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Efficient Targeted Energy Transfer in Coupled Nonlinear Oscillators Through 1:1 Transient Resonance Captures

Oleg Gendelman, Alexander Vakakis, Themistoklis Sapsis, Dane Quinn, Lawrence Bergman, Gaetan Kerschen
We study targeted energy transfer (TET) in a two degree-of-freedom damped system caused by 1 : 1 transient resonance capture. The system consists of a linear oscillator strongly coupled to an essentially nonlinear attachment. First, we study the underlying structure of the Hamiltonian dynamics of the system, and then show that, for sufficiently small values of viscous damping, the nonlinear damped transitions are strongly influenced by the underlying topological structure of periodic and quasiperiodic orbits of the hamiltonian system. Then, a detailed computational study of the different types of nonlinear transitions that occur in the weakly damped system is presented. As a result of these studies, conditions that lead to effective or even optimal TET from the linear system to the nonlinear attachment are determined. Finally, direct analytical treatment of the governing strongly nonlinear damped equations of motion
is performed through slow/fast partition of the transient responses, in order to analytically model the dynamics the region of optimal TET, 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.
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