Flexural Vibrations of a Ring of Rectangular Cross Section

Abstract

Various theories have been established concerning the two-dimensional type of flexural vibrations of a ring of rectangular cross section. However, for the three-dimensional type no adequate theory is given yet for a wide range of the length-to-diameter ratios of a ring. In this paper, the natural frequencies for both types are obtained by solving the characteristicvalue problem for a finite, circular cylindrical shell with both ends free and by means of a numerical evaluation using a digital computer. The paper involves two kinds of analyses : One starts from Love's fundamental equations for a thin, circular cylindrical shell. The other is based on a Timoshenko-type theory of a shell. Compared with the experimental results, the theoretical results prove to be valid for a wide range of the dimensional parameters of a ring, even for the ring whose length is about equal to or less than the thickness.