Free vibration analysis of beams by using a third-order shear deformation theory |
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Authors: | Mesut Şi̇mşek Turgut Kocatürk |
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Affiliation: | (1) Department of Civil Engineering, Yildiz Technical University, Yildiz, 34349, Istanbul, Turkey |
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Abstract: | In this study, free vibration of beams with different boundary conditions is analysed within the framework of the third-order
shear deformation theory. The boundary conditions of beams are satisfied using Lagrange multipliers. To apply the Lagrange’s
equations, trial functions denoting the deflections and the rotations of the cross-section of the beam are expressed in polynomial
form. Using Lagrange’s equations, the problem is reduced to the solution of a system of algebraic equations. The first six
eigenvalues of the considered beams are calculated for different thickness-to-length ratios. The results are compared with
the previous results based on Timoshenko and Euler-Bernoulli beam theories. |
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Keywords: | Free vibrations of beams the third-order shear deformation theory Lagrange’ s equations Lagrange multipliers |
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