Reduced-order modeling for a cantilever beam subjected to harmonic forcing

Abstract : Large-amplitude vibrations of a clamped-free beam are considered. Reduced-order models (ROMs) are derived for this problem, within the framework of non-linear normal modes (NNMs), defined as invariant manifolds in phase space. The method of real normal form theory, which allows computation of all NNMs in a single operation, is used. A specific development enables to handle the non-linear inertia terms stemming from the large rotation beam model. The dynamics onto the manifold is derived up to order five. Non-linear mode shapes are exhibited, as well as frequency-amplitude relationships. Finally, the case of a harmonic base-excitation is considered.
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Cyril Touzé, Olivier Thomas. Reduced-order modeling for a cantilever beam subjected to harmonic forcing. EUROMECH 457, Nonlinear modes of vibrating systems, Jun 2004, Fréjus, France. ⟨hal-01154710⟩

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