On the natural frequencies of vibration of a ring surrounded by and/or containing a fluid

Abstract

An energy approach is used to derive simple expressions for the effective modal mass and effective modal stiffness of a thin, uniform, circular ring when vibrating freely in an inextensional ring mode. These expressions include both the circumferential and radial inertia of the ring, and the additional mass of fluid both within and without the ring; they also allow for the destabilizing (or stiffening) effect of ring compression (or tension) due to pressure loading which is always normal to the surface. The natural frequencies of these inextensional modes of vibration of the ring, which are derived from the effective mass and effective stiffness, are exact to the first order of small quantities. Numerous special cases are contained within the general result, including all the classical results.