Dynamic testing of nonlinear vibrating structures using nonlinear normal modes |
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Authors: | M Peeters G Kerschen |
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Institution: | Structural Dynamics Research Group, Department of Aerospace and Mechanical Engineering, University of Liège, 1 Chemin des Chevreuils (B52/3), B-4000 Liège, Belgium |
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Abstract: | 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. |
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