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Réduction par apprentissage multi-nombres d'onde pour les guides d'ondes ouverts ou hétérogènes : application à la dynamique de la voie ferrée

Abstract : The main goal of this work is to propose a waveguide model representing the whole length to handlethe variability between geometrically periodic cells, suited to time-based computations to deal with non-linearities,and with reduction to allow simulations in a time sufficiently small for use in a design group. The analysis ofwaveguides is a recurring subject in the literature. Bloch-Floquet theory is often used to compute solutions definedon a reference cell at several wavenumbers. However, this formulation does not allow variability between periodiccells, is not suited for time-based computations, and may lead to a significant numerical cost if the interface betweencells is large. To address these limitations, a reduction strategy is proposed, based on the building of a learningsubspace from computed static and modal forms within a frequency range of interest, and for few wavenumbers. Amodel of the full guide is built from reduced cell models and can account for variability. By adjusting the extremecells of the model, this strategy can be adapted for both finite and infinite periodic structures.This reduction strategy is applied to the study of a heterogeneous periodic structure, generated from randomfields. The presence of frequency bandgaps and local modes is assessed. The learning phase manages to takecorrectly these phenomena into account. The strategy is extended to non-periodic heterogeneous structures bycombining several periodic samples.Another goal is to approach radiation in an open medium with absorbing PML boundaries, while maintainingthe possibility to achieve both time and frequency-based computations, which is a requirement of the reductionstrategy. To that end, a FEM implementation with 3D wave attenuation is detailed. The frequency-based analysis ofthis formulation raising contionning issues, conditions are proposed that are sufficient avoid the problem. Theapplication case of a train pass-by on a track shows another limitation : a wrong asymptotic behavior at lowfrequencies.For each of the three main topics, the proposed methodologies are applied to railway track models. They give abetter understanding of the behavior of ballasted or discontinuous slab tracks at low frequencies.
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Submitted on : Thursday, February 4, 2021 - 4:34:10 PM
Last modification on : Tuesday, September 27, 2022 - 10:30:58 AM
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  • HAL Id : tel-03131802, version 1


Hadrien Pinault. Réduction par apprentissage multi-nombres d'onde pour les guides d'ondes ouverts ou hétérogènes : application à la dynamique de la voie ferrée. Dynamique, vibrations. HESAM Université, 2020. Français. ⟨NNT : 2020HESAE049⟩. ⟨tel-03131802⟩



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