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.
Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders With Clamped Edge Boundaries
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Ye, J. Q., and Soldatos, K. P. (July 1, 1997). "Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders With Clamped Edge Boundaries." ASME. J. Vib. Acoust. July 1997; 119(3): 317–323. https://doi.org/10.1115/1.2889726
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