In-Plane Flexural Vibrations of Circular Rings

An equation of motion governing the free, in-plane vibrations of a circular ring is developed to include the effects of shear deformation and rotatory inertia. This equation is solved to find the natural frequencies of vibration of free rings and stiffened rings and the results compared with those given by a classical formula. The frequencies for a free ring are found to compare well with the experimental values of Kuhl [5]. Natural frequencies of circular arcs are calculated from the classical equation with hinged and fixed end conditions and the results compared with the approximate values given by Den Hartog [8, 9].