Reference : Efficiency of TET in coupled oscillators associated with 1: resonance: Part 1
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Engineering, computing & technology : Mechanical engineering
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Efficiency of TET in coupled oscillators associated with 1: resonance: Part 1
Quinn, D. Dane [The University of Akron > Department of Mechanical Engineering, > > >]
Gendelman, Oleg [Technion—Israel Institute of Technology > Faculty of Mechanical Engineering > > >]
Kerschen, Gaëtan mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux >]
Sapsis, Themistoklis P. [University of Cambridge > Department of Mechanical Engineering, Massachusetts Institute of Technology, > > >]
Bergman, Lawrence A. [University of Illinois at Urbana-Champaign > Department of Aerospace Engineering > > >]
Vakakis, Alexander F. [National Technical University of Athens > Department of Mechanical Science and Engineering > > >]
Journal of Sound and Vibration
Academic Press
Yes (verified by ORBi)
United Kingdom
[en] Efficiency of targeted energy transfers ; nonlinear oscillators ; resonance captures
[en] We study targeted energy transfers and nonlinear transitions in the damped dynamics of a two degree-of-freedom system of coupled oscillators (a linear oscillator with a lightweight, essentially nonlinear, ungrounded attachment), caused by 1:1 resonance captures of the dynamics. Part I of this work deals with the underlying structure of the Hamiltonian dynamics of the system, and demonstrates that, for sufficiently small values of viscous damping, the damped transitions are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the corresponding Hamiltonian system. Focusing exclusively on 1:1 resonance captures in the system, it is shown that the topology of these damped transitions affect drastically the efficiency of passive energy transfer from the linear system to the nonlinear attachment.
Then, a detailed computational study of the different types of nonlinear transitions that occur in the weakly damped system is presented, together with an analytical treatment of the nonlinear stability of certain families of periodic solutions of the underlying Hamiltonian system that strongly influence the said transitions. As a result of these studies, conditions on the system and forcing parameters that lead to effective or even optimal energy transfer from the linear system to the nonlinear attachment are determined. In Part II of this work, direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed, in order to analytically model the dynamics in the region of optimal energy transfer, and to determine the characteristic time scales of the dynamics that influence the capacity of the nonlinear attachment to passively absorb and locally dissipate broadband energy from the linear oscillator.
r 2007 Elsevier Ltd. All rights reserved
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