References of "Kerschen, Gaëtan"
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See detailToward a fundamental understanding of the HHT in nonlinear structural dynamics
Kerschen, Gaëtan ULg; Vakakis, Alexander F.; Lee, Y. S. et al

in 24th International Modal Analysis Conference, Saint-Louis, 2006 (2006)

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-flow model identification method, which is demonstrated using numerical examples. [less ▲]

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See detailIrreversible passive energy transfer in coupled oscillators with essential nonlinearity
Kerschen, Gaëtan ULg; Lee, Young Sup; Vakakis, Alexander F. et al

in SIAM Journal on Applied Mathematics (2006), 66(2), 648-679

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 by either 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 by either 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 at both 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 ungrounded essentially nonlinear end attachment discussed in this work can find application in numerous practical settings, including vibration and shock isolation of structures, seismic isolation,. utter suppression, and packaging. [less ▲]

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See detailNonlinear MDOF system characterization and identi cation using the Hilbert-Huang transform
Kerschen, Gaëtan ULg; Vakakis, Alexander F.; Lee, Young.S et al

in International Conference on Noise and Vibration Engineering, Leuven, 2006 (2006)

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems thanks to the extraction of backbone curves from ... [more ▼]

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, it is inherently limited to the analysis of single-degree-of-freedom systems. In this study, the joint application of the complexification-averaging method and the empirical mode decomposition enables us to develop a new technique, the slow-flow model identification method. Through numerical and experimental applications, we demonstrate that the proposed method is adequate for characterizing and identifying multi-degree-offreedom nonlinear systems. [less ▲]

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See detailDevelopment of Numerical Algorithms for Practical Computation of Nonlinear Normal Modes
Peeters, Maxime ULg; Georgiades, Fotios; Viguié, Régis ULg et al

in International Conference on Noise and vibration Engineering, Leuven, 2006 (2006)

When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the ... [more ▼]

When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a nonlinear bladed disk is considered to demonstrate the developments. [less ▲]

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See detailNonlinear energy pumping: a new paradigm for vibration mitigation
Kerschen, Gaëtan ULg; Lee, Young-Sup; McFarland, D. M. et al

in 7ème congrès national de Mécanique Th. et App., Mons, 2006 (2006)

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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 detailExperimental modal analysis using blind source separation techniques
Poncelet, Fabien ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in International Conference on Noise and Vibration Engineering, Leuven, 2006 (2006)

Recently, statistical and empirical signal processing techniques such as the proper orthogonal decomposition and the Hilbert-Huang transform have shown promise for structural system identification. In the ... [more ▼]

Recently, statistical and empirical signal processing techniques such as the proper orthogonal decomposition and the Hilbert-Huang transform have shown promise for structural system identification. In the present study, experimental modal analysis is carried out by employing blind source separation techniques and by interpreting the response of a mechanical system as a static mixture of sources. Specifically, it is shown under which circumstances the normal coordinates of the vibration modes may be interpreted as virtual sources. The advantages and limitations of the proposed method will be discussed, and the procedure will be demonstrated using numerical applications. [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, J. J.; McFarland, D. M. et al

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

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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 detailPARTICIPATION OF UNDERGRADUATE STUDENTS TO THE SOLAR PANELS DESIGN OF THE EDUCATIONAL SPACECRAFT ESEO
Bolland, M.; Collignon, G.; Vandenplas, X. et al

Conference (2006)

The objective of this presentation is to discuss the participation of students at the University of Liège to the educational spacecraft project SSETI-ESEO proposed by the European Space Agency.

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See detailTriggering mechanisms of limit cycle oscillations due to aeroelastic instability
Lee, Y. S.; Vakakis, Alexander F.; Bergman, Lawrence A. et al

in Journal of Fluids & Structures (2005), 21

We show that a cascade of resonance captures constitutes the triggering mechanism of limit cycle oscillations (LCOs) due to aeroelastic instability of rigid wings in flow. We consider a two-degree-of ... [more ▼]

We show that a cascade of resonance captures constitutes the triggering mechanism of limit cycle oscillations (LCOs) due to aeroelastic instability of rigid wings in flow. We consider a two-degree-of-freedom (2-dof) wing model in subsonic flow with cubic nonlinear stiffnesses at the support. Under the assumption of quasi-steady aerodynamics, we apply a complexification/averaging technique to express the dynamics of fluid-structure interactions in terms of three fast-frequency components; these are the two linear natural frequencies corresponding to heave and pitch, and a superharmonic at three times the pitch frequency. Bifurcation analysis of the resulting set of modulation equations governing the slow dynamics is carried out via the method of numerical continuation, and reveals the different types of steady state motions realized as parameters vary. It turns out that the LCO triggering mechanism consists of a combination of different dynamic phenomena, taking place at three main stages or regimes: attraction to transient resonance captures (TRCs), escapes from these captures and, finally, entrapments into permanent resonance captures (PRCs). We examine numerically and analytically the dynamics at each of these stages by means of wavelet transform analysis, study of the evolution of appropriately defined phase variables in projections of the phase space of the dynamics, and analysis of instantaneous energy exchanges between the various nonlinear modes involved. The general conclusion is that an initial excitation of the heave mode by the flow acts as the triggering mechanism for the excitation of the pitch mode through nonlinear interactions resulting from the resonance captures and escapes. The eventual excitation of the pitch mode signifies the appearance of an LCO of the in-flow wing. (c) 2005 Elsevier Ltd. All rights reserved. [less ▲]

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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 detailSecond-order blind identification for operational modal analysis
Poncelet, Fabien ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

Conference given outside the academic context (2005)

For modal analysis of large structures, it is unpractical and expensive to use artificial excitation (e.g., shakers). However, engineering structures are most often subject to ambient loads(e.g., traffic ... [more ▼]

For modal analysis of large structures, it is unpractical and expensive to use artificial excitation (e.g., shakers). However, engineering structures are most often subject to ambient loads(e.g., traffic and wind) that can be exploited for modal parameter estimation. One difficulty is that the actual loading conditions cannot generally be measured, and output-only measurements are available. This paper proposes to explore the utility of blind source separation (BSS) techniques for operational modal analysis. The basic idea of BSS is to recover unobserved source signals from their observed mixtures. The feasibility and practicality of the proposed method are demonstrated using an experimental application. [less ▲]

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See detailDynamic analysis of the nonlinear behavior of MEMS using the finite element formulation
Rochus, Véronique ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

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

The dynamic response of a mass-spring model of electrostatically actuated MEMS is analyzed when a voltage step is applied. The dynamics of a clamped-clamped beam representing a micro-bridge system are ... [more ▼]

The dynamic response of a mass-spring model of electrostatically actuated MEMS is analyzed when a voltage step is applied. The dynamics of a clamped-clamped beam representing a micro-bridge system are also considered. To model and simulate the strong coupling between the electric and mechanical fields, a general finite element program has been developed based on a new monolithic formulation. The methodology proposed in this program does not require any iterative numerical scheme based on separate electrostatic and mechanical solvers, respectively. [less ▲]

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See detailSurprisingly complicated dynamics of a SDOF linear oscillator coupled to a nonlinear attachment
Lee, Young Sup; Kerschen, Gaëtan ULg; 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 the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on ... [more ▼]

We study the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on non-smooth temporal transformations to determine its periodic solutions in a frequency–energy plot. It turns out that there is a sequence of periodic solutions bifurcating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using the complexification / averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. [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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See detailExperimental irreversible passive energy transfer in coupled nonlinear oscillators
McFarland, D. Michael; Kerschen, Gaëtan ULg; Kowtko, Jeffrey J. et al

in Fifth EUROMECH Nonlinear Dynamics Conference, Eindhoven, 2005 (2005, August)

Experimental verification of passive nonlinear energy pumping in two configurations of coupled oscillators with essential nonlinearities is carried out. In the experiments presented the nonlinear ... [more ▼]

Experimental verification of passive nonlinear energy pumping in two configurations of coupled oscillators with essential nonlinearities is carried out. In the experiments presented the nonlinear attachment interacts with a single linear mode, and passive targeted energy transfer occurs at a single ‘fast’ frequency in the neighborhood of the eigen frequency of a linear mode. Good agreement between simulated and experimental results is observed, in spite of the strongly (essentially) nonlinear and transient nature of the dynamics of the systems considered. The experiments bear out earlier predictions that a significant fraction of the energy introduced directly to a linear structure by an external impulsive (broadband) load can be transferred (pumped) to an essentially nonlinear attachment, and dissipated there locally without spreading back to the system. In addition, the reported experimental results confirm that (a) nonlinear energy pumping in systems of coupled oscillators can occur only above a certain threshold of the input energy, and (b) there is an optimal value of the energy input at which a maximum portion of the energy is absorbed and dissipated at the NES. [less ▲]

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