Definition of a linear equivalent model for a non-linear system with impacts

Modal characteristics of non-linear system are typically studied through response to harmonic excitation and using various definitions of non-linear modes. However, few results are available for systems under broadband excitation. The end objective sought here is to generate a linear system, in some sense equivalent to the non-linear system, whose modal characteristics evolve with a level of non-linearity. The considered application is the contact non-linearity found between the tubes of heat exchangers and their support plates. Such tubes, present in nuclear plants, participate to the nuclear safety and can be significantly excited by the fluid flow, so that their dynamic behavior is critical. The turbulent nature of the flow implies broadband excitation and the small gaps between the tubes and the support plate generate very significant non-linear behavior. The proposed equivalent linear system is based on a bilateral contact law whose stiffness and damping characteristics evolve with the amplitude of excitation. A non-linear model is first validated by correlation with experiments. It is then shown that three different indicators (bandwidth of main resonance, operational modal analysis of non-linear power spectral density and correlation of operational deflection shapes) lead to similar values of contact stiffness and damping in the equivalent linear model. This model is hus shown to be a very efficient tool to analyze the impact of the amplitude dependence of the non-linear behavior in the considered system

Definition of a linear equivalent model for a non-linear system with impacts

International audienceModal characteristics of non-linear system are typically studied through response to harmonic excitation and using various definitions of non-linear modes. However, few results are available for systems under broadband excitation. The end objective sought here is to generate a linear system, in some sense equivalent to the non-linear system, whose modal characteristics evolve with a level of non-linearity. The considered application is the contact non-linearity found between the tubes of heat exchangers and their support plates. Such tubes, present in nuclear plants, participate to the nuclear safety and can be significantly excited by the fluid flow, so that their dynamic behavior is critical. The turbulent nature of the flow implies broadband excitation and the small gaps between the tubes and the support plate generate very significant non-linear behavior. The proposed equivalent linear system is based on a bilateral contact law whose stiffness and damping characteristics evolve with the amplitude of excitation. A non-linear model is first validated by correlation with experiments. It is then shown that three different indicators (bandwidth of main resonance, operational modal analysis of non-linear power spectral density and correlation of operational deflection shapes) lead to similar values of contact stiffness and damping in the equivalent linear model. This model is hus shown to be a very efficient tool to analyze the impact of the amplitude dependence of the non-linear behavior in the considered system

Robust expansion of experimental mode shapes under epistemic uncertainties

International audienceImportant variations in response behaviors of power plant generators are observed in a population of nominally identica installations due to numerous and significant sources of variability. As a result, it proves to be extremely difficult to implement a predictive and reliable physics-based model. The present study attempts to leverage an existing non validated numerical model to reconstruct information on unobserved degrees of freedom based on the results of modal tests. An expansion method is proposed based on the concept of the constitutive relation error (CRE). This method leads to minimization of an energy-based functional that takes into account both errors in the model and in the test data. Due to lack of knowledge, commonplace in this kind of complex system, the expansion will be presented in the framework of robust approach. More precisely, the first objective of this article is to assess the robustness of the mode shape expansion in presence of large epistemic uncertainties that are represented as info-gap models. Secondly, a strategy will be presented to maximize the robustness of the expansion by appropriately selecting the model decision variables for a given horizon of uncertainty. The proposed methodology is illustrated on simple academic test cases

Numerical simulation and experimental validation of gap supported tube subjected to fluid-elastic coupling forces for hybrid characterization tests

International audienceIn steam generators, the primary loop tubes are subjected to fluid coupling forces and impacts. Understanding the behavior of these tubes is crucial when designing steam generators. In fact, it can afford an optimization of produced energy and a long average life of the structure. Up to now, the effect of the coupling forces on structural behavior was identified on reduced scale structures. Thus, the aim of our research is to give a better understanding of stabilizing effects of shock and coupling with fluid elastic forces. In order to validate numerical investigations, since fluid elastic forces are difficult simulate and expensive to reproduce experimentally, the fluid coupling forces will be assumed to be represented using velocity dependant (fluid and structure) damping and stiffness matrices, and experimentally reproduced using active vibration control into hybrid experimental tests to simplify big structure characterization. In this paper, a method for modeling the structure behavior in order to estimate the effects of the coupling between the fluid elastic forces and impacts is presented. This strategy implies lower costs and avoids difficulties associated to the case of fluid in the experiments. This model will be implemented in the active control loop in the next step of the study

Amélioration de méthodes de modification structurale par utilisation de techniques d'expansion et de réduction de modèle.

This work deals with the improvements of methods devoted to estimate the influence of modifications on the dynamic behaviour of a structure (addition of stiffeners or masses, boundary condition changes). The input data for the method are an experimentally derived model of the initial structure and a numerical model of the modification. Based on a coarse model of the structure to be modified, the proposed methodology tackles two major difficulties : efficient predictions for distributed modifications and handling of the lack of measurement points on the coupling interface. In addition, displacements bases introduced to reconstruct unmeasured behaviour of the interface limit error propagation through the process. Moreover, two indicators are introduced to select the optimal prediction. A number of industrial examples illustrate the performance of this approach, in terms of reactivity as well as quality of the predictions of dynamic behaviour.Les méthodes de modification structurale sont l'ensemble des techniques qui permettent d'estimer l'influence d'une modification quelconque sur le comportement dynamique d'une structure. Dans le cadre général, le modèle de comportement de la structure cible, comme celui de la modification, peut être aussi bien numérique qu'expérimental. Dans le cadre de ce travail, seul le cas particulier du couplage d'un modèle expérimental de la structure et d'un modèle numérique de la modification sera traité.Les concepts fondamentaux utilisés dans cette thèse sont ensuite présentés. Les relations de la dynamique des structures pour les problèmes discrets sont rappelées, ainsi que les principes de la synthèse modale, de la sous-structuration dynamique et de la réduction de modèle, tout comme la notion de modes d'interface. Les formulations classiques des méthodes de modification structurale sont ensuite détaillées pour en illustrer les limitations et les restrictions.Une formulation originale permettant de prendre en compte les incompatibilités entre les mesures et les DDL de l'interface structure/modification et de régulariser la construction d'un modèle de comportement couplé est alors proposée. Cette première contribution de la thèse repose sur l'utilisation des techniques d'expansion de données et de réduction de modèle. Des indicateurs sont également construits pour estimer la cohérence de la prédiction réalisée. Les évolutions sont appliquées au cas d'un démonstrateur numériques et les résultats sont comparés avec les prédictions réalisées par les méthodes classiques. La méthodologie associée à cette nouvelle formulation est alors largement exposée.L'influence des différents facteurs intervenant dans la construction du modèle couplé et la qualité de la prédiction est ensuite analysée en détail. Cette analyse permet de dresser une liste non exhaustive des précautions à prendre lors de la mise en œuvre de la méthode proposée, depuis la réalisation pratique de l'analyse modale expérimentale jusqu'à l'interprétation des premiers résultats.Enfin, plusieurs applications sont présentées. Une première structure académique démontre la faisabilité de la méthode. Une deuxième étude, réalisée sur un cas industriel, illustre les gains de temps potentiels en comparant la prédiction avec les résultats d'une étude basée sur un modèle EF recalé de la structure. La troisième étude illustre l'application de la méthode dans un cas type. L'analyse modale de la structure cible permet de comprendre le problème, une modification est conçue, réalisée et mise en place. La prédiction est ensuite comparée aux résultats de l'analyse modale de la structure modifiée. Enfin, la dernière application montre les limites de la méthodologie. L'étude multi-objectifs sur une large bande de fréquences d'une structure industrielle permet de faire une ouverture vers la suite des travaux et montre la nature des difficultés à surmonter

Amélioration des méthodes de modification structurale par utilisation de techniques d'expansion et de réduction de modèle

Ce travail porte sur l'amélioration des méthodes permettant d'estimer rapidement l'influence d'une modification (ajout de raidisseurs ou de masses, modification d'ancrages) sur le comportement vibratoire d'une structure à partir d'un modèle expérimental de la structure initiale et d'un modèle numérique de la modification. En s'appuyant sur un modèle grossier de la structure à modifier, la méthodologie développée n'impose pas de disposer de points de mesure sur l'interface de couplage et permet entre autre de prendre efficacement en compte des modifications présentant une interface continue avec la structure. L'introduction d'une base de déplacements pour reconstruire les mouvements de l'interface permet également de limiter la propagation des différentes erreurs expérimentales. Deux critères de qualité de la prédiction sont également proposés. De nombreux exemples industriels illustrent les performances de la méthode, tant en terme de réactivité que de qualité des prédictions de comportement vibratoire.CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF

A priori verification of local FE model based force identification

International audienceThe paper revisits force identification methods. Rather than using the classical inversion of the estimated transfers, one prefers to use a local model to generate an estimator of the modal states. The pseudo inverse in the force estimation process is then limited to the well-conditioned inversion of the dynamic stiffness in modal coordinates. The local model is also used to define physical loads rather than using the classical equivalent loads at sensors. The proposed strategy is illustrated on a numerical test case representing a pump motor. The objective of such simulations is not only to validate the methodology but also to show how the ability to identify forces should be validated a priori. Such validations can be performed for a given sensor configuration or used as the objective guiding a sensor placement algorithm that is presented

Méthodes de modifications structurales dissipatives: Validation expérimentale

International audienceThe structural dynamic modification methods are used to predict the effect of adding mass, stiffness or damping on an only-experimentally-known structure. This article presents the experimental validation of the method for a dissipative modification on a mock-up example.Les méthodes de modification structurales s'attachent à prédire l'effet de l'ajout de masse, de raideur ou d'amortissement sur une structure qu'on ne connaît que de manière expérimentale. Le présent article décrit la validation expérimentale de la méthode pour des modifications structurales dissipatives sur un démonstrateur semi-industriel