Article (Scientific journals)
Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures:Part II, analytical study
Sapsis, T. P.; Vakakis, Alexander F.; Gendelman, O. V. et al.
2009In Journal of Sound and Vibration
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Keywords :
Efficiency oftargetedenergytransfers; nonlinear oscillators associated; Hamiltoniandynamicsofthissystem; quasiperiodicorbits
Abstract :
[en] We study targeted energy transfer in a two degree-of-freedom damped system under the conditionof1:1transient resonance capture. The system consists of a linear oscillator strongly coupled to an essentially nonlinear attachment or nonlinear energy sink. In a companion paper[ Quinnetal., Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with1:1resonance captures: part I, Journal of Sound and Vibration 311 (2008)1228–1248]we studied the under lying structure of the Hamiltonian dynamics of this system ,and showed that for sufficiently small values of viscous damping , nonlinear damped transitions are strongly influenced by the under lying topological structure of periodic and quasi periodic or bits of the Hamiltonian system. In this work direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed through slow/fast partitions of the transient responses, in order to investigate analytically the parameter region of optimal targeted energy transfer .To this end, we determine the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broad band energy from the linear oscillator. Then, we prove that optimal targeted energy transfer is realized for initial energies close to the neighbourhood of a homo clinic or bit of the under lying Hamiltonian system. We study analytically transient orbits resulting as perturbations of the homo clinic or bit in the weak lydamped system, and show that this yields an additional slow-time scale in the averaged dynamics, and leads to optimal targeted energy transfer from the linear oscillator to the nonlinear energy sink in a single ‘‘super-slow’’ half-cycle. We show that at higher energies, this ‘‘super-slow’’ half-cycle is replaced by strong nonlinear beats, which lead to significant but suboptimal targeted energy transfer efficiency. Finally, we investigate numerically targeted energy transfer efficiency in this system over a wide range of system parameter sand verify the analytical predictions. 2009 Elsevier Ltd .All rights reserved.
Disciplines :
Physics
Engineering, computing & technology: Multidisciplinary, general & others
Mechanical engineering
Author, co-author :
Sapsis, T. P.;  MassachusettsInstituteofTechnology,USA > Department of Mechanical Engineering,
Vakakis, Alexander F.;  National Technical University of Athens, Greece > Department of Applied Mathematicaland Physical Sciences,
Gendelman, O. V.;  University of Illinois at Urbana-Champaign,USA > Department of Mechanical and Industrial Engineering
Bergman, L. A.;  University of Illinois at Urbana-Champaign,USA > Department of Mechanical and Industrial Engineering
Kerschen, Gaëtan  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Quinn, D. D.
Language :
English
Title :
Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1:1 resonance captures:Part II, analytical study
Publication date :
February 2009
Journal title :
Journal of Sound and Vibration
ISSN :
0022-460X
eISSN :
1095-8568
Publisher :
Academic Press, London, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 10 August 2009

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