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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 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 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 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 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 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 detailIdentifying Triggering Mechanisms and Suppressing Aeroelastic Instabilities by Passive Targeted Energy Transfers: Nonlinear System Identification, Modal Interactions and Resonance Captures
Lee, Young S; Vakakis, Alexander F.; McFarland, D. M. et al

in 44th Aeroelasticity and Fluid/Structure Interaction Symposium, College Station, 2007 (2007)

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See detailSuppression of limit cycle oscillations with a nonlineart energy sink: theoretical basis
Lee, Young S.; Vakakis, Alexander F.; McFarland, D. Michael et al

in 47th AIAA Structural Dynamics and Materials Conference, Newport, 2006 (2006, May)

Limit cycle oscillations (LCOs) commonly require restrictions on the operation of high- performance aircraft and have the potential to cause structural damage or failure. This paper summarizes recent ... [more ▼]

Limit cycle oscillations (LCOs) commonly require restrictions on the operation of high- performance aircraft and have the potential to cause structural damage or failure. This paper summarizes recent theoretical findings on the application of passive and targeted nonlinear energy transfer (\nonlinear energy pumping") for the reduction or elimination of LCOs in self-excited systems. This NES has been used successfully to suppress LCOs of an elastically mounted, rigid airfoil in flow. The theoretical results are in agreement with experimental studies of a practical airfoil with an attached NES. These experimental results, presented in full in a separate paper, verify the capacity of the NES to reduce or even eliminate these undesired oscillations and to extend the operating speed range of the wing. [less ▲]

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See detailExperimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity
Kerschen, Gaëtan ULg; McFarland, D. Michael; Kowtko, Jeffrey J. et al

in Journal of Sound & Vibration (2006), 299(4-5), 822-838

The purpose of this paper is to report an experimental study of transient resonance capture that may occur in a system of two coupled oscillators with essential (i.e., nonlinearizable) nonlinearity. It is ... [more ▼]

The purpose of this paper is to report an experimental study of transient resonance capture that may occur in a system of two coupled oscillators with essential (i.e., nonlinearizable) nonlinearity. It is shown that during transient resonance capture the two oscillators are in a state of resonance, the frequency of which varies with time, which leads to targeted nonlinear energy transfer. Further evidence of resonance capture is a non-time-like behavior of the phase difference between the oscillators; this quantity is monitored using the Hilbert transform or the Huang Hilbert transform in the case of multifrequency response signals. (c) 2006 Elsevier Ltd. All rights reserved. [less ▲]

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See detailSuppression of limit cycle oscillations with a nonlinear energy sink: experimental results
Hill, W. Joel; Strganac, Thomas W.; Lee, Young S. et al

in 47th AIAA Structural Dynamics and Materials Conference, Newport, 2006 (2006)

The presence of limit cycle oscillations within the flight envelopes of existing aircraft is well documented. Future air vehicle designs are also likely to encounter limit cycle oscillations under certain ... [more ▼]

The presence of limit cycle oscillations within the flight envelopes of existing aircraft is well documented. Future air vehicle designs are also likely to encounter limit cycle oscillations under certain loading conditions. These steady-state constant amplitude oscillations are detrimental to mission effectiveness and lead to increased fatigue of aircraft structures. Previous efforts to suppress limit cycle oscillations have focused primarily on active control methods. These efforts have been effective but require significant measurement and control resources. In this study the investigators test a passive method for suppressing limit cycle behavior. A nonlinear energy sink, based on the principle of nonlinear energy pumping, is shown to be effective for increasing the stability threshold of a nonlinear two degree of freedom aeroelastic system. [less ▲]

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See detailAn Overview of Targeted Energy Transfer Phenomena in Coupled Oscillators: Theoretical and Experimental Results and System Identification
Lee, Young S.; Kerschen, Gaëtan ULg; McFarland, D. M. et al

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

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See detailTARGETED ENERGY TRANSFERS AND SUPPRESSION OF AEROELASTIC INSTABILITIES
Lee, Young S; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in 2nd International Conf. on NNMs and Localization in Vibrating Systems, Samos, 2006 (2006)

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See detailEnergy transfers in a system of two coupled oscillators with essential nonlinearity: 1 : 1 resonance manifold and transient bridging orbits
Kerschen, Gaëtan ULg; Vakakis, Alexander F.; Lee, Young S. et al

in Nonlinear Dynamics (2005), 42(3), 283-303

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear ... [more ▼]

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. [less ▲]

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See detailIrreversible passive TEF in the damped response of coupled oscillators with nonlinearity
Kerschen, Gaëtan ULg; Lee, Young S.; Vakakis, Alexander F. et al

in ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, 2005 (2005, September)

We study, numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused either by fundamental or ... [more ▼]

We study, numerically and analytically the dynamics of passive energy transfer from a damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused either by fundamental or subharmonic resonance capture, and in some cases is initiated by nonlinear beat phenomena. It is shown that, due to the essential nonlinearity, the end attachment is capable of passively absorbing broadband energy both at high and low frequencies, acting, in essence, as a passive broadband boundary controller. Complicated transitions in the damped dynamics can be interpreted based on the topological structure and bifurcations of the periodic solutions of the underlying undamped system. Moreover, complex resonance capture cascades are numerically encountered when we increase the number of degrees of freedom of the system. The grounded, essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation, flutter suppression and packaging. [less ▲]

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See detailTriggering mechanisms of limit cycle oscillations in a 2DOF wing flutter model
Lee, Young S.; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Long Beach, 2005 (2005, September)

We show numerically that the triggering mechanisms of limit cycle oscillations (LCOs) due to aeroelastic instability are composed of a series of resonance captures. We consider a two degree-of-freedom ... [more ▼]

We show numerically that the triggering mechanisms of limit cycle oscillations (LCOs) due to aeroelastic instability are composed of a series of resonance captures. We consider a two degree-of-freedom (DOF) wing model with cubic nonlinear stiffnesses in the support, assuming quasi-steady aerodynamics and subsonic flow around the wing. Then, we establish the slow flow dynamics model, using the complexification / averaging technique and considering three frequency components; i.e., the two linear natural frequencies corresponding to heave and pitch and the superharmonic component which appears as three times the pitch frequency. It turns out that the LCO triggering mechanisms consist of mainly three stages: (i) transient resonance capture (TRC); (ii) escape; and (iii) permanent resonance capture (PRC). We examine the characteristics of each stage by way of time response, wavelet transform, phase plane, and instantaneous energy. [less ▲]

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See detailExperimental investigation of targeted energy transfers in strongly and nonlinearly coupled oscillators
McFarland, D. Michael; Kerschen, Gaëtan ULg; Kowtko, Jeffrey J. et al

in Journal of the Acoustical Society of America (2005), 118(2), 791-799

Our focus in this study is on experimental investigation of the transient dynamics of an impulsively loaded linear oscillator coupled to a lightweight nonlinear energy sink. It is shown that this ... [more ▼]

Our focus in this study is on experimental investigation of the transient dynamics of an impulsively loaded linear oscillator coupled to a lightweight nonlinear energy sink. It is shown that this seemingly simple system exhibits complicated dynamics, including nonlinear beating phenomena and resonance captures. It is also demonstrated that, by facilitating targeted energy transfers to the nonlinear energy sink, a significant portion of the total input energy can be absorbed and dissipated in this oscillator. (C) 2005 Acoustical Society of America. [less ▲]

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