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Computational dynamics of geometrically nonlinear structures coupled with acoustic fluids in presence of sloshing and capillarity : uncertainty quantification

Abstract : In this thesis, we are interested in computationally modeling and simulating coupled fluid-structure systems constituted of an elastic structure partially filled with a fluid with a free surface, considering the effects of sloshing and capillarity. The internal fluid is linear, acoustic, dissipative, and the linear elastic structure is submitted to large displacements inducing geometrical nonlinearities. The work presented in this manuscript first details the theoretical study regarding such coupled fluid-structure systems and focuses on the construction and implementation of the computational model using an adapted nonlinear reduced-order model. This reduced-order model allows for performing the nonlinear dynamical simulations and for better understanding the phenomena related to each subset of the coupled system. Several numerical applications are then presented to analyze various phenomena related to the different coupling mechanisms and energy transfers in such fluid-structure system. The first development axis consists in quantifying and reducing the computational resources required for the construction of the projection basis of the reduced-order model when dealing with very-large dimension fluid-structure computational models. A new methodology is presented, which allows for reducing the computational costs required for solving three generalized eigenvalue problems that cannot be solved on medium-power computers. A second development axis is devoted to the quantification of the influence of the coupling operator between the structure and the free surface of the internal liquid allowing for taking into account the capillary contact angle condition on the triple line while considering a deformable structure. The third axis is based on experimental research published in 1962 in the framework of NASA researches for orbital launchers, which highlighted an unexpected phenomenon of large amplitude and low-frequency sloshing of an internal liquid for a medium-frequency excitation of the tank. We propose to revisit these experimental results and to explain the causes of such unexpected phenomenon through a numerical simulation taking into account the geometrical nonlinearities of the structure. Finally, the last development axis is devoted to the propagation of nonparametric uncertainties of the structure in the system by the different coupling mechanisms. The nonparametric stochastic model is the nonparametric probabilistic approach using the random matrix theory. A methodology for identifying the hyperparameter is presented, based on an experimental data set and on an inverse statistical problem. A numerical validation of this method on a simulated experimental data set is presented
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Quentin Akkaoui. Computational dynamics of geometrically nonlinear structures coupled with acoustic fluids in presence of sloshing and capillarity : uncertainty quantification. Mechanics [physics.med-ph]. Université Paris-Est, 2019. English. ⟨NNT : 2019PESC2001⟩. ⟨tel-02477170⟩

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