INFLUENCE OF BOUNDARY CONDITIONS ON THE MODAL CHARACTERISTICS OF THIN CYLINDRICAL SHELLS.
LOCKHEED MISSILES AND SPACE CO PALO ALTO CALIF
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The modal characteristics of thin cylindrical shells have previously been determined only for three sets of boundary conditions. In the present analysis, all sixteen sets of homogeneous boundary conditions have been examined at each end of the shell each set contains four conditions. The equations of motion developed by Fliigge for thin, circular cylindrical shells are used. The general solution to these equations can easily be written down. One can select a circumferential modal pattern, eight boundary conditions, and a length of shell, and then iterate numerically to find the frequency of vibration 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, contrary to the rather common assumption, the condition placed on the longitudinal displacement u in many cases is more influential than restrictions on the slope or moment. It has been found that even for long cylinders length to radius ratio of 40 or more the minimum natural frequency may differ by more than 50 depending upon whether u 0 or the longitudinal stress resultant N sub x 0 at both ends. Author