Three-dimensional vibrations of cross-ply laminated hollow cylinders with clamped edge boundaries

Using fully three-dimensional elasticity considerations, this paper presents a free vibration analysis of cross-ply laminated hollow cylinders having clamped edge boundaries. The analysis is based on a recursive solution that has been published elsewhere and is suitable for three-dimensional vibration analysis of corresponding simply supported cylinders. Clamped boundary conditions are initially imposed by means of a number of fixed circles located at the edge(s) of the cylinder considered. Using certain dynamic considerations together with the Lagrange multipliers method, this is achieved by suitably coupling a certain number of different normal modes of vibration of the corresponding simply supported cylinder Hence, an approximate solution, which however is practically very close to the exact three-dimensional solution, is finally obtained by appropriately increasing either the number of the coupled vibration modes or the number of fixed circles on a clamped edge.