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4TITRE et RESUME en anglais:Expérimental non-linear modal analysisIntroducing modal analysis in the context of non-linear mechanical structures may appearlike a paradox. That because the several methods which can be put behind this term apply oniyin the case where the system under study can be considered like a linear one. Gathering "modalbases" by means of these widely spread methods is very useful in the domain of engineeringfor many reasons : dynamic caracterisation of structures, response prediction, sub-structuring,model updatingIn the meantime, the extension of the vibration mode concept, developed in the 60's, to aparticular class of non-linear systems is less known. Linear systems' modes appear then as aparticular case of non-linear modes which are defined as motions with some particularities andwhose existence have been verified. More recently, several advancement, mostly analytical, havebeen carried out in the study of dynamical systems using non-linear normal modes.Actual structures often exhibit some non-linear behavior that may lead to potential difficultiesin modeling and analysis. So, it seems important, to look for the usefulness, the applicabilityand the efficiency of methods based on extended modal concepts in an experimental and industrialcontext.In this work, some non-linear normal mode computing technics are shown and applied toexperimental, and afterwards to industrial cases, after some appropriate vibratory tests.We show some possibilities and some limits in the experimental analysis of vibrating structuresusing non-linear modal concepts.DISCIPLINE:MécaniqueMOTS-CLES:MODES NON-LINEAIRES, IDENTIFICATION, EXPERIMENTAL, ANALYSE MODALE.INTITULE ET ADRESSE DU LABORATOIRE:Laboratoire de Tribologie et de Dynamique des Systèmes (LTDS)Ecole Centrale de lyon36 avenue Guy de Collongue69134 Ecully CedexFRANCE
Table des matièresIntroductioni Les modes normaux de Rosenberg1.1 Introduction1.2 Systèmes et mouvements admissibles1.2.1 Systèmes admissibles1.2.2 Mouvements admissibles1.2.3 Equations des trajectoires admissibles1.3 Modes normaux des systèmes admissibles1.3.1 Définition des modes normaux1.3.2 Caractérisation géométrique des modes normaux1.3.3 Existence et obtention des modes non linéaires1.3.4 Equations modales1.3.5 Bifurcation et surabondance des modes normaux1.3.6 Stabilité des modes de Rosenberg1.4 Réponse en oscillations forcées1.4.1 Vibrations à l'unisson du système forcé1.4.2 Résonances au voisinage des modes1.5 Conclusion2 Approximation des modes non-linéaires2.1 Introduction2.2 Oscillations en mode normal2.2.1 Forme de l'approximation2.2.2 Expression des modes non-linéaires dans la base modale linéaire2.2.3 Normalisation des modes2.3 Calcul des modes normaux non-linéaires2.3.1 Problème aux valeurs propres non-linéaire2.3.2 Non-linéarité unique2.3.3 Non-linéarités multiples2.3.4 Calcul des modes à l'aide de réponses forcées2.4 Exemples, calcul des modes2.4.1 Système discret comportant une seule non-linéarité2.4.2 Système comportant plusieurs non-linéarités2.4.3 Systèmes continus2.5 Réponses forcées81111111112131414151619202222222427292930303133343436363838384243495
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Page 12 and 13: 6 TABLE DES MATIÈRES2.5.1 Introduc
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m2x2+c2x2+k2(x2xl)+k3(x2x3)+a2(x2--
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Chapitre 4Analyse des phénomènesn
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78 CHAPITRE 4. ANALYSE DES PHÉNOM
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Chapitre 5Identification non-linéa
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98 CHAPITRE 5. IDENTIFICATION NON-L
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looCHAPITRE 5. IDENTIFICATION NON-L
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102 CHAPITRE 5. IDENTIFICATION NON-
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Chapitre 6Application industrielle6
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140 CHAPITRE 6. APPLICATION IND UST
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142 CHAPITRE 6. APPLICATION INDUSTR
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156 CONCLUSION GÉNÉRALEConclusion
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Table des figures1.1 Mouvements adm
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160 TABLE DES FIG URES5.3 Méthode
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Bibliographie[ 1] T.J. Anderson, B.
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164 BIBLIOGRAPHIEL. Jézequel. Synt
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J.C. Slater. A numerical method for
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RESUME:L'introduction de l'analyse
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