Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the variational iteration method

Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.