BEHAVIOR OF HARMONICS GENERATED BY A DUFFING TYPE EQUATION WITH A NONLINEAR DAMPING: PART II

Abstract

This paper is Part II of an earlier paper dealing with the numerical study of a two-dimensional nonautonomous ordinary differential equation with a strong cubic nonlinearity, and an external periodical excitation of period τ = 2π/ω (amplitude E). In the absence of this excitation, this equation of Duffing type does not give rise to self-oscillations. Part I was essentially devoted to analyze the harmonics behavior of period τ solutions, more precisely the behavior of rank-p harmonics according to the points of the parameter plane (ω,E). The present Part II deals with period kτ solutions related to a cascade of closed fold bifurcation curves related to fractional harmonics p/k, k = 3, p = 3,4,…. With respect to the organization of bifurcation curves associated with rank-p harmonics of the basic period τ, this study shows that the situation is a lot more complex for the sequence of bifurcation curves related to rank-p/3 harmonics.