Nonlinear Analysis of a Large-Amplitude Forced Harmonic Oscillation System using Differential Transformation Method-Padé Approximant Technique

This work presents the nonlinear analysis of forced harmonic oscillation system using differential transformation method-Padé approximant techniques. Without any series expansion of the included sine and cosine of the angular displacement in the nonlinear model of the system, an improved analytical solution of the dynamic model is presented. The high level of accuracy and validity of the analytical solutions obtained by the differential transformation method are shown through comparison of the results of the solution with the corresponding numerical solutions obtained by fourth-fifth-order Runge-Kutta method, homotopy perturbation method and energy balance methods. Also, with the aid of the analytical solutions, parametric studies are carried to study the impacts of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The method avoids any numerical complexity and it is very simple, suitable and useful as a mathematical tool for dealing the nonlinear problems.