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Bridging the gap between Nonlinear Normal Modes and Modal Derivatives
Sombroek, Cees; Renson, Ludovic; Tiso, Paolo et al.
2015In Proceedings of the International Modal Analysis Conference (IMAC) XXXIII
 

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Keywords :
Model Reduction; Nonlinear Normal Modes; Modal Derivatives; Quadratic Manifold Transformation
Abstract :
[en] Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associated with NNMs is that their calculation for large-scale models is expensive, particularly for distributed nonlinearities. Repeated direct time integrations need to be carried out together with extensive sensitivity analysis to reproduce the frequency-energy dependence of the modes of interest. In the present paper, NNMs are computed from a reduced model obtained using a quadratic transformation comprising LNMs and Modal Derivatives (MDs). Previous studies have shown that MDs can capture the essential dynamics of geometrically nonlinear structures and can greatly reduce the computational cost of time integration. A direct comparison with the NNMs computed from another standard reduction technique highlights the capability of the proposed reduction method to capture the essential nonlinear phenomena. The methodology is demonstrated using simple examples with 2 and 4 degrees of freedom.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Sombroek, Cees;  Delft University of Technology > Dep. Precision and Microsystems Engineering
Renson, Ludovic ;  Université de Liège - ULiège > R&D Direction : Chercheurs ULiège en mobilité
Tiso, Paolo;  Delft University of Technology > Dep. Precision and Microsystems Engineering
Kerschen, Gaëtan  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Bridging the gap between Nonlinear Normal Modes and Modal Derivatives
Publication date :
February 2015
Event name :
International Modal Analysis Conference (IMAC) XXXIII
Event organizer :
Society for Experimental Mechanics (SEM)
Event place :
Orlando, United States - Florida
Event date :
du 2 février au 5 février 2015
Audience :
International
Main work title :
Proceedings of the International Modal Analysis Conference (IMAC) XXXIII
Name of the research project :
BeIPD-COFUND outgoing fellowship: Managing bifurcations of nonlinear mechanical systems using experimental continuation techniques
Funders :
UE - Union Européenne [BE]
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