An Analytical Technique for Solving Second Order Strongly Damped Nonlinear Oscillator with a Fractional Power Restoring Force

Abstract

In this thesis, an analytical technique has been developed for solving strongly nonlinear damped systems with 1/ 3 x restoring force by combining He’s homotopy perturbation method (HPM) and the extended form of the Krylov-Bogoliubov-Mitropolskii (KBM) method. The presented method has been justified by an example. We have also established the relationship between amplitude and approximate angular frequency. In this study, the presented technique gives desired results avoiding any numerical complexity. Graphical representation of any physical system is important. So, approximate solutions are compared with those numerical solutions obtained by fourth order Runge-Kutta method in graphically. The results in figures show that the approximations are of extreme accuracy with small and significant damping. The presented method is simple and suitable for solving the above mentioned nonlinear damped systems.