A new method for solving Rayleigh differential equation

In this study, nonlinear differential equations governing vibrating beam columns with variable cross-section of the new method is applied to solve. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach which was named Akbari- Ganji's Method or AGM. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. According to the explanations given about the capabilities of this method (AGM), non-linear par- tial differential equations governing the vibration of the beam-column are investigated for dynamic systems.