Application of variational iteration method to large vibration analysis of slenderness beams considering mid-plane stretching

In this paper, the nonlinear vibration of transversely vibrated beams with large slenderness and immovable ends is analyzed using the Variational Iteration Method (VIM). The nonlinear partial dierential equation of motion is converted to a set of coupled ordinary dierential equations using the Galerkin technique. A two mode expansion for the system response is considered and a second order analytical solution of the equations is obtained using VIM. Two algebraic coupled equations are also developed to nd 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, a frequency analysis is performed for a range of initial amplitudes of vibration.