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International audience; It is essential to predict accurately the critical speeds and associated vibration amplitudes of rotating machineries to ensure a correct design to limit noise nuisance and fatigue failure. However, numerous uncertainties are present, due to environmental variations or manufacturing tolerances for e.g., and must be taken into consideration in the design stage to limit their impact on the system dynamics. These uncertainties are usually modelled with a probability law and the dynamic response becomes stochastic. On the other side, during the design stage, a few key parameters, often called design parameters, are identified and tuned to ensure a robust conception of the rotor w.r.t to the uncertain model parameters. In this context, one must tackle a high-dimension parametric problem but numerous parameters of different nature. The efficiency of an advanced meta-modelling technique that couple polynomial chaos expansion and kriging is demonstrated here. The kriging efficiency is improved by introducing physical properties of the rotor. A finite element model of a rotor subjected to nine uncertain parameters is studied. The hybrid surrogate model gives a direct access to the Sobol indices, exploited to conduct an extensive sensitivity analysis.

International audience; This study focuses on the prediction of the stability behavior of an industrial automotive brake system under structural and environmental uncertainties. Uncertainties are modeled with a random distribution or an interval and are propagated with a hybrid surrogate model associating polynomial chaos and kriging. The objective is to create a surrogate model of each eigenvalue computed with the complex eigenvalue analysis (CEA). As the modes can be tracked only when unstable, the effective size of the training sets can become extremely small. Despite this limitation, it is shown the hybrid meta-model is still able to predict the stability of the brake system. Moreover, the hybrid meta-model gives a direct access to the mean and variance of the eigenvalues with respect to the design parameters without any additional Monte Carlo simulations (MCS). By considering different probability density function for the friction coefficient, it is shown it has a high influence on the stability and the latter should be accurately estimated.

International audience; In this study the authors propose to take into account the nonlinear effects induced by the presence of a transverse crack to carry out vibratory monitoring and detect transverse cracks in rotating systems subject to model uncertainties. More precisely, we focus more particularly on the global complexity of the nonlinear dynamic behaviour of cracked rotors and the evolution of their harmonic components as a function of the parameters of a transverse breathing crack (its position and depth) when numerous uncertainties are considered. These random uncertainties correspond to random geometric imperfections (two disc thicknesses), random material properties (Young modulus and material density) and boundary conditions uncertainty (two bearing stiffnesses). The objective of the present work is to identify robust indicators capable of determining the presence of a crack and its status even though numerous uncertainties are present. To conduct such a study, an advanced surrogate modelling technique based on kriging and Polynomial Chaos Expansion (PCE) is proposed for the prediction of both the critical speeds and the harmonic components × during passage through sub-critical resonances. An extensive study to ensure the validation of the surrogate models and a relevant choice of both the parametric and random Design of Experiments (i.e. kriging DoE and PCE DoE) is proposed. The proposed methodology is applied on a flexible rotor with a transverse breathing crack and subjected to random geometric imperfections and fluctuations in material properties of the rotor system.

In order to ensure the integrity of rotating machines, it is necessary to predict the critical speeds and associated vibration amplitudes. The design of such structures requires considering the variability of a large number of parameters of different natures. This work proposes to predict the dynamic behaviour of a rotor modelled by a finite element model subjected to numerous uncertain parameters. The aim is to carry out an efficient parametric study of the stochastic system. For this purpose, a hybrid metamodelling method coupling kriging and polynomial chaos is used. The efficiency of the method is increased by introducing the symmetry properties of the mechanical problem in the kriging part. The results allow an accurate prediction of the dynamic behaviour of the rotor and a sensitivity study showing the complex phenomena involved., Afin d'assurer l'intégrité des machines tournantes, il est nécessaire de prédire les vitesses critiques et les amplitudes vibratoires associées. Le dimensionnement de telles structures nécessite de prendre en compte la variabilité d'un grand nombre de paramètres de différentes natures. Ce travail propose de prédire le comportement dynamique d'un rotor modélisé par un modèle éléments finis soumis à de nombreux paramètres incertains. Le but est de réaliser de façon efficace une étude paramétrique du système stochastique. Pour ce faire, une méthode de méta-modélisation hybride couplant krigeage et chaos polynomial est utilisée. L'efficacité de la méthode est augmentée par l'introduction des propriétés de symétrie du problème mécanique dans la partie krigeage. Les résultats permettent de prédire avec précision le comportement dynamique du rotor et de réaliser une étude de sensibilité montrant les phénomènes complexes étant mis en jeu.

International audience; Abstract In this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.

International audience; Rotating machinery are present in many engineering applications. Such rotor systems often subjected to high vibration loads that can be at the origin of noise or failure. For these reasons, it is of main importance to predict with accuracy the critical speeds and the dynamic response amplitude of such structures. However, they are often subjected to many potential uncertainties that may rise from environmental variations or manufacturing tolerances. These uncertain parameters, often described as random, are often numerous and must be taken into consideration during the design stage. For this, some design parameters are usually adjusted to propose a robust design of the rotor, considering the possible variation of the random parameters. Performing such studies require to be able to deal with a high number of uncertain parameters and with parameters of different nature, namely parametric and random.This work proposes to illustrate the efficiency of advanced kriging-based surrogate modelling in order to achieve such a goal. The proposed hybrid surrogate-model combines polynomial chaos expansion and kriging to deal with both parameter natures, to consider nine varying parameters of a full finite element model of the rotating system under study. For the first time, this hybrid surrogate model is applied to perform rotordynamics analysis and more specifically the prediction of critical speeds and the associated unbalance responses for a complex rotor system with uncertainties. Compared to previous works, the kriging performances are significantly increased by integrating some physical properties of the rotor directly in its construction. Finally, the hybrid surrogate model gives a direct access to the Sobol indices which makes it possible to carry out without additional computation costs an extensive sensitivity analysis.

This data article comprises data to investigate the non-linear dynamic behavior of the CEA-beam benchmark structure subjected to one stochastic broadband excitation. Experiments have been performed on the CEA-CESTA laboratory. The data provided include the input Power Spectral Density for four levels of excitation and the associated output nonlinear dynamic behavior of the CEA-beam benchmark structure. All the results from this data will help researchers and engineers in proper analysis of hardening effect and the enlargement of the response peak due to one stochastic broadband excitation, as well as the presence of harmonics. One of the main original contributions is to share the data sets to give the opportunity to researchers for testing and validating analytical or numerical models of a nonlinear beam with non-ideal boundary conditions and subjected to one stochastic broadband excitation. This Data in Brief article is an additional item directly alongside the following paper published in the Communications in Nonlinear Science and Numerical Simulation (CNSNS) journal: T. Roncen, J-P. Lambelin and J-J. Sinou, Nonlinear vibrations of a beam with non-ideal boundary conditions and stochastic excitations - experiments, modeling and simulations, Communications in Nonlinear Science and Numerical Simulation,74 (2019) 14-29. doi.org/10.1016/j.cnsns.2019.03.006

14ème Congrès Français d'Acoustique (CFA'18), LE HAVRE, FRANCE, 23-/04/2018 - 27/04/2018; Grâce aux nombreux travaux de recherche réalisés ces dernières années, les principaux phénomènes vibratoires à l'origine du crissement des freins à disque en moyenne et haute fréquence sont aujourd'hui bien identifiés. Dans la plupart des cas, des instabilités par couplage modal de l'équilibre quasi-statique glissant semblent être responsables des vibrations auto-entretenues du système. Ces instabilités peuvent être caractérisées en première approche à l'aide d'une analyse fréquentielle linéarisée. Toutefois, l'estimation des amplitudes et du contenu spectral complet des oscillations en régime stationnaire nécessite une analyse non linéaire plus délicate à mettre en øeuvre d'un point de vue calculatoire. Les deux techniques les plus utilisées sont l'intégration numérique dans le domaine temporel à partir de conditions initiales données et l'équilibrage harmonique permettant la recherche directe de régimes périodiques ou quasi-périodiques. Dans le cas de modèles éléments finis comportant de nombreux degrés de libertés les deux méthodes conduisent souvent à des coûts de calcul (charge et mémoire) trop importants pour être utilisés en pratique. Dans ce papier, une alternative est proposée pour l'estimation de régimes périodiques dans les cas mono-instables. Il s'agit d'une méthode de tir réduite permettant une approximation des vibrations auto-entretenues en quelques itérations. La méthode est testée sur un modèle simplifié de frein à disque ferroviaire.

International audience; L’assemblage métallique étudié comprend neuf plots viscoélastiques en élastomère. La réponse vibratoire est influencée par le comportement non linéaire des plots. Un modèle élément fini de l’assemblage complet ainsi qu’un modèle de non-linéarité empirique issu d’essais unitaires sur des plots viscoélastiques seuls sont proposés. La méthode de simulation utilisée se base sur une réduction de modèle et une résolution par la méthode d’équilibrage harmonique incrémentale. Dans un second temps, la réponse dynamique non linéaire en présence d’incertitudes est proposée par l’intermédiaire du Chaos Polynomial non intrusif. Des comparaisons essais-calculs à l’échelle du plot et de l’assemblage sont présentées.

International audience; Ce papier propose d’étudier les vibrations auto-entretenues d’un modèle éléments finis de frein ferroviaire s oumis à des lois de contact unilatéral et de frottement de Coulomb à coefficient de frottement constant. En premier lieu la stabilité du système est étudiée en fonction du coefficient de frottement afin de déterminer les zones instables pour lesquelles des vibrations auto- entretenues peuvent apparaître. Une solution périodique non- linéaire est ensuite recherchée à l’aide d’une méthode itérative de tir combinée à une approche énergétique simplifiée pour l’estimation initiale.