Akbari–Ganji Method for Solving Equations of Euler–Bernoulli Beam with Quintic Nonlinearity

In many real word applications, beam has nonlinear transversely vibrations. Solving systems is complicated because of the high dependency system variables and boundary conditions. It important to have an accurate parametric analysis for understanding vibration characteristics. This paper presents approximate solution a vibrating with odd even terms using Akbari–Ganji Method (AGM). method effective approach solve differential equations. AGM already used in heat transfer science solving equations, this research first time, it applied find beam. The advantage creating new conditions additional predefined checked proposed case. To illustrate applicability accuracy AGM, governing equation beams treated different initial Since simply supported clamped-clamped structures can be encountered engineering these two are considered. periodic response curves natural frequency obtained by contrasted energy balance (EBM) numerical solution. results show that present excellent agreements contrast EBM calculations. most cases, straightforwardly obtain frequency– amplitude relationship dynamic behaviour beams. frequencies tested various values clearly stated applicable system. demonstrated technique saves computational time without compromising easily extended other therefore widely sciences.