Relating Backbone Curves to the Forced Responses of Nonlinear Systems

Abstract

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.

Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems

“…The configuration under consideration in this paper is a non-symmetric, two-mass oscillator, with an underlying symmetric system of linear springs similar to that in [2,3,7]; a schematic is given in Figure 1. The two masses in the system are identical and their displacements are denoted x 1 and x 2 , respectively.…”

“…Doing so allows the underlying behaviour of the system to be captured and, although they are not related to any particular forced case, they can still be used to indicate the occurrence of internal resonance within the structure [7]. Further, the techniques need only minor adaptations to give the forced, damped responses.…”