References of "Kerschen, Gaëtan"
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See detailThe method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: An overview
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg; Vakakis, Alexander F. et al

in Nonlinear Dynamics (2005), 41(1-3), 147-169

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New ... [more ▼]

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study. [less ▲]

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See detailComplex dynamics of a linear oscillator with a nonlinear attachment
Lee, Young Sup; Kerschen, Gaëtan ULg; Vakakis, Alexander F. et al

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

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness ... [more ▼]

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. 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 (energy pumping) 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 detailMulti-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments
Tsakirtzis, Stylianos; Kerschen, Gaëtan ULg; Panagopoulos, Panagiotis et al

in Journal of Sound & Vibration (2005), 285(1-2), 483-490

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous ... [more ▼]

We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multi-degree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. (c) 2004 Elsevier Ltd. All rights reserved. [less ▲]

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See detailStructural damage diagnosis under varying environmental conditions - Part I: A linear analysis
Yan, Ai-Min; Kerschen, Gaëtan ULg; De Boe, Pascal et al

in Mechanical Systems & Signal Processing (2005), 19(4), 847-864

A damage detection method is proposed for structural health monitoring under varying environmental and operational conditions. The method is based on principal component analysis (PICA) applied to ... [more ▼]

A damage detection method is proposed for structural health monitoring under varying environmental and operational conditions. The method is based on principal component analysis (PICA) applied to vibration features identified during the monitoring of the structure. The advantage of the method is that it does not require to measure environmental parameters because they are taken into account as embedded variables. The number of principal components of the vibration features is implicitly assumed to correspond to the number of independent environmental factors. Since the environmental effects may be effectively eliminated by the proposed procedure, the residual error of the PCA prediction model remains small if the structure is healthy, and it increases significantly when structural damage occurs. Novelty analysis on the residual errors provides a statistical indication of damage. In the present paper, the environmental conditions are assumed to have a linear (or weakly non-linear) effect on the vibration features, and the PCA-based damage detection method is illustrated using computer-simulated and laboratory testing data. The extension of the proposed method to non-linear cases is addressed in a companion paper where the efficiency of the method is verified using data obtained from a 1-year in situ monitoring of a bridge. 2005 Elsevier Ltd. All rights reserved. [less ▲]

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See detailStructural damage diagnosis under varying environmental conditions - Part II: local PCA for non-linear cases
Yan, A. M.; Kerschen, Gaëtan ULg; De Boe, P. et al

in Mechanical Systems & Signal Processing (2005), 19(4), 865-880

It is well known that changes in vibration features of structures due to damage may be masked by the effects of environmental variations. This influence has to be eliminated in the structural health ... [more ▼]

It is well known that changes in vibration features of structures due to damage may be masked by the effects of environmental variations. This influence has to be eliminated in the structural health-monitoring process, especially when a long-term in situ monitoring is expected. In the companion paper [1] a linear method based on principal component analysis (PCA) has been proposed and has shown encouraging results for linear or even weakly non-linear cases. The present paper concerns a further extension of the proposed method to handle non-linear cases, which may be encountered in some complex structures. The method involves a two-step procedure, namely a clustering of the data space into several regions and then the application of PCA La each local region. The application of local PCA allows performing a piecewise linearisation of the non-linear problem. A close look at the choice of the distortion function used in data clustering leads to two new clustering strategies. Whereas the first strategy is specifically suitable for the application treated in this paper, the second one is more general. The local PCA-based damage detection method is applied for the structural health monitoring of a real bridge using vibration data measured in situ over a one-year period. 2005 Elsevier Ltd. All rights reserved. [less ▲]

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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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See detailComplicated dynamics of a linear oscillator with a light, essentially nonlinear attachment
Lee, Young Sup; Kerschen, Gaëtan ULg; Vakakis, Alexander F. et al

in Physica D: Nonlinear Phenomena (2005), 204(1-2), 41-69

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness ... [more ▼]

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. We consider first the undamped system and perform a numerical study based on non-smooth transformations to determine its periodic solutions in a frequency-energy plot. It is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using a 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 (energy pumping) from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]

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See detailDistortion function and clustering for local linear models
Kerschen, Gaëtan ULg; Yan, Ai Min; Golinval, Jean-Claude ULg

in Journal of Sound & Vibration (2005), 280(1-2), 443-448

Principal component analysis (PCA) is a ubiquitous statistical technique for data analysis. PCA is however limited by its linearity and may sometimes be too simple for dealing with real-world data ... [more ▼]

Principal component analysis (PCA) is a ubiquitous statistical technique for data analysis. PCA is however limited by its linearity and may sometimes be too simple for dealing with real-world data especially when the relations among variables are nonlinear. Recent years have witnessed the emergence of nonlinear generalizations of PCA, as for instance nonlinear principal component analysis (NLPCA) [1] or vector quantization principal component analysis (VQPCA) [2]. VQPCA involves a two-step procedure, namely a clustering of the data space into several regions and the application of PCA in each local region. In Ref. [3], VQPCA was applied for the reconstruction of dynamical response and it was shown that it is potentially a more effective tool than conventional PCA. The purpose of this technical note is to further investigate VQPCA and to have a closer look at the choice of the distortion function used for clustering the data space. [less ▲]

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See detailTransient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment
Vakakis, Alexander F.; Manevitch, Leonid I.; Musienko, Andrey I. et al

in Wave Motion (2005), 41(2), 109-132

We consider the dynamics of a dispersive semi-infinite linear rod weakly connected to an essentially nonlinear end attachment. Using a Green's function formulation we reduce the dynamics to an integro ... [more ▼]

We consider the dynamics of a dispersive semi-infinite linear rod weakly connected to an essentially nonlinear end attachment. Using a Green's function formulation we reduce the dynamics to an integro-differential equation, which we express in the form of an infinite set of ordinary differential equations using Neumann expansions. We examine resonant interactions of the attachment with incident traveling waves propagating in the pass band of the rod, as well as resonance capture phenomena where the attachment engages in transient 1:1 internal resonance with the in-phase mode of the rod, at the bounding frequency of its pass and stop bands. The studied resonant interactions of the nonlinear attachment with traveling waves are similar to resonance capture cascades occurring in finite-chain nonlinear attachment configurations; these are the transient dynamics of the attachment as it engages in a series of instantaneous resonances with a continuous spectrum of frequencies in the pass band of the medium. As the energy of the attachment decreases due to damping and energy radiation back to the rod, the attachment engages in 1:1 resonance capture with the in-phase mode of the rod; this resonance capture occurs due to the dispersion property in the linear medium. It is shown that the transient dynamics of resonance capture can be reduced to a set of two 'slow flow' amplitude and phase modulation equations. The analytical results are in agreement with direct numerical simulations. (C) 2004 Elsevier B.V. All rights reserved. [less ▲]

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See detailSensor validation using principal component analysis
Kerschen, Gaëtan ULg; De Boe, Pascal; Golinval, Jean-Claude ULg et al

in Smart Materials & Structures (2005), 14(1), 36-42

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or ... [more ▼]

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or maintenance activities. The problem of sensor validation is therefore a critical part of structural health monitoring. The objective of the present study is to present a procedure based on principal component analysis which is able to perform detection, isolation and reconstruction of a faulty sensor. Its efficiency is assessed using an experimental application. [less ▲]

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See detailGeneration of accurate finite element models of nonlinear systems - Application to an aeroplane-like structure
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in Nonlinear Dynamics (2005), 39(1-2), 129-142

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the ... [more ▼]

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure. [less ▲]

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See detailA 2-step methodology for the generation of accurate FE models of nonlinear systems,
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in ASME Internaional Mechanical Engineering Congress, Anaheim, 2004 (2004, November)

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the ... [more ▼]

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure. [less ▲]

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See detailA model updating strategy of non-linear vibrating structures
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in International Journal for Numerical Methods in Engineering (2004), 60(13), 2147-2164

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention ... [more ▼]

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention is devoted to the features extracted from the proper orthogonal decomposition and one of its non-linear generalizations based on auto-associative neural networks. The efficiency of the proposed procedure is illustrated using simulated data from a three-dimensional portal frame. Copyright (C) 2004 John Wiley Sons, Ltd. [less ▲]

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See detailComments on "interpreting proper orthogonal modes of randomly excited linear vibration systems"
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in Journal of Sound & Vibration (2004), 274(3-5), 1091-1092

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See detailFeature extraction using auto-associative neural networks
Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg

in Smart Materials & Structures (2004), 13(1), 211-219

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal ... [more ▼]

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal analysis is limited to structures showing a linear behaviour. In non-linear structural dynamics, it is well known that mode shapes are no longer useful for the characterization of the dynamic response. The purpose of the present paper is to define new features which efficiently capture the dynamics of a non-linear structure. The proposed methodology takes advantage of auto-associative neural networks to compute one-dimensional curves which allow for non-linear dependences between the coordinates. Synthetic data sampled from a non-linear normal mode motion are used to illustrate the method and to develop intuition about its implementation. [less ▲]

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See detailNonlinear energy pumpin: A new paradigm for vibration isolation
Vakakis, Alexander F.; McFArland, D. Michael; Kerschen, Gaëtan ULg et al

in 3rd China-Japan US Symposium on Health Mondial and Control of Structures, Dalian, 2004 (2004)

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively ... [more ▼]

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively absorb vibrational energy from the main structure in a one-way, irreversible fashion. We demonstrate the occurrence of pumping cascades, where an appropriately designed NES passively extracts energy sequentially from a number of modes of the main (linear) structure, interacting individually with each mode before moving to the next. Experimental results confirm our theoretical findings. The applications of the nonlinear energy pumping phenomenon to the problem of vibration and shock isolation will be discussed. [less ▲]

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See detailPassive energy transfer and dissipation for isolation from transcient broadband disturbances
Kerschen, Gaëtan ULg; McFarland, D. Michael; Kowtko, J. et al

in US-Korea Joint Seminar/Workshop on Smart Structures Technologies, Seoul, 2004 (2004)

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively ... [more ▼]

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively absorb vibrational energy from the main structure in a one-way, irreversible fashion. We demonstrate the occurrence of pumping cascades, where an appropriately designed NES passively extracts energy sequentially from a number of modes of the main (linear) structure, interacting individually with each mode before moving to the next. Experimental results confirm our theoretical findings. The applications of the nonlinear energy pumping phenomenon to the problem of vibration and shock isolation will be discussed [less ▲]

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See detailValidation of two nonlinear system identification techniques using an experimental testbed
Lenaerts, V.; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in Shock and Vibration (2004), 11(3-4), 365-375

The identification of a nonlinear system is performed using experimental data and two different techniques, i.e. a method based on the Wavelet transform and the Restoring Force Surface method. Both ... [more ▼]

The identification of a nonlinear system is performed using experimental data and two different techniques, i.e. a method based on the Wavelet transform and the Restoring Force Surface method. Both techniques exploit the system free response and result in the estimation of linear and nonlinear physical parameters. [less ▲]

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See detailSensor Validation for On-line Vibration Monitoring
Kerschen, Gaëtan ULg; De Boe, Pascal; Golinval, Jean-Claude ULg et al

in 2nd European Workshop on Structural Health Monitoring, Munich, 2004 (2004)

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or ... [more ▼]

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or maintenance activities. The problem of sensor validation is therefore a critical part or structural identification. The objective of the present study is to present a procedure based on principal component analysis, which is able to perform detection, isolation and reconstruction of a faulty sensor. Its e ciency is assessed using an experimental application. [less ▲]

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See detailProper Orthogonal modes for the characterisation of nonlinear dynamic systems
Kerschen, Gaëtan ULg; Lenaerts, Vincent; Golinval, Jean-Claude ULg et al

in Euromech Colloquim on Nonlinear Modes of Vibrating Systems, Frejus, 2004 (2004)

Modal analysis is extensively used for the analysis and design of structures. However, a major concern for structural dynamicists is that its validity is limited to systems showing a linear behaviour. New ... [more ▼]

Modal analysis is extensively used for the analysis and design of structures. However, a major concern for structural dynamicists is that its validity is limited to systems showing a linear behaviour. New developments have thus been proposed in order to tackle nonlinear systems among which the theory based on the nonlinear normal modes is indubitably the most appealing. In this study, a different approach is adopted and the modes extracted from the proper orthogonal decomposition are considered for the characterization of nonlinear systems. [less ▲]

Detailed reference viewed: 30 (2 ULg)