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Mathematical Problems in Engineering
Volume 2013, Article ID 470927, 7 pages
Research Article

Analytical Solution for Free Vibration Analysis of Beam on Elastic Foundation with Different Support Conditions

1Department of Civil Engineering, Faculty of Engineering, Hacettepe University, 06800 Ankara, Turkey
2Department of Civil Engineering, Faculty of Engineering, Kocaeli University, 41380 Kocaeli, Turkey

Received 15 December 2012; Accepted 17 April 2013

Academic Editor: Mehmet Atay

Copyright © 2013 Baki Ozturk and Safa Bozkurt Coskun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Analytical solutions for free vibration analyses of a beam on elastic foundation are obtained for different support conditions. The analytical solutions are applied on three different axially loaded cases, namely; (1) one end clamped, the other end simply supported; (2) both ends clamped, and (3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load, , acting on the beam to Euler buckling load, . The analytical solutions give results which are in excellent agreement with the variational iteration method (VIM) and homotopy perturbation method (HPM) results available in the literature for the particular problem considering all the cases provided in this study and the differential transform method (DTM) results available in the literature for the clamped-pinned case.