Solutions of strong nonlinear dynamics problems using perturbation methods

In this work, MSLP method which is valid for strong nonlinear systems will be applied to nonlinear dynamic problems. The new method is an combination of Method of Multiple Scales and Lindstedt-Poincare Method. In Lindstedt Poincare technique, some transformations and straightforward expansions are made and the solutions valid for strong nonlinear systems are obtained. However, the Lindstedt Poincare technique works for fixed-amplitude problems. The perturbation solutions of strong nonlinear systems for the systems that have variable amplitude are not be obtained. By making some improvements with the MSLP method in multiple scales method, Physical solutions have been produced which can be applied both in constant amplitude and in variable amplitude conditions. The MSLP method is first applied to ordinary differential equations and then to partial differential equations. Multiple time scale method has been applied to the same equations and the approximate solutions are compared with numerical solutions. This comparison is made using Wolfram Mathematica and MATLAB package programs. For strong nonlinear systems,the result that the MSLP method produced solutions with good agreement with the numerical solutions is achieved.