In this paper, a mathematical model of large amplitude vibration of a uniform cantilever beam arising in the structural engineering is proposed. Two efficient and easy mathematical techniques called variational iteration method and He's variational approach are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. An excellent agreement of the approximate frequencies and periodic solutions with the numerical results and published results has been demonstrated. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He's Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.