Flexural vibration of the incomplete circular ring

The flexural vibration of two incomplete circular rings, approximately 360º, fixed at one end and free at the other, is investigated. One ring lies in the thin ring range. The other ring lies in the borderline range between a thick and thin ring. A theoretical approach is used in an attempt to approximate the first three natural frequencies of the rings. These theoretical results are then compared with the results obtained from an experimental investigation.

In an attempt to simplify the general equation of motion of the ring an assumption was made that the tangential inertia term had a negligible effect on the natural frequencies of a thin ring. The frequencies obtained from the resulting frequency equation were found to be poor approximations for the system.

Good approximations were obtained for the first two frequencies of the thin ring, using the method of Rayleigh -Ritz.