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Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling
Faculty
Science
Year:
2013
Type of Publication:
Article
Pages:
186-194
Authors:
Emam, Samir A
DOI:
10.1016/j.compstruct.2012.12.044
Journal:
COMPOSITE STRUCTURES ELSEVIER SCI LTD
Volume:
100
Research Area:
Materials Science
ISSN
ISI:000317537200018
Keywords :
Nonlinear free vibration, Composite beams, Variational method, Analytical solution
Abstract:
We present approximate analytical solutions for the nonlinear free vibrations of symmetrically or asymmetrically laminated composite beams in prebuckling and postbuckling. Simply supported and clamped-clamped boundary conditions are considered. Galerkin's discretization is used to obtain the nonlinear ordinary differential equations governing the large-amplitude vibrations of composite beams in prebuckling and postbuckling, which are found to be of the same form. The variational method of He {[}20,21] is used to derive an approximate analytical solution for the nonlinear natural frequency and the nonlinear load-deflection relation. Results obtained by using the proposed analytical solution is compared with the finite element results available in the literature and a good agreement has been obtained. Numerical results to show the variation of the nonlinear natural frequency with the applied axial load for a variety of composite laminates are presented. The contribution of the amplitude of vibration on the nonlinear load-deflection response and the nonlinear natural frequency is found to be significant. (C) 2013 Elsevier Ltd. All rights reserved.
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