Analytical solution of strongly nonlinear Duffing oscillators

Alexandria Engineering Journal

A.M. El-Naggar¹  G.M. Ismail² 

[1] Department of Mathematics, Faculty of Science, Benha University, Egypt;Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt;

关键词: Analytical solution;    Perturbation technique;    Strongly nonlinear Duffing oscillators;   

DOI  :  10.1016/j.aej.2015.07.017

来源: DOAJ

【 摘 要 】

In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. 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 εbut also for large values of ε.

【 授权许可】

Unknown