This work is on the subject of modelization of structures treated with passive damping elements. A generic "equivalent single layer" plate model using transverse shear warping functions is presented. Several methods to obtain these functions are described, allowing the implementation of classical models and others issued from the litterature. Two new methods for obtaining these functions are also presented.Several discretization methods adapted to the generic plate model are studied. Navier's procedure allows the testing of the quality of each model associated with a set of transverse shear warping functions. Rayleigh-Ritz method allows the study of the vibrational behavior of a rectangular plate treated with one or several constrained damping patches. Several finite elements issued from the literature are also presented.Using Navier's procedure, a numerical study of the static and dynamic behavior of several plate configurations allows the comparison of the different plate models. Rayleigh-Ritz method is used to study the vibrational response of a plate treated with a constrained damping patch. A comparison of the results with those obtained with three dimensional finite element calculations permits the model validation. An energetic study of the patched plate allow us to understand the constrainted damping patch behavior. Finally, an inverse method, allowing the identification of the properties of viscoelastic materials, based on a combination of the presented model and a genetic algorithm, shows a possible application of the model.
