Reference : APPLYING L. MANEVITCH’S COMPLEXIFICATION – AVERAGING METHOD TO ANALYZE CONDITIONS FOR...
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Mechanical engineering
Physical, chemical, mathematical & earth Sciences : Physics
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/18891
APPLYING L. MANEVITCH’S COMPLEXIFICATION – AVERAGING METHOD TO ANALYZE CONDITIONS FOR OPTIMAL TARGETED ENERGY TRANSFER IN COUPLED OSCILLATORS WITH ESSENTIAL STIFFNESS NONLINEARITY
English
Sapsis, Themistoklis [> >]
Quinn, D. Dane [> >]
Gendelman, Oleg [> >]
Vakakis, Alexander. F. [> >]
Bergman, Lawrence A. [> >]
Kerschen, Gaëtan mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux >]
Jul-2008
International Conference on Nonlinear Phenomena in Polymer Solids and Low-Dimensional Systems. Moscou, 2008
No
International
International Conference on Nonlinear Phenomena in Polymer Solids and Low-Dimensional Systems
July, 7–10, 2008
NPPS-2008
Moscow
Russia
[en] Bifurcations ; Modeling
[en] We study targeted energy transfer (TET) [1] from a linear damped oscillator (LO) to a light attachment with essential stiffness nonlinearity, caused by 1:1 transient resonance capture (TRC). First, we study the underlying Hamiltonian dynamics and show that for sufficiently weak damping, the nonlinear damped transitions of the system are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the hamiltonian system. Then, we formulate conditions that lead to effective or even optimal TET from the linear system to the nonlinear attachment. Direct analytical treatment of the governing strongly nonlinear damped equations of motion is performed by applying L. Manevitch’s complexification – averaging (CX-A) method [2] to perform slow-fast partition of the transient responses, and analytically model the dynamics in the region of optimal TET. This analysis determines 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 in an optimal fashion.
Researchers ; Professionals ; Students
http://hdl.handle.net/2268/18891

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