Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques

Abstract : This thesis deals with the development of solid–shell finite elements for vibration modeling of multilayer structures. Indeed, most of multilayer models in the literature show some limitations in certain geometric and material configurations. Considering these restrictions and in order to develop a more efficient calculation tool, we proposed an approach based on the solid–shell concept. This consists of three-dimensional finite elements enhanced through the Assumed Strain Method. First of all, we have formulated the problem of vibrations of sandwich structures with viscoelastic core. The frequency dependence has been taken into account by using a complex constitutive law. To solve the discretized problem, the Asymptotic Numerical Method, coupled with the homotopy technique and the DIAMANT toolbox approach, was adopted due to the excellent results it provides compared to other methods. Benchmark tests have validated the models and highlighted their advantages over existing elements having the same kinematics. In order to increase damping properties, we directed our attention towards an active vibration control. For this purpose, two piezoelectric finite elements have been developed. These finite elements SHB8PSE and SHB20E are extensions, of the elements SHB8PS and SHB20, respectively. The electromechanical coupling consisted in adding an electrical degree of freedom to each node of these elements. A variety of test problems both in static and vibration analysis conducted on multilayer structures ranging from simple beams to structures involving geometric nonlinearities allowed validating the proposed solid–shell elements. Finally, combining the achievements made in chapters 2 and 3, we proposed a modeling approach for multilayer structures composed of elastic, viscoelastic and piezoelectric layers. Active control is introduced using the piezoelectric properties in order to improve the reduction in vibration amplitudes. Thus, a filter has been mounted between the sensors and actuators. This filter allows amplifying or attenuating the generated electric potential in order to reduce the vibration amplitudes. To solve the resulting problem, we extended the resolution method used in chapter 2. To validate the proposed models, active–passive control tests have been conducted on multilayer plate structures. Finally, some control laws, associated with filters, have shown how this procedure can allow reducing or even avoiding amplification of vibrations
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Fessal Kpeky. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques. Autre. Université de Lorraine, 2016. Français. ⟨NNT : 2016LORR0008⟩. ⟨tel-01752207⟩

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