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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 detailThe nonlinear piezoelectric tuned vibration absorber
Soltani, Payam ULg; Kerschen, Gaëtan ULg

Scientific conference (2015, June 03)

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See detailThe nonlinear piezoelectric tuned vibration absorber
Soltani, Payam ULg; Kerschen, Gaëtan ULg

in Smart Materials and Structures (2015), 24(07), 075015

This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new ... [more ▼]

This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new feature of the NPTVA is that its nonlinear restoring force is designed according to a principle of similarity, i.e., the NPTVA should be an electrical analog of the nonlinear host system. Analytical formulas for the NPTVA parameters are derived using the homotopy perturbation method. Doing so, a nonlinear generalization of Den Hartog’s equal-peak tuning rule is developed for piezoelectric vibration absorbers. [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 Schroedinger 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 ... [more ▼]

We show that a nonlinear Schroedinger 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 ▲]

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See detailNonlinear System Identification using Interpolated Short Time Fourier Transform
Shi, Dongfeng; Dimitriadis, Grigorios ULg

in Akay, A.; Arnas, O.; Cooper, J. E. (Eds.) et al Proceedings of 7th Biennial ASME Conference on Engineering Systems Design and Analysis (2004, July)

For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous ... [more ▼]

For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous amplitudes and frequencies of response signals. It is shown that the backbone curves estimated by the ISTFT agree with theoretical backbone curves very well. Additionally, the restoring force can be reconstructed to specify the type of nonlinear stiffness. A curve-fitting technique is introduced to estimate the parameters of nonlinear systems on the basis of theoretical backbone curves. It is shown that a number of typical nonlinear stiffness functions such as cubic, bilinear and pre-compressed springs can be identified accurately using this new method. [less ▲]

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See detailNonlinear Targeted Energy Transfer in Mechanical and Structural Systems I
Vakakis, Alexander F.; Gendelman, O. V.; Bergman, L. A. et al

Book published by Springer (2009)

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See detailNonlinear Targeted Energy Transfer in Mechanical and Structural Systems II
Vakakis, Alexander F.; Gendelman, O. V.; Bergman, L. A. et al

Book published by Springer (2009)

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See detailNonlinear thin shell finite element for steel and concrete structures subjected to fire: theoretical development
Talamona, Didier; Franssen, Jean-Marc ULg

in Journal of Applied Fire Science (2002), 11(4), 291-310

This article describes the features of a quadrilateral thin shell element, based on Marguerre's theory that has ben implemented in the finite element program SAFIR (from the University of Liege.) The ... [more ▼]

This article describes the features of a quadrilateral thin shell element, based on Marguerre's theory that has ben implemented in the finite element program SAFIR (from the University of Liege.) The element has four nodes (one at each corner) and each node has six degrees of freedom, i.e., three translations and three rotations (the sixth degree of freedom is a true one, which can be assimilated to the in-plane rotation.) This article presents some theoretical developments regarding the element formulation. The algorithm strategies for isotropic material (steel for example) and non-isotropic material 'concrete) and their modifications for elevated temperatures are described. Two verifications examples are presented (the patch test and Lee's frame at elevated temperatures). [less ▲]

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See detailNonlinear thin shell finite element for steel and concrete structures subjected to fire: verification and validation
Talamona, Didier; Castagne, Sylvie; Franssen, Jean-Marc ULg

in Journal of Applied Fire Science (2003), 12(1), 65-81

This article presents verification and validation examples for a nonlinear thin shell element developed for structures subjected to fire. The verification benchmarks are: a Z-shaped cantilever, a twisted ... [more ▼]

This article presents verification and validation examples for a nonlinear thin shell element developed for structures subjected to fire. The verification benchmarks are: a Z-shaped cantilever, a twisted cantilever beam, a hemispherical shell, and Lee's frame at room temperature and at elevated temperature. The element shows that it provides results in good agreement with theoretical results and other finite elements. The validation calculations have been performed on an H rolled profile and a concrete slab. The element demonstrates its ability to reproduce local buckling on a H-steel beam under fire conditions and that it predicts accurately the failure of a concrete slab subjected to fire. The theoretical development of this finite element has been published in the Journal of Applied Fire Science, Vol. 11, No. 4, pp. 291-310, "Nonlinear Thin Shell Finite Element for Steel and Concrete Structures Subjected to Fire: Theoretical Development." [less ▲]

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