Analytical solution of strongly nonlinear Duffing oscillators

In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter alpha = alpha(epsilon) is defined such that the value of alpha is always small regardless of the magnitude of the original parameter epsilon. Therefore, the strongly nonlinear Duffing oscillators with large parameter e are transformed into a small parameter system with respect to alpha. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter epsilon but also for large values of epsilon. (C) 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V.