Abstract : This thesis presents a numerical analysis of the structural vibrations damping obtained by passive, active and hybrid active-passive damping treatments. For that, a finite element model of a sandwich beam which layers can be elastic, piezoelectric or viscoelastic is presented. It is validated through comparisons with analytical, experimental and numerical results found in the literature and, then, extended to the case of laminated surface layers. The representation of the frequency-dependence of the viscoelastic materials properties is studied using the Anelastic Displacement Fields (ADF), Golla-Hughes-McTavish (GHM) and iterative Modal Strain Energy (MSE) models. A modal reduction of the resulting state-space system using a complex base is proposed and validated through comparisons with the results found in the literature. An iterative algorithm is proposed to evaluate the optimal control (Linear Quadratic Regulator, LQR) respecting the maximum electric field allowed by the piezoelectric patches. The comparison between the damping performances of the extension and shear piezoelectric actuation mechanisms shows that the latter are more effective for small amplitudes and high frequencies and for sandwich structures with rigid surface layers and soft core. Three hybrid damping treatments, obtained by modifying the relative position of the viscoelastic and piezoelectric layers, were analyzed and compared. It is shown that active constrained layer (ACL) treatments, consisting in replacing the elastic constraining layer by a piezoelectric actuator, are effective only for very thin viscoelastic layers. At the same time, treatments using passive constrained layer (PCL) associated with a piezoelectric actuator bonded directly on the opposite surface of the structure (AC/PCL) or between the viscoelastic layer and the structure (AC/PSOL) are, generally, more effective. However, the three treatments provide effective and robust control systems. The study of the vibration control of a sandwich beam with viscoelastic core, through two piezoelectric patches bonded symmetrically on its upper and lower surfaces, using three controllers, namely LQR, derivative and Linear Quadratic Gaussian (LQG), is carried out. It is shown that optimal controllers LQR and LQG are more effective than the derivative one, since they are less dependent on the colocalisation of the actuators and sensors. Finally, the influence of the operating temperature on the damping performance of an active constrained layer treatment is analyzed. Results show that it is possible to obtain uniform performances in an interval of temperatures.