationship between input (angular velocity) and output (nodal displacement of the ring). The effectiveness of phase-locking for enhancing the output signal is proved and quantitatively analyzed.