Abstract
In this article, an analytical method to study the natural frequencies of free vibrations for a thick cylindrical shell filled with fluid is proposed. Mindlin’s first-order shell theory is extended to derive the equations of motion and corresponding boundary conditions by Hamilton’s principle. Linearized potential flow theory is used to derive the hydrodynamic force. Moreover, the internal fluid pressure acting on the shell wall is obtained by the assumption of a non-penetration condition. The dispersion equations are obtained under the assumption of harmonic motion. The derived shell theory is used to calculate the natural frequencies of cylindrical shells with various thicknesses and lengths, and the results are compared with Flugge’s shell theory and finite-element method (FEM). As a result, the proposed shell theory shows improved accuracy and good agreement with published experimental results.
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