Analysis of cubic nonlinear vibration equation with different perturbation methods

In this thesis, a nonlinear vibration equation in the study were discussed. In section 1, this problem is obtained vibration equation. In section 2, dimensional vibration equation is normalized because it contains the vibration parameter. In section 3, multiple scales methods of solution methods are explained and dimensionless equations are solved with multiple scales method. Then the perturbation-iteration algorithms described and the equation solved with perturbation iteration algorithms. Multiple scales solution methods , PIA(1,1) solution, PIA(1,2) solution were compared with numerical solutions. This three different perturbation solutions were compared with each other and it focuses on different methods for ℇ, μ and a0 values between advantages or disadvantages.