On the numerical computation of nonlinear normal modes for reduced-order modelling of conservative vibratory systems
| Autor: | Jean-François Mercier, Kerem Ege, Cyril Touzé, François Blanc, A.-S. Bonnet Ben-Dhia |
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| Přispěvatelé: | Unité de Mécanique (UME), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Dynamique des Fluides et Acoustique (DFA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Vibrations Acoustique (LVA), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), centre Lyonnais d'Acoustique (CeLyA), Université de Lyon |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Computation
Invariant manifold numerical computation Aerospace Engineering 02 engineering and technology nonlinear vibrations 01 natural sciences 0203 mechanical engineering Control theory Normal mode 0103 physical sciences invariant manifold Invariant (mathematics) 010301 acoustics Civil and Structural Engineering Mathematics [PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] reduced-order models Mechanical Engineering Numerical analysis Mathematical analysis nonlinear normal modes [SPI.MECA.VIBR]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph] Manifold Computer Science Applications Nonlinear system 020303 mechanical engineering & transports Control and Systems Engineering Signal Processing Center manifold |
| Zdroj: | Mechanical Systems and Signal Processing Mechanical Systems and Signal Processing, Elsevier, 2013, 36 (2), pp.520-539. ⟨10.1016/j.ymssp.2012.10.016⟩ Mechanical Systems and Signal Processing, 2013, 36 (2), pp.520-539. ⟨10.1016/j.ymssp.2012.10.016⟩ |
| ISSN: | 0888-3270 1096-1216 |
| DOI: | 10.1016/j.ymssp.2012.10.016⟩ |
| Popis: | International audience; Numerical computation of Nonlinear Normal Modes (NNMs) for conservative vibratory systems is addressed, with the aim of deriving accurate reduced-order models up to large amplitudes. A numerical method is developed, based on the center manifold approach for NNMs, which uses an interpretation of the equations as a transport problem, coupled to a periodicity condition for ensuring manifold's continuity. Systematic comparisons are drawn with other numerical methods, and especially with continuation of periodic orbits, taken as reference solutions. Three di erent mechanical systems, displaying peculiar characteristics allowing for a general view of the performance of the methods for vibratory systems, are selected. Numerical results show that invariant manifolds encounter folding points at large amplitude, generically (but not only) due to internal resonances. These folding points involve an intrinsic limitation to reduced-order models based on the center manifold and on the idea of a functional relationship between slave and master coordinates. Below that amplitude limit, numerical methods are able to produce reduced-order models allowing for a precise prediction of the backbone curve. |
| Databáze: | OpenAIRE |
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