Amirkabir University of Technology AUT Journal of Mechanical Engineering 2588-2937 2 2 2018 12 01 Nonlinear Free Transverse Vibration Analysis of Beams Using Variational Iteration Method 233 242 2761 10.22060/mej.2017.12332.5315 EN K. Torabi Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran D. Sharifi Department of Mechanical Engineering, University of Kashan, Kashan, Iran M. Ghassabi Department of Mechanical Engineering, Iran University of Science & Technology, Tehran, Iran A. Mohebbi Department of Mechanical Engineering, University of Kashan, Kashan, Iran Journal Article 2017 01 03 <span>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. </span> https://ajme.aut.ac.ir/article_2761_eeabbf8d7ab63979fcd87fc36e566ba9.pdf