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This paper presents the characterization of the modal frequencies and the modal orientation of the axisymmetric resonators in Coriolis vibratory gyroscopes based on the approaches of the frequency sweep and the ring down. The modal frequencies and the orientation of the stiffness axis are the key parameters for the mechanical correction of the stiffness imperfections. The frequency sweep method utilizes the zero and the poles in the magnitude-frequency responses of the two-dimensional transfer function to extract the modal orientation information within the frequency domain. The ring down method makes use of the peak and the valley values of the beat signals at the readout electrodes to obtain the modal orientation and the coefficient of the nonlinear stiffness directly within the time domain. The proposed approaches were verified via a silicon ring resonator designed for gyroscopic sensing and the modal information from the experiments exhibited a good agreement between the methods of the frequency sweep and the ring down.

Characterization of Modal Frequencies and Orientation of Axisymmetric Resonators in Coriolis Vibratory Gyroscopes