Modal Testing of Nonlinear Vibrating Structures Based on a Nonlinear Extension of Force Appropriation Available to Purchase

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis 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 investigated in this study in order to isolate one single NNM during the experiments, similarly to what is carried out for ground vibration testing. With the help of time-frequency analysis, the modal curves and the corresponding backbones are then extracted from the time series. The proposed methodology is demonstrated using a numerical benchmark, which consists of a planar cantilever beam with a cubic spring at its free end.