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Analyse numérique et expérimentale de vibrations non linéaires géométrique de structures élastiques et piézoélectriques. Modèles réduits et interactions modales

Abstract : This doctoral dissertation addresses the analysis and the modelling of the large amplitude nonlinear vibrations of thin structures with piezoelectric transduction. This type of system is used in numerous applications, such as Micro-Electromechanical Systems (MEMS), control-based systems or energy harvesting. This work proposes a numerical strategy to compute efficiently the nonlinear dynamics of electromechanical problems with geometric nonlinearities. The methodology is founded on the computation of modal reduced order models obtained from analytical and finite element approaches. In the latter case, the reduced order models are obtained by non-intrusive strategies using existing finite-element codes. Then, they are finally computed with a numerical method of continuation of periodic solutions. Original results are presented, about the validation of the non-intrusive methods and the convergence of the modal reduced order models, for reference thin structures. An experimental strategy is also proposed to highlight nonlinear phenomena on a structure with fully integrated piezoelectric actuation and detection. A phase locked-loop experimental continuation procedure is used to measure exchanges of energy due to internal resonances between asymmetric vibration modes in circular elastic and piezoelectric plates.
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Arthur Givois. Analyse numérique et expérimentale de vibrations non linéaires géométrique de structures élastiques et piézoélectriques. Modèles réduits et interactions modales. Autre [cond-mat.other]. Ecole nationale supérieure d'arts et métiers - ENSAM, 2019. Français. ⟨NNT : 2019ENAM0047⟩. ⟨tel-02489631⟩

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