Three-Dimensional Vibrations of Cross-ply Laminated Hollow Cylinders With Clamped Edge Boundaries

[+] Author and Article Information
J. Q. Ye

Department of Civil Engineering, University of Leeds, Leeds, LS2 9JT, UK

K. P. Soldatos

Department of Theoretical Mechanics, University of Nottingham, Nottingham, NG7 2RD, U.K.

J. Vib. Acoust 119(3), 317-323 (Jul 01, 1997) (7 pages) doi:10.1115/1.2889726 History: Received November 01, 1994; Online February 26, 2008


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.

Copyright © 1997 by The American Society of Mechanical Engineers
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