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The research work reported in this dissertation aims to provide computational methodologies and to further the understanding of physical phenomena that will aid and improve the design of bladed disk assemblies from a structural dynamics standpoint. Bladed disk structures are found in a wide array of applications, including small impeller pumps andautomotive turbo systems; large gas, steam, and hydro turbines for power generation; and jet engines for military and commercial aircraft propulsion.Based on the nominal design, a bladed disk assembly is a rotationally periodic structure. If it is assumed that each disk-blade sector is identical, then the theory of cyclic symmetry may be used to analyze the dynamics of the entire structure based on one fundamental disk-blade sector. In practice, however, there are always small differences among the structural properties of individual blades, which destroy the cyclic symmetry of the bladed disk assembly. These structural irregularities, commonly referred to as mistuning, may derive from manufacturing tolerances, deviations in material properties, or non-uniform operational wear. Mistuning is known to have a potentially dramatic effect on the vibratory behavior of the rotor, since it can lead to spatial localization of the vibration energy. Spatial localization implies that the vibration energy in a bladed disk becomes confined to one or a few blades rather than being uniformly distributed throughout the system. This phenomenon may be explained by viewing the vibration energy of the system as a circumferentially traveling wave. In a perfectly tuned system, the wave propagates through each identical disk-blade sector, yielding uniform vibration amplitudes that differ only in phase. In the mistuned case, however, the structural irregularities may cause the traveling wave to be partially reflected at each sector.This can lead to confinement of vibration energy to a small region of the assembly. As a result, certain blades may experience forced response amplitudes and stresses that are substantially larger than those predicted by an analysis of the nominal design. Hence, certain blades may exhibit much shorter lifespans than would be predicted by a fatigue life assessment based on the nominal assembly.In order to address this concern, some efficient computational methods have been developed that can predict the effects of mistuning on the vibratory response of a turbomachinery rotor stage. Furthermore, these techniques enable analyses of large numbers of randomly mistuned bladed disks in order to estimate the mistuned forced response statistics for a rotor design. However, at the outset of this research effort, no methods possessed the combination of accuracy and computational efficiency required to allow reliable statistical assessments of mistuning sensitivity to be included as an integral part of the turbomachinery rotor design process. Motivated by the turbomachinery community's need for practical design tools that incorporate mistuning effects, three distinct objectives are identified and addressed in this research effort: 1 - To develop highly efficient and accurate reduced order modeling techniques for the free and forced response of tuned and mistuned bladed disks, based on parent finite element representations of arbitrary complexity and detail in a consistent and systematic fashion.2 - To broaden the scope of these reduced order modeling techniques by establishing linearized formulations for shrouded blade designs.3 - To increase the understanding of the underlying physical mechanisms of the mistuning phenomenon, with particular emphasis on the role of disk flexibility and structural stage-to-stage coupling in determining a design's sensitivity to mistuning, leading to formulations for multi-stage synthesis and analysis., Cette thèse s'intéresse à la mise en œuvre de modèles réduits de roues aubagées de moteurs d'avion sujettes au désaccordement. Lors de la modélisation de structures dites à symétrie cyclique, différents niveaux de complexité peuvent être pris en compte. Du fait de la taille des modèles numériques engendrés, il est usuel de mettre en œuvre des méthodes de réduction. Jusqu'à récemment, il était supposé que toutes les aubes étaient identiques, caractéristique mathématique permettant une réduction drastique des temps de calcul, et ce sans approximation sur la solution finale, utiles à l'analyse du comportement vibratoire de l'ensemble de la structure. Il s'avère en fait que cette hypothèse est limitée et que les aubes sont statistiquement toutes différentes les unes des autres, du fait des méthodes de fabrication par exemple, mais aussi des cycles de fonctionnement : c'est ce que l'on nomme communément le "désaccordement". La symétrie cyclique est alors rompue et les hypothèses de travail initiales ne sont plus valides. Il faut alors construire de nouveaux modèles réduits prenant en compte ce désaccordement avec un niveau d'approximation maîtrisé.

International audience; A new nonparametric probabilistic approach is presented for modeling random uncertainties in transient linear elastrodynamics. The information used does not require a description of the local parameters of the mechanical model. The probability model is constructed in the generalized coordinates associated with the elastic eigenmodes. The available information is constituted of the algebraic properties of the generalized mass. damping and stiffness matrices which have to be positive-definite symmetric matrices. and the knowledge of these matrices for the mean reduced matrix model. The convergence of the stochastic solution with respect to the dimension of the random reduced matrix model is analysed.

In many applications, it is advantageous to achieve a thorough understanding of the dynamics of a complex structure. These structures may take many forms, including rotorcraft, buildings, bridges, vehicles, and aircraft. Modern design tools, such as Finite Element Analysis, have greatly expanded the modeling detail available for such structures. However, these techniques are limited in their abilities, especially when the structure dynamics enter a nonlinear regime. This limitation is often countered by sacrificing either time | through a large, expensive computer model, or accuracy | through the elimination of possibly significant in uences. As it is of continual interest to expand the performance envelope of such structures, they are becoming lighter, more exible and, consequently, more nonlinear. This trend points out a need for effcient, analytically rigorous, widely applicable analysis techniques for nonlinear structural systems. The primary goal of this dissertation is to address this need through the further development and implementation of model reduction through nonlinear normal modes. This work extends the invariant manifold approach, with the primary goal of obtaining accurate reduced order models of nonlinear structural systems., Dans de nombreux domaines, il est primordial de bien comprendre la dynamique de structures complexes. Les outils numériques modernes, comme la méthode des éléments finis, ont grandement amélioré le niveau de modélisation mais sont souvent limitées au cadre linéaire. Pourtant l'évolution des structures, plus légères et plus flexibles, vers un comportement non linéaire suggère la mise en œuvre de méthodes adaptées, couplant rapidité et précision. C'est dans cet esprit que ce travail de recherche développe une méthode de réduction de modèles non linéaires basée sur les variétés invariantes.

This paper discusses an optimization-based approach for the design of a product platform for industrial three-axis linear-type robots, which are widely used for handling objects in manufacturing lines. Since the operational specifications of these robots, such as operation speed, working distance and orientation, weight and shape of loads, etc., will vary for different applications, robotic system vendors must provide various types of robots efficiently and effectively to meet a range of market needs. A promising step toward this goal is the concept of a product platform, in which several key elements are commonly used across a series of products, which can then be customized for individual requirements. However the design of a product platform is more complicated than that of each product, due to the need to optimize the design across many products. This paper proposes an optimization-based fundamental framework toward the design of a product platform for industrial three-axis linear-type robots; this framework allows the solution of a complicated design problem and builds an optimal design method of fundamental features of robot frames that are commonly used for a wide range of robots. In this formulation, some key performance metrics of the robot are estimated by a reduced-order model which is configured with beam theory. A multi-objective optimization problem is formulated to represent the trade-offs among key design parameters using a weighted-sum form for a single product. This formulation is integrated into a mini–max type optimization problem across a series of robots as an optimal design formulation for the product platform. Some case studies of optimal platform design for industrial three-axis linear-type robots are presented to demonstrate the applications of a genetic algorithm to such mathematical models.

In this paper, reduced-order models (ROMs) based on the Proper Orthogonal Decomposition (POD) are developed in view of decreasing the computational cost of simulations involving fluid-structure interactions. For that purpose, a truncated POD basis is used to build two types of ROMs from the Galerkin projection of the continuous nonlinear Navier-Stokes equations. First, simulations with a classical POD-Galerkin ROM are performed to reproduce the unsteady vortex shedding process in the wake of a fixed airfoil with a large angle of attack. Then, the ROM formulation is extended to take into account the rigid body motion of the airfoil. To improve the stability, a POD-based Galerkin-free ROM is developed. The aeroelastic response of an airfoil oscillating around an equilibrium position is then reproduced at very low computational cost., Dans cet article, des modèles réduits basés sur la Décomposition Orthogonale Propre (POD) sont développés dans le but de diminuer les coûts de calcul des simulations impliquant des interactions fluide-structure. Pour cela, une base POD tronquée est utilisée pour construire deux types de modèles réduits à partir de la projection de Galerkin des équations non-linéaires continues de Navier-Stokes. Dans un premier temps, des simulations avec un modèle réduit POD-Galerkin classique sont effectuées pour reproduire le processus instationnaire de détachement tourbillonnaire dans le sillage d'un profil fixe fortement incliné. Ensuite, la formulation du modèle réduit est étendue pour tenir compte du mouvement de corps rigide du profil. Pour améliorer la stabilité, un modèle réduit basé sur la POD mais n'utilisant pas de projection de Galerkin est développé. La réponse aéroélastique d'un profil oscillant autour d'une position d'équilibre est alors reproduite avec un coût de calcul très faible.

This book is devoted to mechanical models, variational formulations and discretization for calculating linear vibrations in the frequency domain of complex structures with arbitrary shape, coupled or not with external and internal acoustic fluids at rest. Such coupled systems are encountered in the area of internal and external noise prediction, reduction and control problems. The excitations can arise from different mechanisms such as mechanical forces applied to the structure, internal acoustic sources, external acoustic sources and external incident acoustic plane waves. These excitations can be deterministic or random. We are interested not only in the low-frequency domain for which modal analysis is suitable, but also in the medium-frequency domain for which additional mechanical modeling and appropriate solving methods are necessary. The main objective of the book is to present appropriate theoretical formulations, constructed so as to be directly applicable for developing computer codes for the numerical simulation of complex systems.

In the last two decades, the use of OpenFOAM as a multi-physics library for nuclear applications has grown from a sporadic use for exploratory studies to a widespread application for the analysis of innovative reactor concepts and highly complex problems. This review paper provides an overview of the past and current development efforts in the field and summarizes some of the lessons learned during 10 years of R&D activities participated by the authors. The objective is to provide readers with an understanding of the benefits and challenges of this approach, thus facilitating an informed decision about its potential adoption for future studies.

International audience; The analysis of structures partially filled with liquids (liquid-propellant rockets, liquid cooling systems, etc ...) is of the most interest for the industrial domains like transports or aerospace (aircrafts, satellites, rocket launchers, etc ...). Many experimental and computational research have been performed to better understand the behavior of such coupled fluid-structure systems. Some crucial aspects when analyzing the dynamical vibrations of a fluid-structure system are the sloshing and capillarity phenomena in fluid containers (see for instance Morand & Ohayon, 1992) and have received a great attention these last years. This work is devoted to a computational nonlinear dynamical analysis of a fluid-structure system taking into account surface tension and sloshing effects.The formulation used is the one lately introduced in (Ohayon & Soize, 2016) that allows for taking into account the weak geometrical nonlinearities of the structure through the use of an adapted nonlinear reduced-order model. The fluid-structure computational model is obtained by using the finite element method for which the boundary value problem is expressed in terms of the displacements of the structure, the pressure in the fluid, and the elevation of the free surface of the fluid.The construction of the reduced-order model is based on a projection basis constituted of the linear elastic modes, the linear acoustic modes, and the linear sloshing-capillarity modes. Such construction involves solving generalized eigenvalue problems. For large-scale fluid-structure systems, an optimized computational strategy has been proposed allowing for reducing the computational costs of this calculation. Note that the operators of the nonlinear reduced-order model are explicitly constructed in the finite element context. Finally, a numerical application consisting of a cylindrical tank partially filled with water is presented.

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM (R) and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeNFoam, a similarly OpenFOAM (R)-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 - 10(5).

International audience; The present work concerns the experimental identification of an uncertain nonlinear computational model in the context of the post-buckling analysis of a cylindrical shell. Theproposed methodology is adapted to the analysis of large static deformations of geometrically nonlinear structural systems in the presence of both system parameters uncertainties and model uncertainties. The available experimental data is made up of the nonlinear static deflection of a cylindrical shell. The deterministic nonlinear computational model is constructed using the finite element method and the corresponding nonlinear response is used as a reference deterministic solution for which a reduced-order basis is deduced using the POD analysis. The mean reduced-order nonlinear computational model is then explicitly constructed. The nonparametric probabilistic methodology for constructing the uncertain nonlinear reduced-order computational model is used. Finally, the experimental identification of the uncertain nonlinear computational model is carried out in order to validate the proposed methodology.