This thesis is focused on beam vibration control using piezoelectric transducers and passive electric networks. The first part of this study deals with the modeling and the analysis of stepped piezoelectric beams. A refined one-dimensional model is derived and experimentally validated. The modal properties are determined with four numerical methods. A homogenized model of stepped periodic piezoelectric beams is derived by using two-scale convergence. The second part deals with the performance analysis of three passive circuits in damping structural vibrations: the piezoelectric shunting, the second order transmission line and the fourth order transmission line. The effects of uncertainties of the electric parameters on the system performances are analyzed. Theoretical predictions are validated through different experimental setup
