References of "Kerschen, Gaëtan"
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See detailClassification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression
Detroux, Thibaut ULg; Starosvetsky, Yuli; Kerschen, Gaëtan ULg et al

in Nonlinear Dynamics (2014), 76(April 2014), 673-696

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i ... [more ▼]

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i.e., under condition of 1:1 resonance); this type of Hamiltonian periodic orbits have been labeled as nonlinear normal modes. To this end we formulate an auxiliary system which consists of a two-dimensional, vibro-impact lattice composed of non-uniform “effective particles” oscillating in an anti-phase fashion. The analysis is based on the idea of balancing linear momentum in both horizontal and vertical directions for separate, groups of particles, whereby each such a group is represented by the single effective particle of the auxiliary system. It is important to emphasize that the auxiliary model can be defined for general finite, squarely packed granular crystals composed of n rows and m columns. The auxiliary model is successful in predicting the total number of such periodic orbits, as well as the amplitude ratios for different periodic regimes including strongly localized ones. In fact this methodology enables one to systematically study the generation of mode localization in these strongly nonlinear, highly degenerate dynamical systems. Good correspondence between the results of the theoretical model and direct numerical simulations is observed. The results presented herein can be further extended to study the intrinsic dynamics of the more complex granular materials, such as heterogeneous two-dimensional and three-dimensional granular crystals and multi-layered structures. [less ▲]

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See detailRobust optimal rendezvous using differential drag
Dell'Elce, Lamberto ULg; Martinusi, Vladimir ULg; Kerschen, Gaëtan ULg

in Proceedings of the AIAA/AAS Astrodynamics Specialist Conference (2014)

The practical realization of the differential drag technique for orbital relative maneuvers must cope with the several and severe uncertainty sources affecting drag modeling. Neglecting these ... [more ▼]

The practical realization of the differential drag technique for orbital relative maneuvers must cope with the several and severe uncertainty sources affecting drag modeling. Neglecting these uncertainties might yield to oversimplified solutions whose representation of a real-life scenario is questionable. The first outcome of this study consists in the synthesis of a robust optimal controller which combines differential flatness theory and the scenario approach to generate a reference path which can be easily followed. The second outcome is the characterization of the relevant uncertainties of the differential drag problem, with a special focus on the aerodynamic force. The developments are validated in a highly detailed simulation environment including, among the perturbations, advanced drag modeling and coupled attitude and orbital dynamics. [less ▲]

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See detailAn effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Deliège, Geoffrey ULg; Kerschen, Gaëtan ULg

in Meccanica (2014), 49(8), 1901-1916

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline ... [more ▼]

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov-Galerkin method with mesh moving and domain prediction-correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples. [less ▲]

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See detailValidation of differential drag propellantless maneuvers using 6 DoF simulations and stochastic dynamics
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the 9th International ESA Conference on Guidance, Navigation & Control Systems (2014)

Differential drag is regarded as a promising technique in low-Earth orbits, since it allows to turn the often-undesired drag perturbation into a control force for relative maneuvers. Nonetheless, relevant ... [more ▼]

Differential drag is regarded as a promising technique in low-Earth orbits, since it allows to turn the often-undesired drag perturbation into a control force for relative maneuvers. Nonetheless, relevant uncertainties in drag modeling make its practical realization a challenge, especially if no other propulsive means is available to accommodate them. The main outcome of this study is the identification and characterization of the uncertainty sources affecting differential-drag-based maneuvers. This characterization is carried out by using statistical methods in conjunction with mechanical modeling considerations to infer a probabilistic model of the sources from observed data. The developments are illustrated in the framework of the QARMAN mission through high-fidelity simulations involving coupled attitude and orbital dynamics. [less ▲]

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See detailAnalytic Model for The Motion About An Oblate Planet in The Presence Atmospheric Drag
Martinusi, Vladimir ULg; Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Advances in The Astronautical Sciences (2014)

The paper introduces a new model for the motion about an oblate planet under the influence of the atmospheric drag. Both qualitative and quantitative insights are revealed, as well as closed-form ... [more ▼]

The paper introduces a new model for the motion about an oblate planet under the influence of the atmospheric drag. Both qualitative and quantitative insights are revealed, as well as closed-form equations of motion. The main tool consists in averaging the effects of both perturbations (oblateness and drag), and deriving the variational equations for the vectorial orbital elements. The model is singularity-free and may serve as an initial guess for control problems, as well as an analytic propagator. [less ▲]

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See detailRobust rendez-vous planning using the scenario approach and differential flatness
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Advances in the Astronautical Sciences (2014)

There is a growing interest in uncertainty handling in the spacecraft dynamics community. In particular, robust optimization of spacecraft maneuvers is regarded as an important challenge. This paper ... [more ▼]

There is a growing interest in uncertainty handling in the spacecraft dynamics community. In particular, robust optimization of spacecraft maneuvers is regarded as an important challenge. This paper proposes an optimal control approach for orbital rendez-vous planning under stochastic dynamics and constraints. The method combines differential flatness theory with the scenario approach for optimization under uncertainties. By mapping state and control variables into a set of flat outputs, the enforcement of dynamics equations and boundary conditions is automatically satisfied. The rigorous foundations of the scenario approach lead to a finite-dimensional formulation of the problem which guarantees the feasibility of the solution within an arbitrary portion of the stochastic domain. The methodology is illustrated by means of two case studies involving a rendez-vous in elliptic orbit and a propellantless maneuver using differential drag, respectively. [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 detailRay tracing enhancement for space thermal analysis: isocell method
Jacques, Lionel ULg; Masset, Luc ULg; Kerschen, Gaëtan ULg

Conference (2013, December 04)

The finite element method (FEM) is widely used in mechanical engineering, especially for space structure design. However, FEM is not yet often used for thermal engineering of space structures where the ... [more ▼]

The finite element method (FEM) is widely used in mechanical engineering, especially for space structure design. However, FEM is not yet often used for thermal engineering of space structures where the lumped parameter method is still dominant. Radiative exchange factors (REFs), used to calculate radiative thermal exchanges in space, are usually computed through Monte Carlo ray-tracing. Due to the large number of elements composing a FE model, the computation of the REFs is prohibitively expensive. In the frame of a global approach, several research axes will be investigated to reduce the computational effort of the REFs with FEM. The first one focuses on accelerating the convergence and enhancing the accuracy of the ray-tracing process to decrease the number of rays required to achieve a given accuracy. The developments of the new Isocell quasi-Monte Carlo ray tracing method are presented. Based on Nusselt’s analogy, the ray direction sampling is carried out by sampling the unit disc to derive the ray directions. The unit disc is divided into cells into which random points are then generated. The cells have the particularity of presenting almost the same area and shape. This enhances the uniformity of the generated quasi-random sequence of ray directions and leads to faster convergence. This Isocell method has been associated with different surface sampling to derive the REFs. The method is benchmarked against ESARAD, the standard thermal analysis software used in the European aerospace industry. Various geometries have been used. In particular, one entrance baffle of the Extreme Ultraviolet Imager (EUI) instrument developed at the Centre Spatial de Liège in Belgium is used. The EUI instrument of the Solar Orbiter European Space Agency mission and will be launched in a Sun-centered (0.28 perihelion) orbit in 2018. [less ▲]

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See detailFrequency-domain subspace identification for nonlinear mechanical systems
Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Mechanical Systems & Signal Processing (2013), 40

This paper introduces a new frequency-domain subspace-based method for the identification of nonlinear mechanical systems. The technique exploits frequency-domain data and interprets nonlinearities as ... [more ▼]

This paper introduces a new frequency-domain subspace-based method for the identification of nonlinear mechanical systems. The technique exploits frequency-domain data and interprets nonlinearities as feedback forces exciting the underlying linear system. It is first demonstrated using two academic examples, namely a Duffing oscillator and a five-degree-of-freedom system comprising two nonlinearities. The identification of an experimental beam exhibiting geometrically nonlinear behaviour is then addressed. [less ▲]

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See detailUncertainty quantification of the orbital lifetime of a LEO spacecraft
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the Astrodynamics Specialist Conference (2013, August 12)

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic ... [more ▼]

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic assessment of orbital lifetime is likely to be bound to failure. This is why the present paper performs uncertainty quantification of satellite orbital lifetime estimation. Uncertainties in the initial state of the satellite and in the atmospheric drag force, as well as uncertainties introduced by modeling limitations associated with atmospheric density models, are considered. Mathematical statistics methods in conjunction with mechanical modeling considerations are used to infer the probabilistic characterization of these uncertainties from experimental data and atmospheric density models. Monte Carlo propagation is then exploited to achieve a probabilistic description of the orbital lifetime. [less ▲]

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See detailNumerical computation of nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the ASME IDETC/CIE 2013 (2013, August)

Since linear modal analysis fails in the presence of nonlinear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of ... [more ▼]

Since linear modal analysis fails in the presence of nonlinear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of linear normal modes to nonlinear systems. Initially defined as periodic solutions, numerical techniques such as the continuation of periodic solutions were used to compute 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, the partial differential equations governing the manifold geometry are considered as transport equations and an adequate finite element technique is proposed to solve them. The method is first demonstrated on a conservative nonlinear beam and the results are compared to standard continuation techniques. Then, linear damping is introduced in the system and the applicability of the method is demonstrated. [less ▲]

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See detailExperimental identification of the complex dynamics of a strongly nonlinear spacecraft structure
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the ASME IDETC/CIE 2013 (2013, August)

The present paper addresses the identification of a real-life spacecraft structure possessing an impact-type nonlinear component. The complete identification procedure, i.e. from nonlinearity detection to ... [more ▼]

The present paper addresses the identification of a real-life spacecraft structure possessing an impact-type nonlinear component. The complete identification procedure, i.e. from nonlinearity detection to parameter estimation, is carried out using experimental data collected during a typical spacecraft qualification test campaign. The complementary use of several techniques reveals particularly interesting and complex phenomena such as nonlinear jumps, nonlinear modal interactions, internal force relaxation and chattering during impacts. [less ▲]

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See detailIdentification of mechanical systems with local nonlinearities through discrete-time Volterra series and Kautz functions
Shiki, Sidney Bruce; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg et al

in Proceedings of the 11th International Conference on Recent Advances in Structural Dynamics (2013, July)

Mathematical modeling of mechanical structures is an important research area in structural dynamics. One of the goals of this area is to obtain a model that accurately predicts the dynamics of the system ... [more ▼]

Mathematical modeling of mechanical structures is an important research area in structural dynamics. One of the goals of this area is to obtain a model that accurately predicts the dynamics of the system. However, the nonlinear eff ects caused by large displacements and boundary conditions like gap, backlash or joint are not as well understood as the linear counterpart. This paper identifies a non-parametric discrete-time Volterra model of a benchmark nonlinear structure consisting of a cantilever beam connected to a thin beam at its free end. Time-domain data experimentally measured are used to identify the Volterra kernels, which are expanded with orthogonal Kautz functions to facilitate the identification process. The nonlinear parameters are then estimated through a model updating process involving optimization of the residue between the numerical and experimental kernels. The advantages and drawbacks of the Volterra series for modeling the behavior of nonlinear structures are finally indicated with suggestions to overcome the disadvantages found during the tests. [less ▲]

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See detailA new computational method for nonlinear normal modes of nonconservative systems
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

in Proceedings of the Euromech Colloquium n. 541 - New Advances in the Nonlinear Dynamics and Control of Composites for Smart Engineering Design (2013, June)

The concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of normal modes to nonlinear systems. Initially, NNMs were defined as periodic solutions of ... [more ▼]

The concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of normal modes to nonlinear systems. Initially, NNMs were defined as periodic solutions of the underlying conservative system, and continuation algorithms were recently exploited to compute them. To extend the concept of NNMs to nonconservative systems, Shaw and Pierre defined an NNM as a two-dimensional invariant manifold in the system’s phase space. This contribution presents a novel algorithm for solving the set of partial differential equations governing the manifold geometry numerically. The resolution strategy takes advantage of the hyperbolic nature of the equations to progressively solve them in annular regions. Each region is defined by two different iso-energy curves and equations are discretized using a specific finite element technique. The proposed strategy also offers the opportunity to estimate the frequency-energy dependence of the mode without using time integration. The algorithm is applied to both conservative and nonconservative systems. [less ▲]

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See detailNonlinear dynamic analysis of an F-16 aircraft using GVT data
Noël, Jean-Philippe ULg; Renson, Ludovic ULg; Kerschen, Gaëtan ULg et al

in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics (2013, June)

This paper aims at investigating the nonlinear dynamics of an F-16 aircraft, based upon sine-sweep data collected during a ground vibration test (GVT) campaign. Various analysis techniques, including the ... [more ▼]

This paper aims at investigating the nonlinear dynamics of an F-16 aircraft, based upon sine-sweep data collected during a ground vibration test (GVT) campaign. Various analysis techniques, including the mere visual inspection of the time series, the wavelet transform and the restoring force surface method, are utilised and reveal that the F-16 wing-to-payload mounting interfaces exhibit both softening and hardening nonlinearities. [less ▲]

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See detailComparison between analytical and optimal control techniques in the differential drag based rendez-vous
Dell'Elce, Lamberto ULg; Kerschen, Gaëtan ULg

in Proceedings of the 5th International Conference on Spacecraft Formation Flying Missions & Technologies (2013, May 29)

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight ... [more ▼]

The focus of this study is on differential drag for propellantless satellite rendez-vous. This technique is particularly attractive for low-Earth-orbit small satellites for which stringent weight constraints apply. Most existing contributions are based on bang-bang strategies, which may be difficult to implement in practice. This is why the present paper proposes a novel strategy integrating pseudospectral optimal control for maneuver planning and model predictive control for dealing with uncertainties and unmodeled dynamics. One important advantage of this methodology is that it can naturally account for attitude dynamics and constraints, which, in turn, paves the way for the practical realization of differential drag-based rendez-vous. A realistic scenario involving two nanosatellites of the QB50 constellation is considered to illustrate and validate the proposed developments. In addition, a comparison of this numerical technique with an existing analytic solution is carried out, and their respective pros and cons are discussed. [less ▲]

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See detailComputation of nonlinear normal modes through continuation methods
Renson, Ludovic ULg; Kerschen, Gaëtan ULg

Conference (2013, May)

In mechanical engineering, performance enhancement usually results in lighter and more flexible structures and pushes the limits of the system operating envelope. Nonlinearity is therefore becoming a ... [more ▼]

In mechanical engineering, performance enhancement usually results in lighter and more flexible structures and pushes the limits of the system operating envelope. Nonlinearity is therefore becoming a frequent occurrence and linear design tools show their limitations. To overcome these issues, nonlinear normal modes (NNMs) were introduced in structural dynamics as a direct extension of linear normal modes to nonlinear systems. Our contribution reviews the history and the new trends for the computation of NNMs in mechanical engineering. Specifically, algorithms for the continuation of periodic solutions were first developed. Such algorithms are now well-established and applicable to large-scale systems such as real-life aerospace structures. To further extend the concept of NNMs to nonconservative systems, the definition of an NNM as an invariant manifold in the system’s phase space was introduced. Again, continuation techniques are particularly well suited for computing these invariant manifolds. The geodesic level set method developed by Krauskopf and Osinga [1] as well as the “PDE formulation” method of Guckenheimer and Vladimirsky [2] are both considered. [1] Krauskopf, B. and H. Osinga (2003). "Computing Geodesic Level Sets on Global (Un)stable Manifolds of Vector Fields." SIAM Journal on Applied Dynamical Systems 2(4): 546-569. [2] Guckenheimer, J. and A. Vladimirsky (2004). "A Fast Method for Approximating Invariant Manifolds." SIAM Journal on Applied Dynamical Systems 3(3): 232-260. [less ▲]

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See detailFrequency-domain subspace identification of nonlinear mechanical systems
Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Proceedings of the 5th International Operational Modal Analysis Conference (2013, May)

The objective of the present paper is to address the identification of a real-life strongly nonlinear space structure, the EADS-Astrium SmallSat spacecraft. To this end, a new nonlinear subspace ... [more ▼]

The objective of the present paper is to address the identification of a real-life strongly nonlinear space structure, the EADS-Astrium SmallSat spacecraft. To this end, a new nonlinear subspace identification method formulated in the frequency domain is exploited, referred to as the FNSI method. The frequency response functions of the underlying linear spacecraft and the amplitudes of the nonlinear internal forces are estimated based on a periodic-random data set corrupted by noise. This application is challenging for several reasons, including high modal density, highly non-proportional damping and the non-smooth nature of the nonlinearities. [less ▲]

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See detailNonparametric subspace identification of nonlinear structures - Application to a spacecraft
Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

in Proceedings of the 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2013, April)

The objective of the present paper is to address the identification of a strongly nonlinear satellite structure by exploiting a new nonlinear subspace identification method formulated in the frequency ... [more ▼]

The objective of the present paper is to address the identification of a strongly nonlinear satellite structure by exploiting a new nonlinear subspace identification method formulated in the frequency domain, referred to as the FNSI method. The modal parameters of the underlying linear structure and the coefficients of the nonlinear internal forces will be estimated by this approach. Moreover, because a priori knowledge about nonlinear behaviour may be limited, the paper also proposes a nonparametric spline-based modelling strategy, encapsulated in the FNSI method. The application of interest is the SmallSat spacecraft developed by EADS-Astrium, which possesses an impact-type nonlinear device consisting of eight mechanical stops limiting the motion of an inertia wheel mounted on an elastomeric interface. [less ▲]

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See detailFrequency-domain subspace identification of nonlinear mechanical systems - Application to a solar array structure
Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg; Foltête, Emmanuel et al

in Proceedings of the International Modal Analysis Conference (IMAC) XXXI (2013, February)

The present paper addresses the experimental identification of a simplified realisation of a solar array structure in folded configuration. To this end, a nonlinear subspace identification technique ... [more ▼]

The present paper addresses the experimental identification of a simplified realisation of a solar array structure in folded configuration. To this end, a nonlinear subspace identification technique formulated in the frequency domain, referred to as the FNSI method, is exploited. The frequency response functions of the underlying linear structure and the nonlinear coefficients are estimated by this approach. Nonlinearity is caused by impacts between adjacent panels and friction and gaps appearing in their clamping interfaces. This application is challenging for several reasons, which include high modal density and the complicated nature of the involved nonlinear mechanisms. [less ▲]

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