Un Problème Aux Limites Gouverné par l'Opérateur Dynamique de Vibrations Non-Linéaire des Plaques

Abstract

In this thesis, we propose to study a nonlinear boundary value problem governed by the dynamic equations of nonlinear plate vibrations. Since the field of application of vibrating plates is very broad, the geometric shape, the mass density of the material constituting the plate, the plate thickness, as well as Poisson's ratio, will be taken into account in order to meet users' needs. As this problem involves a coupling between the Airy stress function F and the transverse displacement u, the adopted approach consists in reducing it to a nonlinear hyperbolic system. To this end, the Airy function is eliminated from the system, and an existence theorem for the considered evolution equation, together with a uniqueness theorem for the modified evolution equation, is established. As a possible extension, this study can be applied to the field of thin structures (beams, plates, and shells) equipped with