References of "Kerschen, Gaëtan"
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See detailThe harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
Detroux, Thibaut ULg; Renson, Ludovic ULg; Masset, Luc ULg et al

in Computer Methods in Applied Mechanics and Engineering (2015), 296

The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation ... [more ▼]

The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark–Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device. [less ▲]

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See detailBifurcation Analysis of a Spacecraft Structure Using the Harmonic Balance Method
Detroux, Thibaut ULg; Renson, Ludovic ULg; Masset, Luc ULg et al

in Proceedings of the ASME 2015 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE 2015) (2015, August)

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the ... [more ▼]

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors. [less ▲]

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See detailPerformance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
Detroux, Thibaut ULg; Habib, Giuseppe ULg; Masset, Luc ULg et al

in Mechanical Systems & Signal Processing (2015), 60-61

The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of ... [more ▼]

The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated. [less ▲]

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See detailTheoretical and experimental investigation of a structurally and aerodynamically nonlinear pitch and flap wing
Verstraelen, Edouard ULg; Boutet, Johan ULg; Grappasonni, Chiara ULg et al

in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics, IFASD 2015 (2015, June 29)

This paper presents and experimental and theoretical investigation of a novel nonlinear aeroelastic system. It consists of a wing with pitch and flap degrees of freedom, suspended from a leaf spring ... [more ▼]

This paper presents and experimental and theoretical investigation of a novel nonlinear aeroelastic system. It consists of a wing with pitch and flap degrees of freedom, suspended from a leaf spring secured in a nonlinear clamp. Both the structural and the aerodynamic forces acting on the wing can be nonlinear, depending on the amplitude of oscillations. Wind tunnel experiments show that the system undergoes a supercritical Hopf bifurcation that leads to small amplitude limit cycle oscillations. At a particular airspeed, the pitch amplitude jumps to a much higher value and dynamic stall starts to occur. Three mathematical models of the system are formulated, one based on linear aerodynamics and two based on the Leishman-Beddoes dynamic stall model. The objective of the modelling is to determine whether the jump in pitch oscillation amplitude is due to dynamic stall. The predictions for amplitude, frequency and mean angle of the limit cycle oscillations are compared to the experimental observations. All three models predict the small amplitude oscillations with satisfactory accuracy. The complete Leishman-Beddoes model predicts the occurrence of a jump in pitch amplitude but the magnitude of this jump is signi cantly overestimated. The other two models completely fail to model the jump. The failure of the Leishman-Beddoes model to predict the correct post-jump oscillation amplitude may be due to the values selected for the model parameters. [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 ground vibration identification of an F-16 aircraft - Part 2: Parameter estimation using a frequency-domain subspace method
Dossogne, Tilàn ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg et al

in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics (2015, June)

Although they are generally modelled as linear systems, aircraft structures are known to be prone to nonlinear phenomena. A specific challenge encountered with fighter aircraft, besides aeroelastic ... [more ▼]

Although they are generally modelled as linear systems, aircraft structures are known to be prone to nonlinear phenomena. A specific challenge encountered with fighter aircraft, besides aeroelastic nonlinearity, is the modelling of the wing-to-payload mounting interfaces. For large amplitudes of vibration, friction and gaps may be triggered in these connections and markedly impact the dynamic behaviour of the complete structure. In this series of two papers, the nonlinear dynamics of an F-16 aircraft is investigated using rigorous methods applied to real data collected during a ground vibration test campaign. The present work focuses on the construction of an experimental mathematical model of the F-16 structural dynamics. A nonlinear generalisation in the frequency domain of the so-called subspace identification algorithms, termed FNSI method, is exploited to this end. The frequency response functions of the underlying linear aircraft and the coefficients of the nonlinearities are reliably estimated by this approach based on periodic random data. The use of stabilisation diagram in nonlinear system identification is also discussed. The application of the FNSI method is made challenging by the high modal density of the structure, and the complexity of the nonlinear stiffness and damping mechanisms involved within the wing-to-payload connections. [less ▲]

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See detailA frequency-domain method for identifying nonlinear vibrating structures
Noël, Jean-Philippe ULg; Dossogne, Tilàn ULg; Kerschen, Gaëtan ULg

Conference (2015, June)

System identification, which refers to the construction of mathematical models from experimental data, plays a key role in the design process of engineering systems. In structural dynamics, the ... [more ▼]

System identification, which refers to the construction of mathematical models from experimental data, plays a key role in the design process of engineering systems. In structural dynamics, the theoretical and experimental aspects of linear system identification have been successfully addressed since the early seventies, and mature analytical, computational and testing tools have emerged. Nonlinear system identification of vibrating structures has also enjoyed significant advances during the past few years. However, the common practice in industry is to ignore nonlinearities, arguably because their analysis is still regarded as impractical. The present work describes a rigorous nonlinear generalisation in the frequency domain of the classical subspace identification algorithms, termed FNSI method. This method is applicable to large-scale systems comprising strong nonlinearities, closely-spaced modes and potentially high, nonproportional damping. Another distinct advantage of the approach is that it offers a convenient way to select an appropriate order for the nonlinear model by means of stabilisation diagrams. The FNSI method is demonstrated in this study using a complete satellite structure with nonsmooth nonlinearities, and a solar panel assembly exhibiting complex nonlinear stiffness and damping mechanisms. [less ▲]

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See detailNumerical study of intrinsic features of isolas in a 2-dof nonlinear system
Detroux, Thibaut ULg; Noël, Jean-Philippe ULg; Masset, Luc ULg et al

in Proceedings of the ICEDyn conference (2015, June)

In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the ... [more ▼]

In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis. [less ▲]

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See detailNonlinear ground vibration identification of an F-16 aircraft - Part 1: Fast nonparametric analysis of distortions in FRF measurements
Vaes, Mark; Schoukens, Johan; Peeters, Bart et al

in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics (2015, June)

Although they are generally modelled as linear systems, aircraft structures are known to be prone to nonlinear phenomena. A specific challenge encountered with fighter aircraft, besides aeroelastic ... [more ▼]

Although they are generally modelled as linear systems, aircraft structures are known to be prone to nonlinear phenomena. A specific challenge encountered with fighter aircraft, besides aeroelastic nonlinearity, is the modelling of the wing-to-payload mounting interfaces. For large amplitudes of vibration, friction and gaps may be triggered in these connections and markedly impact the dynamic behaviour of the complete structure. In this series of two papers, the nonlinear dynamics of an F-16 aircraft is investigated using rigorous methods applied to real data collected during a ground vibration test campaign. The present work focuses on the detection, qualification and quantification of nonlinear distortions affecting frequency response function (FRF) measurements. The key idea of the approach is to excite the structure using a random signal with a user-defined amplitude spectrum, where only a set of well-selected frequencies is different from zero in the band of interest. It is demonstrated that this careful choice of the input frequencies allows, without any further user interaction, to quantify the importance of odd and even nonlinear distortions in the output spectra with respect to the noise level. At high excitation amplitude, the F-16 dynamics is found to exhibit substantial odd nonlinearities and less significant, yet not negligible, even nonlinearities. [less ▲]

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See detailNonlinear model updating by means of identified nonlinear normal modes
Song, Mingming; Renson, Ludovic ULg; Noël, Jean-Philippe ULg et al

Conference (2015, June)

Modal parameters are the most common features used for linear model updating. Although the modal analysis theory does not hold for nonlinear dynamic systems, its popularity encouraged researchers to come ... [more ▼]

Modal parameters are the most common features used for linear model updating. Although the modal analysis theory does not hold for nonlinear dynamic systems, its popularity encouraged researchers to come up with an equivalent version of normal modes for nonlinear systems, i.e., nonlinear normal modes (NNMs). A nonlinear system vibrates in NNMs when all masses have periodic motions of the same period, and at any time, the position of all the masses is uniquely defined by the position of any one of them. This paper investigates the feasibility of nonlinear model updating by minimizing the difference between the model-predicted and measured/identified nonlinear normal modes. A two degree-of-freedom mass-spring system with three linear springs and a cubic nonlinear spring is considered as the case study. The energy-dependent natural frequency and NNM of the first vibration mode of the system are identified at three different levels of energy. The stiffness parameters of the system are estimated by minimizing an objective function which is defined as the discrepancy between model-predicted natural frequency and NNM of the first mode, and their identified counterparts at the three measured energy levels. Performance of the proposed updating approach is evaluated at different levels of noise and different levels of modeling errors (i.e., nonlinear model classes). [less ▲]

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See detailBifurcation Analysis of Large-Scale Dynamical Systems Using the Harmonic Balance Method
Detroux, Thibaut ULg; Renson, Ludovic ULg; Masset, Luc ULg et al

Conference (2015, May 22)

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear industrial models. However, in its classical formulation the HB method is ... [more ▼]

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear industrial models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft and its bifurcations are studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. [less ▲]

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See detailTesting of a Spacecraft Structure with Non-Smooth Nonlinearities
Renson, Ludovic ULg; Noël, Jean-Philippe ULg; Kerschen, Gaëtan ULg

Conference (2015, May)

The dynamics of the SmallSat, a real-life spacecraft possessing a complex isolation device with multiple nonsmooth nonlinearities is investigated. Experiments show that nonlinearities induce modal ... [more ▼]

The dynamics of the SmallSat, a real-life spacecraft possessing a complex isolation device with multiple nonsmooth nonlinearities is investigated. Experiments show that nonlinearities induce modal interactions between modes with non-commensurate linear frequencies. A model of the structure with a simplified description of the nonlinear connections is first built using techniques available in industry. Numerical continuation is then exploited to compute nonlinear normal modes and uncover interaction phenomena that can jeopardize the structural integrity. [less ▲]

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See detailFinite Element Model Reduction of Thermal Systems with Conductive and Radiative Heat Transfers
Jacques, Lionel ULg; Masset, Luc ULg; Kerschen, Gaëtan ULg

Scientific conference (2015, March 24)

The Lumped parameter method (LPM) is the main method used for space structures thermal design. It is very versatile and allows easy integration of user-defined components but the computation of the ... [more ▼]

The Lumped parameter method (LPM) is the main method used for space structures thermal design. It is very versatile and allows easy integration of user-defined components but the computation of the conductive links is error-prone and still too often computed by hand. Widely used in structural design, the finite element method (FEM) is however not yet often used for thermal analysis. One of the main reasons is that the radiative exchange factors, usually computed through Monte Carlo ray tracing, are extremely expensive to compute due to the large number of elements composing a FE model. A new global approach for FE model reduction of thermal systems is presented. The method is based on an automated FE mesh partitioning leading to super-faces and super-nodes. It is tailored for radiative exchange factors computation, taking into account selected quadric recognition and material constraints. The method also provides accurate conductive links computation and enables a direct mapping of the reduced temperatures back onto the detailed FE mesh (for e.g. thermo-elastic analyses). The application to two instruments developed at the Centre Spatial de Liège in Belgium will be presented, namely the Extreme Ultraviolet Imager (EUI) onboard Solar Orbiter and the Back Telescope Assembly (BTA) onboard Meteosat Third Generation. [less ▲]

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See detailMeasuring nonlinear distortions: from test case to an F-16 fighter
Vaes, Mark; Schoukens, Johan; Rolain, Yves et al

Conference (2015, March)

What are the similarities and differences between the behavior of a small vibrating test system and an F-16 fighter? To find it out, we compare measurements of the test system to measurements from the ... [more ▼]

What are the similarities and differences between the behavior of a small vibrating test system and an F-16 fighter? To find it out, we compare measurements of the test system to measurements from the bolted connection of the wing and the missile of a F-16 Fighter Falcon from the Belgian air force. These measurements were done during a ground vibration test (GVT) campaign. Essentially, the behavior of these systems match, even though the test system is only the heart of a self-study kit for nonlinear system identification and the F-16 is a complex real life mechanical structure. This clearly shows the added value of an experiment driven nonlinear educational system identification package. It provides safe small-scale toy examples for hands-on exercises that react like real systems. We believe that this practical approach lowers the gap between learning system identification concepts and applying it on real systems. [less ▲]

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See detailA comparison of grey-box and black-box approaches in nonlinear state-space modelling and identification
Noël, Jean-Philippe ULg; Schoukens, Johan; Kerschen, Gaëtan ULg

Conference (2015, March)

In the present contribution, it is shown that, in the case of mechanical systems where nonlinearities are physically localised, the general structure of black-box nonlinear state-space models can be ... [more ▼]

In the present contribution, it is shown that, in the case of mechanical systems where nonlinearities are physically localised, the general structure of black-box nonlinear state-space models can be drastically simplified. A more parsimonious, grey-box state-space representation is derived, which is found to be compatible with Newton's second law of dynamics. For demonstration purposes, black-box and grey-box state-space models of the Silverbox benchmark, i.e. an electrical mimicry of a single-degree-of-freedom mechanical system with cubic nonlinearity, are identified using a maximum likelihood estimator. It is found that the grey-box approach allows to reduce markedly modelling errors with respect to a black-box model with a comparable number of parameters. It is also suggested that the greater accuracy of the grey-box model lends itself to the computation of reliable confidence bounds on the model parameters. [less ▲]

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See detailSuppression of Limit Cycle Oscillations using the Nonlinear Tuned Vibration Absorber
Habib, Giuseppe ULg; Kerschen, Gaëtan ULg

in Proceeding IMAC XXXIII A Conference and Exposition on Structural Dynamics, Orlando 2-5 February 2015 (2015, February 03)

The objective of the present study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration ... [more ▼]

The objective of the present study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated numerically using the MATCONT software. The proposed developments are illustrated using a Van der Pol-Du ng primary system. [less ▲]

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See detailBridging the gap between Nonlinear Normal Modes and Modal Derivatives
Sombroek, Cees; Renson, Ludovic ULg; Tiso, Paolo et al

in Proceedings of the International Modal Analysis Conference (IMAC) XXXIII (2015, February)

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear ... [more ▼]

Nonlinear Normal Modes (NNMs) have a clear conceptual relation to the classical linear normal modes (LNMs), yet they offer a solid theoretical framework for interpreting a wide class of non-linear dynamical phenomena with no linear counterpart. The main difficulty associated with NNMs is that their calculation for large-scale models is expensive, particularly for distributed nonlinearities. Repeated direct time integrations need to be carried out together with extensive sensitivity analysis to reproduce the frequency-energy dependence of the modes of interest. In the present paper, NNMs are computed from a reduced model obtained using a quadratic transformation comprising LNMs and Modal Derivatives (MDs). Previous studies have shown that MDs can capture the essential dynamics of geometrically nonlinear structures and can greatly reduce the computational cost of time integration. A direct comparison with the NNMs computed from another standard reduction technique highlights the capability of the proposed reduction method to capture the essential nonlinear phenomena. The methodology is demonstrated using simple examples with 2 and 4 degrees of freedom. [less ▲]

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See detailExperimental demonstration of a 3D-printed nonlinear tuned vibration absorber
Grappasonni, Chiara ULg; Habib, Giuseppe ULg; Detroux, Thibaut ULg et al

in Proceedings of the International Modal Analysis Conference (IMAC) XXXIII (2015, February)

Engineering structures are designed to be lighter and more flexible, hence reducing the extent of application of linear dynamic models. Concurrently, vibration mitigation is required for enhancing the ... [more ▼]

Engineering structures are designed to be lighter and more flexible, hence reducing the extent of application of linear dynamic models. Concurrently, vibration mitigation is required for enhancing the performance, comfort or safety in real-life applications. Passive linear vibration absorbers are purpose-built, often designed using Den Hartog's equal-peak strategy. However, nonlinear systems are known to exhibit frequency-energy-dependent oscillations which linear absorbers cannot effectively damp out. In this context, the paper introduces a new nonlinear tuned vibration absorber (NLTVA) whose nonlinear functional form is tailored according to the frequency-energy dependence of the nonlinear primary structure. The NLTVA design aims at ensuring equal peaks in the nonlinear receptance function for an as large as possible range of forcing amplitudes, hence generalizing Den Hartog's method to nonlinear systems. Our focus in this study is on experimental demonstration of the NLTVA performance using a primary structure consisting of a cantilever beam with a geometrically nonlinear component at its free end. The absorber is implemented using a doubly-clamped beam fabricated thanks to 3D printing. The NLTVA performance is also compared with that of the classical linear tuned vibration absorber. [less ▲]

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See detailNonlinear generalization of Den Hartog׳s equal-peak method
Habib, Giuseppe ULg; Detroux, Thibaut ULg; Viguié, Régis et al

in Mechanical Systems & Signal Processing (2015), 52-53

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

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An 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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