Semi-Analytical Solution for Nonlinear Maglev Oscillation using the Lindstedt's Perturbation Method

Abstract

This paper focuses on the development of an approach for solving nonlinear mechanical maglev oscillation systems. The original physical information included in the governing equations is mostly transferred into analytical and numerical solutions. The analytical method based on the Lindstedt’s perturbation method is used and compared to general numerical solution using the direct Runge-Kutta integration. General procedures for nonlinear oscillation problems are formulated in detail for allocation in the dynamic analysis. Nonlinear oscillation systems with cubic nonlinearities are solved to demonstrate the applications of the present approach. The works reveal that the employed analytical solution can be used for the nonlinear analysis as good as the numerical Runge-Kutta method. The studies also provide an explanation on the behavior of the oscillation system with high nonlinearity. The secondary amplitudes of the higher nonlinearities only occur at the minimum/maximum amplitude of the systems with small or no nonlinearities.