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See detailNonlinear normal modes of real-world structures: application to a full-scale aircraft
Peeters, Maxime ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in Proceedings of the ASME International Design Engineering Technical Conferences (2011)

The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this ... [more ▼]

The objective of this paper is to demonstrate that the numerical computation of the nonlinear normal modes (NNMs) of complex real-world structures is now within reach. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft, whose ground vibration tests have exhibited some nonlinear structural behaviors. The finite element model of this aircraft, elaborated from drawings, has more than 80000 degrees of freedom, and softening nonlinearities exist in the connection between the external fuel tanks and the wing tips. From this model, a reduced-order model, which is accurate in the [0-100Hz] range, is constructed using the Craig- Bampton technique. The NNMs of the reduced model are then computed using a numerical algorithm combining shooting and pseudo-arclength continuation. The results show that the NNMs of this full-scale structure can be computed accurately even in strongly nonlinear regimes and with a reasonable computational burden. Nonlinear modal interactions are also highlighted by the algorithm and are discussed. [less ▲]

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See detailNonlinear normal modes, Part 1: Useful framework for the structural dynamicist
Kerschen, Gaëtan ULg; Peeters, Maxime ULg; Golinval, Jean-Claude ULg et al

in Mechanical Systems & Signal Processing (2009), 23

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartII.BecausethereisvirtuallynoapplicationoftheNNMstolarge-scale engineeringstructures ... [more ▼]

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartII.BecausethereisvirtuallynoapplicationoftheNNMstolarge-scale engineeringstructures,thesepapersareanattempttohighlightseveralaspectsthat mightdrivetheirdevelopmentinthefuture.Specifically,wesupportthat(i)numerical methodsforthecontinuationofperiodicsolutionspavethewayforaneffectiveand practical computationofNNMs,and(ii)time–frequencyanalysisisparticularlysuitable fortheanalysisoftheresultingdynamics.Anotherobjectiveofthepresentpaperisto describe,insimpleterms,andtoillustratethefundamentalpropertiesofNNMs.Thisis achievedtoconvincethestructuraldynamicistnotnecessarilyacquaintedwiththemthat theyareausefulframeworkfortheanalysisofnonlinearvibratingstructures. & 2008ElsevierLtd.Allrightsreserved [less ▲]

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See detailNonlinear normal modes, Part 2: Toward a pratical computation using numerical continuation techniques
Peeters, Maxime ULg; Viguié, Régis ULg; Sérandour, Guillaume ULg et al

in Mechanical Systems & Signal Processing (2009), 23

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical ... [more ▼]

The conceptofnonlinearnormalmodes(NNMs)isdiscussedinthepresentpaperandits companion,PartI.OnereasonofthestilllimiteduseofNNMsinstructuraldynamicsis that theircomputationisoftenregardedasimpractical.However,whenresortingto numericalalgorithms,weshowthattheNNMcomputationispossiblewithlimited implementationeffort,whichpavesthewaytoapracticalmethodfordeterminingthe NNMsofnonlinearmechanicalsystems.Theproposedalgorithmreliesontwomain techniques,namelyashootingprocedureandamethodforthecontinuationofNNM motions. Thealgorithmisdemonstratedusingfourdifferentmechanicalsystems,a weakly andastronglynonlineartwo-degree-of-freedomsystem,asimplifieddiscrete modelofanonlinearbladeddiskandanonlinearcantileverbeamdiscretizedbythefinite elementmethod. [less ▲]

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See detailNonlinear Normal Modes, Part I: An Attempt To Demystify Them
Kerschen, Gaëtan ULg; Peeters, Maxime ULg; Golinval, Jean-Claude ULg et al

in 26th International Modal Analysis Conference, Orlando, 2008 (2008)

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering ... [more ▼]

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time-frequency analysis is particularly suitable for the analysis of the resulting dynamics. Another objective of the present paper is to describe, in simple terms, and to illustrate the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures. [less ▲]

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See detailNonlinear Normal Modes, Part II: Practical Computation using Numerical Continuation Techniques
Peeters, Maxime ULg; Viguié, Régis ULg; Sérandour, Guillaume et al

in 26th International Modal Analysis Conference, Orlando, 2008 (2008)

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is ... [more ▼]

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the 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 algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using two different mechanical systems, a nonlinear two-degree-of-freedom system and a nonlinear cantilever beam discretized by the finite element method. [less ▲]

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See detailNonlinear Normal Modes: A Finite Element Approach
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

Conference (2011)

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See detailNonlinear numerical analysis of ship impact on lock gates
Gernay, Thomas ULg

in Van Schel, L (Ed.) PIANC Yearbook 2010 (2011)

This paper focuses on ship impact analysis on lock gate. First, the lock gate structure is determined by an elastic design and optimization process. Then, a nonlinear numerical analysis by finite elements ... [more ▼]

This paper focuses on ship impact analysis on lock gate. First, the lock gate structure is determined by an elastic design and optimization process. Then, a nonlinear numerical analysis by finite elements is conducted to study the response of the lock gate in case of ship impact. It is shown that the elastically optimized structure is not able to resist significant impacts, because of the buckling of its reinforcement elements; the gate is thus reinforced. Finally, several ship impact analyses are conducted on the reinforced gate and they highlight the influence of the stiffener dimensions and the impact zone on the structural behavior of the gate. The results of the numerical analyses underline the importance of the development of a global plastic mechanism with the purpose of dissipating a large amount of energy. [less ▲]

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See detailNonlinear optical susceptibilities, Raman efficiencies, and electro-optic tensors from first-principles density functional perturbation theory
Veithen, M.; Gonze, X.; Ghosez, Philippe ULg

in Physical Review. B, Condensed Matter and Materials Physics (2005), 71

The nonlinear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach ... [more ▼]

The nonlinear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n+1 theorem applied to an electric-field-dependent energy functional. We report the expressions for the calculation of the nonlinear optical susceptibilities, Raman scattering efficiencies, and electro-optic (EO) coefficients. Different formulations of third-order energy derivatives are examined and their convergence with respect to the k-point sampling is discussed. We apply our method to a few simple cases and compare our results to those obtained with distinct techniques. Finally, we discuss the effect of a scissors correction on the EO coefficients and nonlinear optical susceptibilities. [less ▲]

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See detailThe nonlinear optical, magnetic, and Mossbauer spectral properties of some iron(III) doped silica xerogels
Rebbouh, L.; Rosso, Vanessa ULg; Renotte, Yvon ULg et al

in Journal of Materials Science (2006), 41(10), 2839-2849

Iron(III) species dispersed in silica have been synthesized with a sol-gel process. The iron(III) was introduced as the acetylacetonate complex into a solution of tetraethoxysilane to yield, after ... [more ▼]

Iron(III) species dispersed in silica have been synthesized with a sol-gel process. The iron(III) was introduced as the acetylacetonate complex into a solution of tetraethoxysilane to yield, after evaporative drying, pellets or monoliths. Two gels were dried very slowly over a period of five months in order to prepare a defect free monolith useful for nonlinear optical studies. Z-scan experimental studies on the resulting, transparent, monolithic, doped solid revealed an optical Kerr effect, a third order nonlinear optical phenomenon showing a linear dependence of the refractive index on the irradiance with a nonlinear refractive index, n(2), of -1.95 x 10(-11) cm(2)/W. Magnetic susceptibility studies between 4.2 and 295 K revealed paramagnetic behavior with a Curie constant of 4.433 (emu/mol)K and a Weiss temperature of -7.1 K. Magnetization studies at 5 K and at applied fields of up to 4 T and Mossbauer spectral studies between 4.2 and 295 K revealed a 50:50 mixture of paramagnetic species and nanoparticles with an average particle radius of 1.3 +/- 0.2 nm. A blocking temperature of 70 K and a magnetic anisotropy energy of 2.4 x 10(5) J/m(3) stop are derived from the Mossbauer spectra. (c) 2006 Springer Science + Business Media, Inc. [less ▲]

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See detailNonlinear regression with censored data
Heuchenne, Cédric ULg; Van Keilegom, Ingrid

in Technometrics (2007), 49(1), 34-44

Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + sigma(X)epsilon, where m(.) = E(Y vertical bar.) belongs to some parametric class (m(theta)(.):theta is an element of Theta ... [more ▼]

Suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + sigma(X)epsilon, where m(.) = E(Y vertical bar.) belongs to some parametric class (m(theta)(.):theta is an element of Theta) of regression functions, sigma(2)(.) = var(Y vertical bar.) is unknown, and e is independent of X. The response Y is subject to random right censoring, and the covariate X is completely observed. A new estimation procedure for the true, unknown parameter vector theta(0) is proposed that extends the classical least squares procedure for nonlinear regression to the case where the response is subject to censoring. The consistency and asymptotic normality of the proposed estimator are established. The estimator is compared through simulations with an estimator proposed by Stute in 1999, and both methods are also applied to a fatigue life dataset of strain-controlled materials. [less ▲]

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See detailNonlinear resonant transport of Bose-Einstein condensates
Paul, T.; Richter, K.; Schlagheck, Peter ULg

in Physical Review Letters (2005), 94(2),

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a ... [more ▼]

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales. [less ▲]

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See detailNonlinear Schrödinger wave equation with linear quantum behavior
Richardson, Christopher ULg; Schlagheck, Peter ULg; Martin, John ULg et al

in Physical Review. A (2014), 89

We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the ... [more ▼]

We show that a nonlinear Schro ̈dinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schro ̈dinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantumlike features appear and is equivalent to scaling Planck’s constant. [less ▲]

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See detailNonlinear Sensitivity Analysis of Biochemical Reaction Networks, by Bilinear Approximation
Streif, Stefan; Findeisen, Rolf; Bullinger, Eric ULg

in Proc. of the 2nd Foundations of Systems Biology in Engineering FOSBE 2007, 9–12 September, Stuttgart Germany (2007)

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See detailNonlinear Structural Dynamics: Theory, Simulation and Testing, KEYNOTE LECTURE
Kerschen, Gaëtan ULg

in Proceedings of the 18th Symposium on Vibrations, Shocks and Noise (2012)

Nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical phenomena that cannot be observed in linear structures. The analysis of the dynamics of ... [more ▼]

Nonlinearity is a frequent occurrence in engineering structures. It is at the origin of rich and complex dynamical phenomena that cannot be observed in linear structures. The analysis of the dynamics of nonlinear systems therefore warrants the development of rigorous and effective methods and is the focus of this presentation. Several theoretical, computational and experimental methods will be presented and applied to a real-life, full-scale nonlinear structure, the EADS- Astrium SmallSat spacecraft. [less ▲]

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See detailNonlinear System Identification in Structural Dynamics: A Short (and Biased) History
Worden, K.; Kerschen, Gaëtan ULg; Vakakis, Alexander F. et al

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

Although linear systems are now very well-understood in the context of structural dynamics, this is not at all the case for nonlinear systems. In particular, despite huge advances in the mathematical ... [more ▼]

Although linear systems are now very well-understood in the context of structural dynamics, this is not at all the case for nonlinear systems. In particular, despite huge advances in the mathematical theory of nonlinear dynamical systems, progress in the difficult field of nonlinear system identification (learning of models from measured input/output data) has largely remained fairly slow and incremental. This is not to say that there have been no major successes in the field in its comparatively short history, and the objective of this paper is to present some of the highlights, as perceived by the authors, and to pave the way for a second paper discussing new developments and possibilities for the future. [less ▲]

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See detailNonlinear System Identification in Structural Dynamics: Current Status and Future Directions
Kerschen, Gaëtan ULg; Worden, K.; Vakakis, Alexander F. et al

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

Nonlinear system identification aims at developing high-fidelity mathematical models in the presence of nonlinearity from input and output measurements performed on the real structure. The present paper ... [more ▼]

Nonlinear system identification aims at developing high-fidelity mathematical models in the presence of nonlinearity from input and output measurements performed on the real structure. The present paper is a discussion of the recent developments in this research field. Three of the latest approaches are presented, and application examples are considered to illustrate their fundamental concepts, advantages and limitations. Another objective of this paper is to identify future research needs, which would make the identification of structures with a high modal density in abroad frequency range viable. [less ▲]

Detailed reference viewed: 83 (0 ULg)