On the Vibration of a Thick Ring in Its Own Plane

Abstract

A method based on beam theory is developed to describe the bending vibrations of nonthin, complete circular rings of rectangular cross section. Bending, shear, and extensional strain energies are considered together with translational and rotatory kinetic energies. The notion of the average shear angle is used. It is also shown that a slightly simplified analysis, neglecting extensional energies, avoids certain computational difficulties. The solution for resonant frequencies is given in a nondimensional form and the theoretical results compared with the results of a thin-ring theory and with experiments.