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See detailNonlinear Dynamics Of A Drill Bit Under Percussive Activation
Depouhon, Alexandre ULg; Denoël, Vincent ULg; Detournay, Emmanuel

in Proceedings of ICTAM 2012, Beijing (2012, August)

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See detailNonlinear electromagnetic modes in astrophysical plasmas with dust distributions
Verheest, F.; Cattaert, Tom ULg

in Astronomy and Astrophysics (2004), 421(1), 17-21

A derivative nonlinear Schrodinger equation is obtained for parallel electromagnetic modes in plasmas containing polydisperse charged dust. The coefficient of the dispersive term in that equation is ... [more ▼]

A derivative nonlinear Schrodinger equation is obtained for parallel electromagnetic modes in plasmas containing polydisperse charged dust. The coefficient of the dispersive term in that equation is dominated by the dust rather than the (plasma) ions, and polydisperse dust yields a larger coefficient in absolute value than an equivalent monodisperse description. This leads to a significant broadening of the nonlinear structure due to the presence of polydisperse rather than monodisperse dust, the latter contributing in itself already to a substantial increase in the width of envelope solitons compared to dust-free plasmas. When modelling the charged dust by a power-law distribution occurring in planetary ring and other astrophysical systems, it depends very much on the power-law index whether the smaller or the larger grains are more important. For certain indices the more numerous smaller grains determine the charge and mass densities, but the larger dust dominates the linear and nonlinear dispersive effects. [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 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 detailNOnlinear finite element approach to simulate wake-induced oscillation in transmission system
Snegovskiy, Dmitry; Lilien, Jean-Louis ULg

in Proceedings of ASME 2010 3rd Joint US-euorpean Fluids Engineering (FEDSM2010) (2010, August)

Wake-induced oscillations (WIO) in transmission line bundle conductors are simulated using finite-element nonlinear formulation. This allows obtaining the conductor oscillations in the line spans equipped ... [more ▼]

Wake-induced oscillations (WIO) in transmission line bundle conductors are simulated using finite-element nonlinear formulation. This allows obtaining the conductor oscillations in the line spans equipped either with spacers or with spacer dampers. Within this approach, the interaction of subconductors due to the wake is represented using Simpson’s aeroelastic model. A special force element is created to introduce the aerodynamic loads due to the wake. The aeroelastic properties of the wake force field are tuned to meet the wake-induced instability properties as measured by Price. Extension of the wake interaction sample onto the full line span is done taking into account the inertia-stiffness properties of the line fittings (spacer dampers). It is emphasized that in WIO the ability of spacer (spacer damper) to transfer the loads and motions plays essential role. Thus, the transfer matrix logic to simulate the spacer, established by Diana, Rawlins and other researchers, is now transferred into the finite element model of WIO. Some important structural specifics of transmission line fittings are thus highlighted by the performed simulations. All these developments are introduced into the FE package SAMCEF Mecano. Results of a series of calculations are presented to illustrate the feasibility of the established model. Comparison of FEM simulations to the benchmarking field test data is presented. [less ▲]

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See detailNonlinear generalization of Den Hartog's equal peak method for nonlinear primary systems
Habib, Giuseppe ULg; Detroux, Thibaut ULg; Kerschen, Gaëtan ULg

in Proceedings of the International Conference on Structural Nonlinear Dynamics and Diagnosis (2014)

This study addresses the mitigation of one problem nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a new nonlinear absorber ... [more ▼]

This study addresses the mitigation of one problem nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a new nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. One unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments. [less ▲]

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See detailNonlinear guitar loudspeaker simulation
Schmitz, Thomas ULg; Embrechts, Jean-Jacques ULg

in Proceedings of the AES 134 th convention (2013, May)

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See detailNonlinear Marangoni Instability in 3D Rigid Boxes
Dauby, Pierre ULg; Lebon, Georgy ULg; Colinet, P.

in Greco, A. M.; Rionero, S. (Eds.) Supplemento ai rendiconti del Circolo matematico di Palermo « The Proceedings of the VIII International Conference on Waves and Stability in continuous Media, Palermo, Italy, oct. 9-14, 1995 », SERIE II – NUMERO 45– ANNO 1996, Palermo, Via Archirafi 34, Italy (1996)

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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 detailNonlinear MDOF System Characterization and Identification using the Hilbert- Huang Transform: Experimental Demonstration
Kerschen, Gaëtan ULg; Vakakis, Alexander F.; Lee, Young.S et al

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

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, this transform is inherently limited to the analysis of single-degree-of-freedom systems; this shortcoming is potentially overcome by the Hilbert-Huang transform (HHT). In this study, the joint application of the complexification-averaging method and the HHT enables us to develop a new technique, the slow-flow model identification method. Through an experimental application, we demonstrate that the proposed method is adequate for characterizing and identifying multi-degreeof-freedom nonlinear systems. [less ▲]

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See detailNonlinear modal analysis and energy localization in a bladed disk assembly
Georgiades, Fotios; Peeters, Maxime ULg; Kerschen, Gaëtan ULg et al

in ASME Turbo Expo 2008: Power for Land, Sea and Air, Berlin, 2008 (2008, June)

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is ... [more ▼]

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedureand a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequencyenergy dependence of nonlinear oscillations. [less ▲]

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See detailNonlinear modal analysis of a full-scale aircraft
Kerschen, Gaëtan ULg; Peeters; Golinval, Jean-Claude ULg et al

in Journal of Aircraft (2013), 50

Nonlinear normal modes (NNMs), which are defined as a nonlinearextension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to ... [more ▼]

Nonlinear normal modes (NNMs), which are defined as a nonlinearextension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to demonstrate that the computation of NNMs and of their oscillation frequencies can now be achieved for complex, real-world aerospace structures. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft. Ground vibration tests of this aircraft exhibited softening nonlinearities in the connection between the external fuel tanks and the wing tips. The NNMs of this aircraft are computed from a reduced-order nonlinear finite element model using a numerical algorithm combining shooting and pseudo-arclength continuation. Several NNMs, involving, e.g., wing bending, wing torsion and tail bending, are presented, which highlights that the aircraft can exhibit very interesting nonlinear phenomena. Specifically, it is shown that modes with distinct linear frequencies can interact and generate additional nonlinear modes with no linear counterpart. [less ▲]

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See detailNonlinear modal analysis of aerospace structures
Peeters, Maxime ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in Proceedings of the 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (2011)

The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why theoretical and ... [more ▼]

The dynamic systems theory is well-established for linear systems and can rely on mature tools such as the theories of linear operators and linear integral transforms. This is why theoretical and experimental modal analysis, i.e., the computation of vibration modes from a mathematical model and from experimental data, respectively, is really quite sophisticated and advanced. Even though linear modal analysis served, and is still serving, the structural dynamics community for applications ranging from bridges to satellites, it is commonly accepted that nonlinearity is a frequent occurrence in engineering structures. Because linear modal analysis fails in the presence of nonlinear dynamical phenomena, the development of a practical nonlinear analog of modal analysis would be an extremely timely contribution; it is clearly missing in the structural dynamics literature. A new framework for nonlinear modal analysis of real-world structures, which includes the computation of nonlinear modes from finite element models, is introduced in this paper. This framework will permit a rigorous, yet understandable by the practicing engineer, analysis of nonlinear dynamical phenomena. It will also provide solid theoretical foundations for extending finite element model validation to nonlinear aerospace structures. [less ▲]

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See detailNonlinear Modal Analysis of Conservative and Nonconservative Aerospace Structures
Renson, Ludovic ULg

Doctoral thesis (2014)

The concept of nonlinear normal modes (NNMs) provides a solid and rigorous theoretical framework for the analysis of the nonlinear oscillations of mechanical systems. If NNMs have been studied since more ... [more ▼]

The concept of nonlinear normal modes (NNMs) provides a solid and rigorous theoretical framework for the analysis of the nonlinear oscillations of mechanical systems. If NNMs have been studied since more than fifty years, it is only very recently that contributions dealing with their numerical calculation have been reported in the literature. Although these methods pave the way for the application of NNMs to more complex systems, they have not yet reached the necessary maturity. In this context, the purpose of this research is (i) to further investigate the performance of an existing method for computing the NNMs of conservative systems and (ii) to propose two new methods for the computation of NNMs of nonconservative systems. The first contribution of this thesis is to calculate the NNMs of a real-life aerospace structure, the SmallSat spacecraft developed by EADS Astrium. An algorithm that combines an advanced shooting method with the pseudo-arclength continuation technique is utilized. We show that the NNMs provide a very useful interpretation of the strongly nonlinear dynamics of the spacecraft. One specific contribution is to numerically reproduce with great fidelity several interactions between modes with noncommensurate linear frequencies that were observed experimentally. The second original contribution of this thesis is to develop two new methods for computing the NNMs of damped systems. The first method solves the partial differential equations (PDEs) governing the geometry of the NNM. The PDEs are recognized as hyperbolic, and it is shown that they require appropriate numerical treatments including specific boundary conditions. The proposed method combines a streamline upwind Petrov-Galerkin finite-element formulation with a resolution strategy based on annular domains to grow sequentially the manifold. The algorithm is demonstrated using a wide variety of systems ranging from two-degree-of-freedom to multi-degree-of-freedom nonlinear systems with linear and nonlinear damping. The applicability of the algorithm to complex real-life structures is demonstrated using a full-scale aircraft. The second method presented in this work computes a NNM as a collection of trajectories defined with boundary value problems (BVPs). The method has the distinctive advantage that it does not rely on a parameterization of the NNM. It is demonstrated on two-degree-of-freedom examples featuring linear and nonlinear damping. [less ▲]

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See detailNonlinear modal analysis of the SmallSat spacecraft
Renson, Ludovic ULg; Kerschen, Gaëtan ULg; Newerla, Alfred

in Proceedings of the SEM IMAC XXX Conference (2012)

Non-linear elements are present in practically all spacecraft structures. The assumption of a (quasi-)linear structure is nevertheless adequate for structural analyses and design verification purposes in ... [more ▼]

Non-linear elements are present in practically all spacecraft structures. The assumption of a (quasi-)linear structure is nevertheless adequate for structural analyses and design verification purposes in those cases where these structural non-linearities are relatively weak or not substantially activated by the mechanical environments encountered during the launch or during ground testing. However, when significant non-linear effects in spacecraft structures are no longer negligible then linear modal analysis will not be able to handle non-linear dynamical phenomena in an adequate manner: the development of a non-linear analogue of linear modal analysis becomes an urgent and important issue. The objective of this paper is to show that nonlinear normal modes (NNMs) represent a useful and practical tool in this context. A full-scale spacecraft structure is considered and is modeled using the finite element method. Its NNMs are computed using advanced numerical algorithms, and the resulting dynamics is then carefully analyzed. Nonlinear phenomena with no linear counterpart including nonlinear modal interactions are also highlighted. [less ▲]

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See detailNonlinear Modal Analysis of the SmallSat Spacecraft
Renson, Ludovic ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg et al

in Proceedings of the European Conference on Spacecraft Structures, Materials & Environmental Testing (2012, March)

Non-linear elements are present in practically all spacecraft structures. When such non-linear effects are important linear modal analysis can no longer be applied. The development of a non-linear ... [more ▼]

Non-linear elements are present in practically all spacecraft structures. When such non-linear effects are important linear modal analysis can no longer be applied. The development of a non-linear analogue of linear modal analysis is therefore an important endeavor. The objective of this paper is to show that nonlinear normal modes (NNMs) represent a useful and practical tool in this context. A full-scale spacecraft structure is considered and is modeled using the finite element method. Its NNMs are computed using advanced numerical algorithms, and the resulting dynamics is then carefully analyzed. Nonlinear phenomena with no linear counterpart including nonlinear modal interactions are also highlighted. [less ▲]

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See detailNonlinear normal modes and band zones in granular chains with no precompression
Jayaprakash, K.R.; Starosvetsky, Y.; Vakakis, A.F. et al

in Nonlinear Dynamics (2011), 63

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are ... [more ▼]

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg, we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances. [less ▲]

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See detailNonlinear Normal Modes of a Full-Scale Aircraft
Peeters, Maxime ULg; Kerschen, Gaëtan ULg; Golinval, Jean-Claude ULg et al

in 29th International Modal Analysis Conference, Jacksonville, 2011 (2011)

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See detailNonlinear Normal Modes of Nonconservative Systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the SEM IMAC XXXI Conference (2013)

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the ... [more ▼]

Linear modal analysis is a mature tool enjoying various applications ranging from bridges to satellites. Nevertheless, modal analysis fails in the presence of nonlinear dynamical phenomena and the development of a practical nonlinear analog of modal analysis is a current research topic. Recently, numerical techniques (e.g., harmonic balance, continuation of periodic solutions) were developed for the computation of nonlinear normal modes (NNMs). Because these methods are limited to conservative systems, the present study targets the computation of NNMs for nonconservative systems. Their definition as invariant manifolds in phase space is considered. Specifically, a new finite element technique is proposed to solve the set of partial differential equations governing the manifold geometry. [less ▲]

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