TY - JOUR
T1 - Energy transfers in a system of two coupled oscillators with essential nonlinearity
T2 - 1:1 Resonance manifold and transient bridging orbits
AU - Kerschen, Gaetan
AU - Vakakis, Alexander F.
AU - Lee, Young S.
AU - McFarland, D. Michael
AU - Kowtko, Jeffrey J.
AU - Bergman, Lawrence A.
N1 - Funding Information:
This work was funded in part by AFOSR Contracts F49620-01-1-0208 and 00-AF-B/V-0813. The author G. Kerschen is supported by a grant from the Belgian National Fund for Scientific Research (FNRS) which is gratefully acknowledged. The support of the Fulbright and Duesberg Foundations which made his visit to the University of Illinois possible is also gratefully acknowledged. The authors would like to acknowledge Panagiotis Panagopoulos for his contributions to the problem.
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2005/11
Y1 - 2005/11
N2 - The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed.
AB - The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed.
KW - Energy transfer
KW - Essential nonlinearity
KW - Nonlinear beat phenomenon
KW - Nonlinear energy pumping
KW - Resonance capture
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U2 - 10.1007/s11071-005-4475-3
DO - 10.1007/s11071-005-4475-3
M3 - Article
AN - SCOPUS:27544508422
SN - 0924-090X
VL - 42
SP - 283
EP - 303
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 3
ER -