Relating backbone curves to the forced responses of nonlinear systems

Backbone curves describe the steady-state responses of unforced, undamped systems, therefore they do not directly relate to any specific forcing and damping configuration. Nevertheless, they can be used to understand the underlying dynamics of nonlinear systems subjected to forcing and damping. Building on this concept, in this paper we describe an analytical technique used to predict the onset of internally-resonant modal interactions in an example system. In conjunction with backbone curve analysis, which can be used to predict the possibility of internally-resonant behaviour, this approach provides an analytical tool for understanding and quantifying internally-resonant regions in the forced responses.