Sharif University of Technology Scientia Iranica 1026-3098 22 5 2015 10 01 Application of Variational Iteration Method to large vibration analysis of slenderness beams considering mid-plane stretching Application of Variational Iteration Method to large vibration analysis of slenderness beams considering mid-plane stretching 1911 1917 3753 EN M. Daeichi Center of Excellence in Design, Robotics and Automation, Mechanical Engineering Department, Sharif University of Technology, Azadi Ave, PO 11365-11155, Tehran, Iran M.T. Ahmadian Center of Excellence in Design, Robotics and Automation, Mechanical Engineering Department, Sharif University of Technology, Azadi Ave, PO 11365-11155, Tehran, Iran Journal Article 2015 03 03    In this paper nonlinear vibration of transversely vibrated beam with large slenderness and immovable ends is analyzed using Variational Iteration Method (VIM). The nonlinear partial differential equation of motion is converted to a set of coupled ordinary differential equations using Galerkin technique. Two mode expansion for the system response is considered and second order analytical solution of the equations is obtained using VIM. Two algebraic coupled equations are also developed to find the nonlinear frequencies of the system. Numerical Simulations are performed for various initial conditions. Close agreement between the numerical and analytical results is achieved. Also the frequency analysis is performed for a range of initial amplitudes of vibration. https://scientiairanica.sharif.edu/article_3753_6c74571a61a48e0a1ae27790f473cd96.pdf