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Vibration model of mode order optimized vibrating ring gyroscope

This paper establishes the vibration model of a mode order optimized vibrating ring gyroscope (VRG) based on the ray tracing method (RTM) to reveal mode properties of proposed VRG. After representing the working principle and the structure design of the VRG, the procedure of RTM is introduced. Due to the cyclic symmetry of proposed VRG, transmission and reflection coefficients at discontinuities of one sector are analyzed through the condition of the displacement continuity and the force equilibrium to obtain the vibration model of the entire structure. The vibration model can obtain mode frequencies and mode shapes to guide the structure design, and its validity is proved by COMSOL finite element simulation. Both the vibration model and the finite element simulation confirm that the n=2 mode can be lower than the n=1 mode of proposed VRG with suitable structural parameters.