The influence of shape imperfections on the vibrations of a ring resonator of a wave solid-state gyroscope

This paper investigates the dynamic characteristics of a simple estimation model of the imperfect resonator of a wave solid-state gyroscope — a circumferential element under planar deformation conditions with initial deviations from the perfect circular form. Particular examples are given to show that the splitting of the bending frequency spectrum of geometrically imperfect rings may arise in cases different from those presented in modern theory. A pattern was established in which the splitting of the bending frequency spectrum of an imperfect ring arises. The unbalancing of the frequency content occurs when the number of forming waves is equal to the number of waves of imperfection of the ring’s shape and when the number of forming waves is twice, three, four and more times larger than that of the waves of shape imperfection. If the number of waves of ring shape imperfection is even, then the splitting of the bending frequency spectrum occurs even in the case where the number of forming waves is half the number of waves of shape imperfection, and also in cases where the number of forming waves is one and a half times, twice, two and a half times, three and a half, and more times larger than that of waves of shape imperfection; in the former case the unbalancing of the frequency content can be very significant.