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Enforcing linear dynamics through the addition of nonlinearity
Habib, G.; Kerschen, Gaëtan; Grappasonni, C.
2016In Conference Proceedings of the Society for Experimental Mechanics Series
 

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Keywords :
Compensation of nonlinearity; Isochronicity; Linearization; Nonlinear normal modes; Perturbation; Linear systems; Nonlinear optics; Nonlinear systems; Structural dynamics; Compensation of nonlinearities; Geometrically nonlinear; Nonlinear structure; Numerical experiments; Oscillation amplitude; Dynamics
Abstract :
[en] The current trend of developing more slender structures is increasing the importance of nonlinearities in engineering design, which, in turn, gives rise to complicated dynamical phenomena. In this study, we evidence the somewhat paradoxical result that adding purposefully nonlinearity to an already nonlinear structure renders the behavior more linear. Isochronicity, i.e., the invariance of natural frequencies with respect to oscillation amplitude, and the force-displacement proportionality are two key properties of linear systems that are lost for nonlinear systems. The objective of this research is to investigate how these properties can be enforced in a nonlinear system through the addition of nonlinearity. To this end, we exploit the nonlinear normal modes theory to derive simple rules, yet applicable to real structures, for the compensation of nonlinear effects. The developments are illustrated using numerical experiments on a cantilever beam possessing a geometrically nonlinear boundary condition. © The Society for Experimental Mechanics, Inc. 2016.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Habib, G.;  Department of Aerospace and Mechanical Engineering, Space Structures and Systems Laboratory (S3L), Structural Dynamics Research Group, University of Liège, Liège, Belgium
Kerschen, Gaëtan  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Grappasonni, C.;  Department of Aerospace and Mechanical Engineering, Space Structures and Systems Laboratory (S3L), Structural Dynamics Research Group, University of Liège, Liège, Belgium
Language :
English
Title :
Enforcing linear dynamics through the addition of nonlinearity
Publication date :
2016
Event name :
34th IMAC, A Conference and Exposition on Structural Dynamics, 2016
Event date :
25 January 2016 through 28 January 2016
Main work title :
Conference Proceedings of the Society for Experimental Mechanics Series
Publisher :
Springer New York LLC
Pages :
11-18
Name of the research project :
307265
Funders :
CER - Conseil Européen de la Recherche [BE]
Commentary :
177419 9783319297385
Available on ORBi :
since 11 November 2017

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