%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