Free Vibration Analysis of Beam on Elastic Foundation by the Variational Iteration Method


Ozturk B.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, vol.10, no.10, pp.1255-1262, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 10
  • Publication Date: 2009
  • Doi Number: 10.1515/ijnsns.2009.10.10.1255
  • Journal Name: INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1255-1262
  • Keywords: Variational iteration method, beam on elastic foundation, free vibration analysis, DIFFERENTIAL TRANSFORM METHOD, EQUATIONS

Abstract

This paper applies the variational iteration method (VIM) to analysis of free vibration of a beam on an elastic foundation. Three different axially loaded cases are considered: 1) one end fixed, the other end simply supported; 2) both ends fixed; and 3) both ends simply supported. Analytical solutions and the frequency factors are obtained for different ratios of axial load acting on the beam to Euler buckling load. The VIM results are in excellent agreement with both analytical solutions for all the cases considered in this paper and the differential transform method (DTM) results available in the literature for the fixed-pinned case.