Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures

Abstract : Non-linear normal modes (NNMs) are used in order to derive accurate reduced-order models for large amplitude vibrations of structural systems displaying geometrical non-linearities. This is achieved through real normal form theory, recovering the definition of a NNM as an invariant manifold in phase space, and allowing definition of new co-ordinates non-linearly related to the initial, modal ones. Two examples are studied: a linear beam resting on a non-linear elastic foundation, and a non-linear clamped-clamped beam. Throughout these examples, the main features of the NNM formulation will be illustrated: prediction of the correct trend of non-linearity for the amplitude-frequency relationship, as well as amplitude-dependent mode shapes. Comparisons between different models - using linear and non-linear modes, different number of degrees of freedom, increasing accuracy in the asymptotic developments - are also provided, in order to quantify the gain in using NNMs instead of linear modes.
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Cyril Touzé, Olivier Thomas, Alexis Huberdeau. Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures. Computers and Structures, Elsevier, 2004, 82 (31-32), pp.2671-2682. ⟨10.1016/j.compstruc.2004.09.003⟩. ⟨hal-00830691⟩

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