References of "Gendelman, Oleg"
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See detailAPPLYING L. MANEVITCH’S COMPLEXIFICATION – AVERAGING METHOD TO ANALYZE CONDITIONS FOR OPTIMAL TARGETED ENERGY TRANSFER IN COUPLED OSCILLATORS WITH ESSENTIAL STIFFNESS NONLINEARITY
Sapsis, Themistoklis; Quinn, D. Dane; Gendelman, Oleg et al

in International Conference on Nonlinear Phenomena in Polymer Solids and Low-Dimensional Systems. Moscou, 2008 (2008, July)

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 ... [more ▼]

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. [less ▲]

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See detailImpulsive periodic and quasi-period orbits in coupled oscillators with essential nonlinearity
Kerschen, Gaëtan ULg; Gendelman, Oleg; Vakakis, Alexander F. et al

in Communications in Nonlinear Science & Numerical Simulation (2008), 13

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi ... [more ▼]

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi-periodic dynamics of the undamped system forced by a single impulse on the linear oscillator and being initially at rest, by considering separately low-, moderateand high-energy impulsive motions. The motivation for studying the impulsive dynamics of this system centers on passive targeted energy transfer properties of the corresponding weakly damped one, that is, of the possibility of one-way, irreversible transfer of energy from the linear oscillator to the nonlinear attachment. A rather surprising aspect of this work is the complexity of the analysis required to study the impulsive dynamics of this system, due to its high degeneracy, as it undergoes a co-dimension three bifurcation. 2006 Elsevier B.V. All rights reserved. [less ▲]

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See detailEfficiency of TET in coupled oscillators associated with 1: resonance: Part 1
Quinn, D. Dane; Gendelman, Oleg; Kerschen, Gaëtan ULg et al

in Journal of Sound & Vibration (2008), 311

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 ... [more ▼]

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 [less ▲]

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See detailEfficient targeted energy transfers in coupled nonlinear oscillators through 1:1 transcient resonance captures:
Sapsis, Themistoklis; Quinn, D. Dane; Gendelman, Oleg et al

in Sixth EUROMECH Nonlinear Dynamics Conference, Saint Petersbourg, 2008 (2008)

We study targeted energy transfer (TET) in a two degree-of-freedom damped system caused by 1:1 transient resonance capture (TRC). The system consists of a linear oscillator strongly coupled to an ... [more ▼]

We study targeted energy transfer (TET) in a two degree-of-freedom damped system caused by 1:1 transient resonance capture (TRC). 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. [less ▲]

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See detailComplex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments
Tsakirtzis, Stylianos; Panagopoulos, Panagiotis; Kerschen, Gaëtan ULg et al

in Nonlinear Dynamics (2007), 48(3), 285-318

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment ... [more ▼]

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency-energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. [less ▲]

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See detailEnergy Transition from a Linear Oscillator to an Attached Mass through an Essential Nonlinearity
Quinn, D. Dane; Kerschen, Gaëtan ULg; Vakakis, Alexander F. et al

in 11th Nonlinear Vib., Stability and Dynamics of Structures Conf., Blacksburg, 2006 (2006)

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See detailMulti-frequency passive non-linear targeted energy transfers in systems of couples oscillators
Tsakirtzis, Stylianos; Panagopoulos, Panagiotis; Kerschen, Gaëtan ULg et al

in 5th GRACM International Congress on Computational Mechanics, Limassol, 2005 (2005, June)

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment ... [more ▼]

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment with damping can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible, over wide frequency and energy ranges. We numerically demonstrate that the topological structure of the periodic orbits in the frequency – energy plane of the underlying hamiltonian system greatly influences the strength of targeted energy transfer in the damped system, and governs to a great extent the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. [less ▲]

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