Dispersion Relations for Waves on Fluid-Loaded Elastic Hollow Cylinders and Cylindrical Shells.

Over the years, investigators have offered many models for the motion of a thin-walled, circular, cylindrical elastic shell. A technique for resolving the issue of how to select a shell theory for a particular problem is presented. A dispersion relation based on the exact theory of elasticity for a hollow cylinder is derived. This dispersion relation is given in the form of a power series in the ratio of shell thickness to shell radius. This leads to the possibility of a term by term comparison between exact elasticity theory and any given shell theory. For the specific cases examined, it is shown that the Donnell-Yu model is often sufficient. When it is not, the so-called correction terms of other thin shell theories may not in fact offer any real correction.