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.
Original language | English |
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Pages (from-to) | 186-194 |
Number of pages | 9 |
Journal | Composite Structures |
Volume | 100 |
DOIs | |
Publication status | Published - Jun 2013 |
Keywords
- Analytical solution
- Composite beams
- Nonlinear free vibration
- Variational method
ASJC Scopus subject areas
- Ceramics and Composites
- Civil and Structural Engineering