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Shock and Vibration
Volume 2014, Article ID 159213, 7 pages
Research Article

An Efficient Analytical Method for Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends

Faculty of Engineering, Department of Civil Engineering, Bilecik Şeyh Edebali University, Gülümbe Kampüsü, 11210 Bilecik, Turkey

Received 27 February 2014; Revised 22 April 2014; Accepted 30 April 2014; Published 14 May 2014

Academic Editor: Toshiaki Natsuki

Copyright © 2014 Mustafa Özgür Yayli et al. 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.


An efficient analytical method for vibration analysis of a Euler-Bernoulli beam on elastic foundation with elastically restrained ends has been reported. A Fourier sine series with Stoke’s transformation is used to obtain the vibration response. The general frequency determinant is developed on the basis of the analytical solution of the governing differential equation for all potential solution cases with rigid or restrained boundary conditions. Numerical analyses are performed to investigate the effects of various parameters, such as the springs at the boundaries to examine how the elastic foundation parameters affect the vibration frequencies.