Nonlinear Free Transverse Vibration Analysis of Beams Using Variational Iteration Method

Document Type : Research Article


1 Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran

2 Department of Mechanical Engineering, University of Kashan, Kashan, Iran

3 Department of Mechanical Engineering, Iran University of Science & Technology, Tehran, Iran


In this study, Variational Iteration Method is employed so as to investigate the linear and non-linear transverse vibration of Euler-Bernoulli beams. This method is a very powerful approach with a high convergence speed providing an analytical and semi-analytical solution to the linear equations and is able to be extended to present semi-analytical solution to the non-linear ones. In this method, firstly, Lagrange`s multiplier and Initial Function should be chosen. The suitable choice of these two elements would effectively affect the convergence speed. In this attempt, in addition to presenting a discussion on how to choose these two functions appropriately, the calculated frequencies in the non-linear state are compared with the available results in the literature, and the accuracy and convergence speed are studied, as well.


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