The use of He’s variational iteration method for obtaining the free vibration of an Euler–Bernoulli beam

This paper presents a way of using He’s variational iteration method to solve free vibration problems for an Euler–Bernoulli beam under various supporting conditions. By employing this technique, the beam’s natural frequencies and mode shapes can be obtained and a rapidly convergent sequence is obtained during the solution. The results obtained are the same as the results obtained by the Adomian decomposition method. It is verified that the present method is accurate and it provides a simple and efficient approach for solving vibration problems for uniform Euler–Bernoulli beams. A robust and efficient algorithm is also programmed using Matlab based on the present method, which can be easily used to solve Euler Bernoulli beam problems.