Nonlinear Vibration Analysis of a cantilever beam with nonlinear geometry

Analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. According to this, an impressive analytical method which is called Modified Iteration Perturbation Method (MIPM) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. This new method is combined by the Mickens and Iteration methods. Moreover, this method don’t require small parameter in the equation which is difficult to be found for nonlinear oscillation. The accuracy of the solution that is obtained by using of MIPM has been shown graphically and compared with exact solution. Comparison shows that good adaptation is obtained and MIPM is a powerful method for solving the vibrational behavior of structures analytically.