Coriolis coupling effects on the vibration of rotating rings

The vibration properties of a ring subjected to angular velocity components applied simultaneously about three mutually perpendicular axes are investigated. Ring structures have potential applications as multi-axis rate sensors and hence the effects of angular velocity on the vibration properties are practically important. Coriolis coupling between in-plane and out-of-plane displacements of a ring due to angular velocity applied about axes in the plane of the ring, and about the polar axis of the ring, allow it to be used as a multi-axis rate sensor. Equations of motion are derived for the rotating ring. The combinations of in-plane and out-of-plane displacement patterns for which Coriolis coupling is present are investigated and the corresponding natural frequencies and mode shapes of the rotating ring are derived. Simple analytical expressions are developed for a number of special cases and some numerical examples are presented. The effect of small imperfection on the natural frequencies of the rotating ring is also considered. (C) 2000 Academic Press.