He's Iteration Perturbation Method to Nonlinear Oscillations of Mechanical Systems With Single-Degree-of Freedom

In this study, an accurate analytical solution for the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities is derived. This solution has been obtained using Iteration Perturbation method (IPM). This study shows that IPM leads to an accurate analytical solution, which is valid for a wide range of considered system parameters. The excellent accuracy of current results is demonstrated by comparing with available analytical and numerical results.