Article (Scientific journals)
Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment
Lee, Young Sup; Kerschen, Gaëtan; Vakakis, Alexander F. et al.
2005In Physica D. Nonlinear Phenomena, 204 (1-2), p. 41-69
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Keywords :
resonance capture; essential nonlinearity; energy transfer
Abstract :
[en] We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. We consider first the undamped system and perform a numerical study based on non-smooth transformations to determine its periodic solutions in a frequency-energy plot. It is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using a complexification/averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer (energy pumping) from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. (c) 2005 Elsevier B.V. All rights reserved.
Disciplines :
Mechanical engineering
Mathematics
Physics
Author, co-author :
Lee, Young Sup
Kerschen, Gaëtan  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Vakakis, Alexander F.
Panagopoulos, Panagiotis
Bergman, Lawrence
McFarland, D. Michael
Language :
English
Title :
Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment
Publication date :
01 May 2005
Journal title :
Physica D. Nonlinear Phenomena
ISSN :
0167-2789
Publisher :
Elsevier Science Bv, Amsterdam, Netherlands
Volume :
204
Issue :
1-2
Pages :
41-69
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 10 August 2009

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