Application of AG method and its improvement to nonlinear damped oscillators

Abstract

In this paper, a new and innovative semi analytical technique, namely Akbari-Ganji's method (AGM), is employed for solving three nonlinear damped oscillatory systems. Applying this method to nonlinear problems is very simple because in solving process only a trial solution, the main differential equation and its derivatives are required. The analytical solutions obtained by the AGM are utilized to study the impact of amplitude on nonlinear frequency and damping ratio. It is found that the AGM leads to acceptable results for the problems considered in this paper. Also, in order to obtain a more accurate solution, instead of using a trial solution with higher-order terms which may result in complicated and time consuming mathematical calculations, the solution obtained by AGM is improved via variational iteration method (VIM). The usefulness and effectiveness of the approach is demonstrated through comparison of the obtained results with those achieved by the numerical method. Hence, the AGM can be applied to nonlinear problems consisting of significant nonlinear damping terms and, if necessary, can be easily improved.