hal-00830691
https://ensta-paris.hal.science/hal-00830691
https://ensta-paris.hal.science/hal-00830691/document
https://ensta-paris.hal.science/hal-00830691/file/CS2003NNMS_hal.pdf
doi:10.1016/j.compstruc.2004.09.003
[ENSTA] ENSTA Paris
[CNAM] Conservatoire National des Arts et Métiers
[ENSTA_UME] Unité de Mécanique
[LMSSC-CNAM] Laboratoire de mécanique des structures et des systèmes couplés
Asymptotic non-linear normal modes for large-amplitude vibrations of continuous structures
Touzé, Cyril
Thomas, Olivier
Huberdeau, Alexis
[PHYS.MECA.GEME] Physics [physics]/Mechanics [physics]/Mechanical engineering [physics.class-ph]
[SPI.MECA.GEME] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph]
ART
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.
2004
2015-06-04
en
Computers & Structures
Elsevier