Fast–Slow Dynamics Analysis of a Coupled Duffing System with Periodic Excitation

Abstract

In this paper, a two-degree-of-freedom nonlinear coupled Duffing equation with an external excitation and two external excitations are studied. For the coupled Duffing system with periodic excitation, the system shows the dynamic behavior on different time scales when the excitation frequency and the inherent frequency of the system are different. Firstly, we discretize the system by using the Euler method, and the discrete equation is obtained. Secondly, the two external excitations are considered as slow variables that are transformed into a slow variable by the Moivre formula, which divides the original system into the fast–slow subsystem. Finally, the oscillation dynamic behavior of the coupled system is discussed by combining fast–slow analysis method and the transformation phase diagram.