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Modes Non Linéaires : Approches réduites par PGD/HBM et applications aux réponses forcées

Abstract : In the field of structural dynamics, taking into account nonlinearities in models is a topical issue, which is gradually being integrated by the industrial sector. The spectacular progress in IT performance that has been taking place in recent decades justifies this growing interest. The objective is to create increasingly realistic models, which makes them more complex and nonlinear in many aspects. The computational cost of these models must be reduced as they often have a high number of degrees of freedom while maintaining the accuracy and reliability of the solutions. The work presented in this PhD thesis consists in the development of numerical methods allowing to quickly and efficiently compute large vibration problems that present various nonlinearities. At the same time, one want to exploit objects related to the modal characteristics intrinsic to the systems. In order to do this, the choice is made to calculate the Nonlinear Normal Modes (NNMs) of the structures. These objects can be considered as an extension of the linear normal modes taking into account systemic nonlinearities. The objective of the first axis of this manuscript is to propose a reduced approach of the calculation of these NNMs. It is based on a NNM branch continuation scheme that combines Proper Generalized Decomposition (PGD) model reduction technique and a frequency domain treatment by harmonic balance method (HBM). The resulting numerical problems are smaller in size, faster to process, and the description of the NNMs obtained is economical in terms of variables to store. The case of damped NNMs is also addressed in order to take into account the dissipative effects to which the structure may be subjected, in particular those of a nonlinear nature. An algorithm similar to the undamped case for computing these objects is implemented and described. The second axis of this work focuses on the use of the modal data contained in NNMs in the computation of forced responses of large nonlinear systems. A fast and low-dimensional estimation of the main resonance peaks is performed through a solver with 3 unknowns: amplitude, phase and frequency. All the methods, from the construction of NNMs to the plotting of frequency response functions (FRF) are illustrated by various examples. The handled models range from cases with a few degrees of freedom to finite element beam models. The nonlinearities studied are of various natures: conservative or dissipative, localized or geometrical.
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Submitted on : Thursday, December 12, 2019 - 6:09:12 PM
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Louis Meyrand. Modes Non Linéaires : Approches réduites par PGD/HBM et applications aux réponses forcées. Mécanique [physics.med-ph]. Aix-Marseile Université, 2019. Français. ⟨tel-02408126⟩

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