Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling

Samir A. Emam

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

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 languageEnglish
Pages (from-to)186-194
Number of pages9
JournalComposite Structures
Volume100
DOIs
Publication statusPublished - Jun 1 2013

Keywords

  • Analytical solution
  • Composite beams
  • Nonlinear free vibration
  • Variational method

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering

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