Examining free vibrationof simply-supported beam with using Euler-Bernolli and Timoshenko beam theories

Free vibration analysis of a simply-supported beam within the framework of bothEuler-Bernoulli and Timoshenko beam theories was analyzed by using Ritz, finite elementand finite differences methods. By using these methods the first sixth eigenvalues of theEuler-Bernoulli and Timoshenko beams are calculated and tabulated. The obtainedeigenvalues are given for different thickness-to-length ratios for Timoshenko beam theory.Convergence studies were made for the different number of degree of the freedom for thethree solution methods. The obtained results according to the three solution methods werecompared to each other. Also, the obtained results were compared with the previouslypublished results. Numerical investigations show that the results of Euler-Bernoulli andTimoshenko beam theories are very close to each other for small values of thickness-to-lengthratios, and the results obtained from the present study are in good agreement with those thepreviously published results. Also, same number of degree of the freedom for finite elementand finite differences methods compared in Timoshenko beam theory. The obtained resultsare very close to each other.Keywords: Euler-Bernoulli beam, Timoshenko beam, free vibration, finite element method,finite differences method, Ritz method, eigenvalueJURY:1.Prof.Dr.Turgut KOCATÜRK (Supervisor) Date:15.02.20062.Prof.Dr. Faruk YÜKSELER Page:643.Prof.Dr. Mehmet H.OMURTAG