Understanding the dynamics of multi-degree-of-freedom nonlinear systems using backbone curves

In this paper we will describe how backbone curves can be used to explain complex dynamic phenomena that can occur in coupled multi-degree-of-freedom physical systems. Three examples will be used to demonstrate some key points. We will describe cases when backbone curves can be decoupled. In the case of nonlinear resonance (or modal interaction) we explain how to distinguish how many modes are interacting, their unison and relative phase characteristics. Bifurcation of higher order interaction curves from the lower order curves will also be discussed. Finally we will consider an example based on the transverse vibration of a thin plate with pinned boundary conditions. Both finite element simulations and a low order differential equation model are developed for this system. The results show the importance of the nonlinear coupling terms in replicating the frequency shift phenomena which is known to occur in structures of this type. Despite its much smaller size, the low order model is able to show qualitative agreement with the finite element model. Knowledge of the backbone curve behaviour for this system, is used to explain the forced damped behaviour.