Variational Method for Calculating the Natural Frequencies and Mode Shapes of a Cantilevered Open Cylindrical Shell.

摘要

This report develops a variational technique for the analysis of the vibration characteristics of an open cylindrical cantilevered shell. The technique is developed by modifying Reissner's principle, which normally applies to static problems, through the use of Hamilton's principle so that it applies to dynamic problems. The variational technique is first derived in general for an elastic system, and then specifically tailored to an open cylindrical cantilevered shell. The technique is implemented by first finding a general solution which satisfies the equations of motion for a cylindrical shell. A method is then formulated to use this general solution to construct a set of trial solution functions. With the variational method, the coefficients to this trial solution function are then calculated so that the function not only satisfies the equations of motion, but also the boundary conditions around the four edges of the shell. A computer method was developed to perform the necessary calculations to implement the variational procedure, but preliminary results have shown that numerical problems must be eliminated before accurate results can be expected. Experimental data for an open cylindrical cantilevered shell was also collected on a modal analyzer.