Bifurcation of nonlinear normal modes in a class of two degree of freedom systems

Abstract

This work concerns the nonlinear vibrations of a class of two-degree-of-freedom autonomous conservative systems consisting of two coupled nonlinear oscillators with cubic coupling forces. For such a system, nonlinear normal modes (NNM’s) have long been studied as “vibrations in unison”, i.e. periodic motions in which x and y simultaneously achieve zero velocity. We investigate the stability and bifurcation of NNM’s by using a perturbation method together with the computer algebra system MACSYMA.