References of "Bergman, Lawrence A"
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See detailUsing passive nonlinear targeted energy transfer to stabilize drill-stringsystems
Viguié, Régis ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in International Colloquium on Non-Linear Dynamics of Deep Drill-String Systems, Liège, 2009 (2009)

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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 detailSUPPRESSION OF AEROELASTIC INSTABILITIES BY BROADBAND PASSIVE TARGETED ENERGY TRANSFERS
Lee, Young S.; McFarland, D. Michael; Vakakis, Alexander F. et al

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

We study passive and nonlinear targeted energy transfers induced by transient resonant interactions between an essentially nonlinear attachment and an in-flow rigid wing model. We show that it is feasible ... [more ▼]

We study passive and nonlinear targeted energy transfers induced by transient resonant interactions between an essentially nonlinear attachment and an in-flow rigid wing model. We show that it is feasible to partially or even completely suppress aeroelastic instabilities in the wing (limit cycle oscillations-LCOs) by passively transferring broadband vibration energy from the wing to the attachment in a one-way irreversible fashion. We study the nonlinear dynamical mechanisms that govern TET and show that they are series of transient or sustained resonance captures in different resonance manifolds of the dynamics. Aeroelastic instability suppression is performed by partially or completely eliminating the triggering mechanism for aeroelastic instability. Through numerical parametric studies we identify three main mechanisms for suppressing aeroelastic instability, and investigate them in detail, both numerically by Empirical Mode decomposition (EMD), and analytically by slow/fast partitions of the transient dynamics. [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 detailTheoretical Understanding of Targeted Energy Transfers for Suppressing Aeroelastic Instabilities in a Nonlinear Aeroelastic Test Apparatus
Lee, Young S.; McFarland, D. Michael; Kerschen, Gaëtan ULg et al

in 45th Technical Meeting of the Society of Engineering Science, Urbana Champaign, 2008 (2008)

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See detailEnhancing robustness of aerolastic instability suppression using MDOF energy sinks
Lee, Young S.; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in AIAA Journal (2008), 46(6), 1371-1394

In this last of a three paper sequence, we use simultaneous multimodal broadband targeted energy transfers to multi-degree-of-freedom nonlinear energy sinks to improve the robustness of aeroelastic ... [more ▼]

In this last of a three paper sequence, we use simultaneous multimodal broadband targeted energy transfers to multi-degree-of-freedom nonlinear energy sinks to improve the robustness of aeroelastic instability suppression of a rigid wing with structural nonlinearities. A numerical bifurcation analysis of limit cycle oscillations of the wing with the multi-degree-of-freedom nonlinear energy sinks attached shows that controlling the lower parameter value for limit point cycle bifurcation to occur above Hopf bifurcation is crucial to enhancing the robustness of limit cycle oscillation suppression. We demonstrate that multi-degree-of-freedom nonlinear energy sinks can greatly enhance the robustness of limit cycle oscillation suppression, compared with single-degree-of-freedom nonlinear energy sinks (which were studied in our previous papers), with a much smaller total mass.We also investigate the nonlinear modal interactions that occur between the aeroelastic modes and the multi-degree-of-freedom nonlinear energy sinks, in an effort to gain a physical understanding of the mechanisms governing instability suppression. We demonstrate that a properly designed multi-degree-of-freedom nonlinear energy sink provides robustness of aeroelastic instability suppression by efficiently, passively, and rapidly transferring a significant portion of unwanted vibration energy to the furthest mass of the nonlinear energy sink. Consideration of other types of multi-degree-of-freedom nonlinear energy sinks suggests that the robustness enhancement is achieved by the concentrated mass effect of the attached nonlinear energy sinks. [less ▲]

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See detailIdentification of the Slow-Flow Dynamics of Transonic Aeroelastic Response from Time-Series Data
Lee, Y. S.; Vakakis, Alexander F.; McFarland, D. M. et al

in 45th Technical Meeting of the Society of Engineering Science, Urbana Champaign, 2008 (2008)

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See detailEmpirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems
Lee, Young S; McFarland, D. Michael; Vakakis, Alexander F. et al

in 49th AIAA Structural Dynamics and Materials Conference, Shaumberg, 2008 (2008)

A relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of ... [more ▼]

A relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identification of a planar rigid airfoil [less ▲]

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See detailTargeted Energy Transfers for Suppressing Aeroelastic Instability due to Unsteady Lift
Vakakis, Alexander F.; Bergman, Lawrence A.; McFarland, D. M. et al

in AVT-152 Symposium on Limit Cycle Oscillations, Norway, 2008 (2008)

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See detailEfficiency of Targeted Energy Transfers in Coupled Nonlinear Oscillators Associated with 1:1 Resonance Captures
Sapsis, T.; Vakakis, Alexander F.; Gendelman, O. V. et al

in 45th Technical Meeting of the Society of Engineering Science, Urbana Champaign, 2008 (2008)

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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 detailEnhancing Robustness of Instability Suppression by Means of Multi-Degree-of-Freedom Nonlinear Energy Sinks
Lee, Young S.; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, 2007 (2007, April)

Multi-degree-of-freedom nonlinear energy sinks (MDOF NESs) are utilized to improve robustness of suppression of limit cycle oscillations (LCOs) due to aeroelastic instability. Bifurcation analysis by a ... [more ▼]

Multi-degree-of-freedom nonlinear energy sinks (MDOF NESs) are utilized to improve robustness of suppression of limit cycle oscillations (LCOs) due to aeroelastic instability. Bifurcation analysis by a numerical continuation technique shows that controlling occurrence of a limit point cycle (LPC or saddle-node) bifurcation point above a Hopf bifurcation point is crucial to enhancing robustness. Not only greatly can MDOF NESs enhance the robustness of suppression against even strong external disturbances, but they can also yield a similar e±ciency even with a smaller mass, compared to the SDOF NESs with the same parameter conditions. Nonlinear modal interactions between the aeroelastic modes and the MDOF NES are examined to demonstrate e±ciency of the MDOF NES. [less ▲]

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See detailTheoretical and experimental study of multimodal targeted energy transfer in a system of coupled oscillators
Kerschen, Gaëtan ULg; Kowtko, Jeffrey J.; McFarland, D. Michael et al

in Nonlinear Dynamics (2007), 47

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated ... [more ▼]

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment. [less ▲]

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See detailIdentification of Linear and Nonlinear Systems using Signal Processing Techniques
Kerschen, Gaëtan ULg; Poncelet, Fabien ULg; Golinval, Jean-Claude ULg et al

in 26th Benelux Meeting on Systems and Control, Lommel, 2007 (2007)

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See detailWING-FLUTTER MITIGATION BY TARGETED ENERGY TRANSFERS INDUCED BY AN ESSENTIALLY NONLINEAR ATTACHMENT
Lee, Young S.; McFarland, D. Michael; Kerschen, Gaëtan ULg et al

in International Symposium on Recent Advances in Mechanics, Dynamical Systems and Probability Theory, Palermo, 2007 (2007)

The problem to be addressed here is the mitigation of limit cycle oscillations (LCO) in a rigid in-°ow wing with nonlinear heave and pitch sti®nesses in quasi-steady °ow, using targeted energy transfer ... [more ▼]

The problem to be addressed here is the mitigation of limit cycle oscillations (LCO) in a rigid in-°ow wing with nonlinear heave and pitch sti®nesses in quasi-steady °ow, using targeted energy transfer (TET). We show through simulation and Wavelet transforms that LCO formation is a process of resonance capture, with heave response triggering the pitch LCO. With the addition of a lightweight, fully passive attachment { a nonlinear energy sink (NES) { to the wing, we analytically predict three distinct mechanisms for LCO mitigation: repeated suppressed burst-outs, partial and complete suppressions of aeroelastic instability. Subsequent wind-tunnel experiments conducted in the Nonlinear Aeroelastic Test Apparatus (NATA) at Texas A&M University fully support these results. [less ▲]

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See detailUsing Targeted Energy Transfer to Stabilize Drill-string Systems
Viguié, Régis ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in 25th International Modal Analysis Conference, Orlando, 2007 (2007)

Torsional vibration of the drill strings used in drilling oil and gas wells arises from a complex interaction of the dynamics of the drilling structure with speed-dependent effective rock-cutting forces ... [more ▼]

Torsional vibration of the drill strings used in drilling oil and gas wells arises from a complex interaction of the dynamics of the drilling structure with speed-dependent effective rock-cutting forces. These forces are often difficult to model, and contribute substantially to the problems of controlling the drilling operation so as to produce steady cutting. We consider here the use of a nonlinear energy sink (NES) , an attachment which has been shown to be effective in reducing or even eliminating self-excited motions in van der Pol and aeroelastic systems. The NES is a completely passive, inherently broadband vibration absorber capable of attracting and dissipating vibrational energy from primary structures, in this case nonlinear discontinuous models of drill-string systems. In this paper we describe a prototypical drill string-NES system, briefly discuss some of the analytical and computational tools suitable for its analysis, and then concentrate on mathematical results on the efficacy of the NES in this application and their physical Interpretation. [less ▲]

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See detailPASSIVE SUPPRESSION OF AEROELASTIC INSTABILITIES OF IN-FLOW WINGS BY TARGETED ENERGY TRANSFERS TO LIGHTWEIGHT ESSENTIALLY NONLINEAR ATTACHMENTS
lee, Young S.; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in International Forum on Aerolasticity and Strucural Dynamics, Stockholm, 2007 (2007)

Theoretical and experimental suppression of aeroelastic instabilities by means of broadband passive targeted energy transfers has been recently studied. A single-degree-offreedom (SDOF) nonlinear energy ... [more ▼]

Theoretical and experimental suppression of aeroelastic instabilities by means of broadband passive targeted energy transfers has been recently studied. A single-degree-offreedom (SDOF) nonlinear energy sink (NES) was coupled to a 2-DOF rigid wing modeled in the low-speed, subsonic regime with quasi-steady aerodynamic theory. The nonlinear attachment was designed and optimized to suppress the critical nonlinear modal energy exchanges between the flow and the (pitch and heave) wing modes, thus suppressing the (transient) triggering mechanism of aeroelastic instability. We performed bifurcation analysis to find regions of robust passive aeroelastic suppression in parameter space. Then, we employed multi-degreeof-freedom nonlinear energy sinks (MDOF NESs) to improve robustness of the aeroelastic instability suppression. Bifurcation analysis by a numerical continuation technique demonstrated that controlling the occurrence of a limit point cycle (LPC or saddle-node) bifurcation point above a Hopf bifurcation point is crucial to enhancing suppression robustness. MDOF NESs not only can enhance robustness of suppression against even strong gust-like disturbances, but they require lower NES mass compared to SDOF NES designs. The validity of the theoretical findings was proven by a series of wind tunnel experiments. [less ▲]

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See detailThe slow-flow method of identification in nonlinear structural dynamics
Kerschen, Gaëtan ULg; Vakakis, Alexander F.; Lee, Young.S et al

in Smart Str. and Mat. & Nondestructive Eval. and Health Mon., San Diego, 2007 (2007)

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode ... [more ▼]

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flowmodel identification method, which is demonstrated using numerical examples. [less ▲]

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See detailTOWARDS MULTI-SCALE NONLINEAR (AND LINEAR) SYSTEM IDENTIFICATION IN STRUCTURAL DYNAMICS
Kerschen, Gaëtan ULg; Lee, Young-Sup; Vakakis, Alexander F. et al

in 8th HSTAM International Congress on Mechanics, Patras, 2007 (2007)

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental oscillatory components, termed the intrinsic mode functions ... [more ▼]

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental oscillatory components, termed the intrinsic mode functions (IMFs). In this presentation, we describe a combination of methods involving numerical integral transforms and theoretical analysis that cumulate to a new nonparametric method for nonlinear system identification based on multiple slow-fast partitions of the dynamics. This method can find wide applicability to linear and (weakly or strongly) nonlinear systems with various damping and/or stiffness nonlinearities. Moreover, through this method we can systematically examine transient resonance captures in the responses of dynamically interacting nonlinear structures, hence, decomposing and identifying the underlying multimodal nonlinear modal interactions that give rise to complex phenomena. [less ▲]

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