Free vibration analysis of a cylindrical shell—circular plate system with general coupling and various boundary conditions

The free vibration of a structure consisting of a finite circular cylindrical shell closed at one end by a circular plate is analyzed in this paper. Emphasis is given to the characterization of structural coupling and boundary conditions. These are incorporated into the model by means of continuous distributions of springs along the shell and the plate interface. A general formulation based on a variational principle is used. This formulation allows a wide spectrum of boundary conditions and coupling conditions between the shell and the plate, an issue the importance of which is clearly shown by a literature review. Very good accuracy of the method is demonstrated by solving test problems for lower order modes of the plate and of the shell, for which some results are available in the literature. Comparisons are also made using finite element analysis on a plate-ended shell, showing that the proposed approach is a convenient, effecient and accurate one for determining the modal behavior of such a complex structural system. Other numerical results are then presented for a shell rigidly attached to a plate, to illustrate the coupling phenomena between the shell and the plate. It is shown that there exist three different types of modes for this combined structure; they are termed plate-controlled modes, shell-controlled modes and strongly coupled modes, respectively. It is also shown that each type is closely related to the modal character of each of uncoupled elements.

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