Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time–frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.