Vibrations of composite circular cylindrical vessels

Free vibrations are analyzed for a laminated composite circular cylindrical vessel consisting of a laminated composite circular cylindrical shell and laminated composite circular plate lids with a hole at both ends. In the analysis, by using the exact solutions of the equations of motion for the circular cylindrical shell and the circular plate, the Lagrangian of the vessel is expressed in a quadratic form of the unknown boundary values. The frequency equations are obtained by minimizing the Lagrangian with respect to the unknown boundary values.