Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

Abstract

Abstract The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging method and Krylov-Bogoliubov (KB) transformation presented by new notations of matrices. The bifurcation function is derived to investigate its dynamic behaviour by singularity theory. The results obtained provide guidance for the nonlinear vibration of symmetric coupled nonlinear oscillators model with clearance.