Analytical periodic solution for solving nonlinear vibration equations

In this study a new kind of analytical methods called He's variational approach method is applied to solve strong nonlinear vibration equations. The He's variational approach method is very easy and contrary to the other conventional methods, only one iteration leads to high accuracy of the solutions for the whole range of initial amplitudes and does not demand small perturbation. Some examples are given to illustrate the effectiveness and convenience of the methodology. The Runge-Kutta's (RK) algorithm was also implemented to achieve the numerical solutions for the examples. The results reveal that the variational approach method is very effective and simple. It is predicted that the VAM can find wide application in engineering problems, as indicated in following examples.