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Dynamic Stability of Beam-type Vibratory Angular Rate Sensors Subjected to Rate Fluctuations

Dynamic stability behavior of a beam-type vibratory structure, for applications in a class of vibratory angular rate sensors is investigated. A suitable mathematical model for a rotating beam perturbed by periodic velocity fluctuations is developed. The natural frequency variations due to the gyroscopic coupling present in the system are characterized. When the system is considered to be under an influence of periodic perturbations in the input angular speed, the dynamic stability is investigated. The method of averaging is employed for this purpose, and closed-form stability conditions are obtained. The analytical results are verified by direct numerical integration of the system equations.