Influence of Boundary Conditions on the Modal Characteristics of Thin Cylindrical Shells

Abstract

The modal characteristics of thin cylindrical shells have previously been determined for only three sets of boundary conditions. In the present analysis, all sixteen sets of homogeneous boundary conditions are considered, at each end of the shell (each set contains four conditions). The equations of motion of thin, circular, cylindrical shells developed by Flügge are used. The general solution to these equations can easily be written down. The difficulty arises in evaluating the constants of integration, and this apparently is the reason no one has followed this approach to its ultimate conclusion. One can assume a circumferential nodal pattern, eight boundary conditions, and a frequency of vibration, and then iterate numerically to find the length of shell that will meet these conditions. The advantage of this approach is that one can obtain a solution to the basic equations for any boundary conditions desired. Results indicate that the condition placed on the longitudinal displacement μ in many cases is more influential than restrictions on the slope or moment. It has been found that even for long cylinders the minimum natural frequency may differ by as much as a factor of two, depending upon whether, at both ends, μ=0 or the longitudinal stress resultant Nx=0.