Abstract :
[en] Modal testing and analysis is well-established for linear vibrating structures. While the common practice is to assume linear behavior, nonlinearity is a frequent occurrence in engineering applications and can drastically alter the behavior of mechanical systems. In this paper, an attempt is made to extend experimental modal analysis methodology to a practical nonlinear analog. 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. Based on a nonlinear extension of phase resonance testing (also called force appropriation), the proposed methodology excites the structure to isolate one single NNM during the experiments. Thanks to the invariance principle, the energy dependence of that nonlinear mode (i.e., the NNM modal curves and their frequencies of oscillation) can be extracted from the resulting free decay response using time-frequency analysis. The proposed method is demonstrated using an experimental cantilever beam with a geometrical nonlinearity.
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