Abstract
An analytical model is developed to predict the modal characteristics of thin-walled circular cylindrical laminated shells with free ends. The shell is orthotropic and has mid-plane symmetry. By using Love's first-approximation shell theory, a strain energy functional containing both bending and stretching effects is formulated. The shell vibration mode shapes are then modelled by utilizing characteristic beam functions in the Rayleigh-Ritz variational procedure and the accuracy of the model is verified by test data. With the developed model, in extensional Rayleigh and Love modes can be identified having frequencies close to each other. The contributions to the strain energy due to various elastic properties are also investigated. Results show that the circumferential modulus provides a major portion of the flexural energy of the vibrating structure while the longitudinal and in-plane shear moduli contribute mostly to the stretching energy. It is also observed that reducing the shell thickness would result in a substantial increase in the ratio of the energies associated with the longitudinal and shear moduli, respectively. By rearranging the lamination stacking sequence, shells can be made to be more resilient to bending or twisting with only minor alterations in natural frequencies.
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