Experimentally measuring an isolated branch of Nonlinear normal modes

Nonlinear normal modes (NNMs) are a key tool for investigating the behaviour of nonlinear dynamic systems. Previous work has shown that branches of NNMs can be isolated from other NNM responses, in a similar manner to isolated, or detached, resonance curves in the forced responses. Their isolated nature poses a significant challenge for the prediction and measurement of these NNM branches. This paper illustrates how isolated NNMs may exist in two-degree-of-freedom systems, with cubic nonlinearities, that exhibit a 1:3 resonance. This is first introduced using a general two-mass oscillator, before considering a two-mode reduced-order model of a continuous cross-beam structure that exhibits a coupling between its primary bending and torsional modes. In both cases, a combination of analytical and numerical techniques is used to show how the isolated NNM branch may evolve from a set of bifurcating NNM branches. A nonlinear force appropriation technique is used to experimentally measure the NNMs of the cross-beam structure. By comparing these measurements to the numerical studies, it is shown that some of these NNMs are on the isolated branch, representing the first experimental confirmation of isolated NNM branches.