On the approximate analytical solution for parametrically excited nonlinear oscillators

In this study we have analytically analyzed the vibration of parametrically excited oscillators based on Mathieu-Duffing equation. He’s Variational iteration method (VIM) is applied to obtain analytical solution, while Runge-Kutta method is used to obtain the numerical solution. It is demonstrated that VIM is very effective and convenient therefore may find wide applicability in engineering and other sciences. Finally, to confirm the validity of the applied method, the results of VIM are compared with those obtained by Runge-Kutta method. The results from VIM indicate an excellent agreement with the numerical solutions.