%0 Journal Article %T Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures %+ Dynamique des Fluides et Acoustique (DFA) %+ Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC) %A Touzé, Cyril %A Thomas, Olivier %A Huberdeau, Alexis %< avec comité de lecture %@ 0045-7949 %J Computers & Structures %I Elsevier %V 82 %N 31-32 %P 2671-2682 %8 2004 %D 2004 %R 10.1016/j.compstruc.2004.09.003 %Z Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph] %Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]Journal articles %X 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. %G English %2 https://ensta-paris.hal.science/hal-00830691/document %2 https://ensta-paris.hal.science/hal-00830691/file/CS2003NNMS_hal.pdf %L hal-00830691 %U https://ensta-paris.hal.science/hal-00830691 %~ ENSTA %~ CNAM %~ ENSTA_UME %~ LMSSC-CNAM