Nonlinear Analysis of Coupled Duffing Oscillators Based on Variable Step-Size Adomian Decomposition Method

Abstract

In this paper, variable step-size Adomian Decomposition Method (VADM) is proposed to obtain approximate analytical solution of coupled Duffing oscillators. Using VADM, analytical expressions for two-degree-of-freedom coupled Duffing equations are derived for different amplitude values of external periodic excitation. The system stability is analyzed by analyzing time-domain graph and phase portraits. Compared with the MATLAB@ ODE45, simulation results reveal that VADM is effectively and well suited for nonlinear dynamic system.