L’amélioration du confort des usagers ainsi que l’augmentation du niveau de sécurité des structures requièrent le développement de techniques permettant de limiter efficacement les vibrations. Dans cette optique, les travaux exposés ici proposent le développement et l’analyse de méthodes de contrôle vibratoire pour des structures de faibles dimensions et utilisant peu d’énergie. Afin de satisfaire à ces deux critères, il est ici proposé d’utiliser des éléments piézoélectriques électriquement interfacés de manière non-linéaire et périodiquement distribués sur la structure-cible à contrôler. Ainsi, l’approche proposée permet de bénéficier à la fois des avantages des techniques de contrôle non-linéaires appliquées aux matériaux intelligents de type piézoélectrique, offrant des performances remarquables tout en étant peu consommatrices d’énergie, avec ceux des structures périodiques exhibant des bandes fréquentielles interdites présentant de fortes atténuations de la propagation d’onde. Plus particulièrement, ce mémoire s’intéresse à différentes architectures d’interconnexion des interfaces électriques non-linéaires permettant un bon compromis entre la bande fréquentielle contrôlée et les performances en termes d’atténuation des vibrations. Ainsi, trois architectures principales sont proposées, allant de structures totalement périodiques, tant au niveau mécanique qu’électrique (interconnexions), à des structures présentant un certain degré d’apériodicité sur le plan électrique (entrelacement), impactant ainsi la propagation de l’onde acoustique en élargissant la bande de contrôle, pour enfin proposer une architecture hybride entre interconnexion et entrelacement conduisant à des systèmes large bande performants. / For ameliorating vibration reduction systems in engineering applications, miscellaneous vibration control methods, including vibration damping systems, have been developed in recent years. As one of intelligent vibration damping systems, nonlinear electronic damping system using smart materials (e.g., piezoelectric materials), is more likely to achieve multimodal vibration control. With the development of meta-structures (a structure based upon metamaterial concepts), electronic vibration damping shunts, such as linear resonant damping or negative capacitance shunts, have been introduced and integrated abundantly in the electromechanical meta-structure design for wave attenuation and vibration reduction control. Herein, semi-passive Synchronized Switch Damping on the Inductor (SSDI) technique (which belongs to nonlinear electronic damping techniques), is combined with smart meta-structure (also called smart periodic structure) concept for broadband wave attenuation and vibration reduction control, especially for low frequency applications. More precisely, smart periodic structure with nonlinear SSDI electrical networks is investigated from the following four aspects, including three new techniques for limiting vibrations: First, in order to dispose of a tool allowing the evaluation of the proposed approaches, previous finite element (FE) modeling methods for piezoelectric beam structures are summarized and a new voltage-based FE modeling method, based on Timoshenko beam theory, is proposed for investigating smart beam structure with complex interconnected electrical networks; then, the first developed technique lies in smart periodic structure with nonlinear SSDI interconnected electrical networks, which involves wave propagation interaction between continuous mechanical and continuous nonlinear electrical media; the second proposed topology lies in smart periodic structures with nonlinear SSDI interleaved / Tri-interleaved electrical networks involving wave propagation interaction between the continuous mechanical medium and the discrete nonlinear electrical medium. Due to unique electrical interleaved configuration and nonlinear SSDI electrical features, electrical irregularities are induced and simultaneously mechanical irregularities are also generated within an investigated periodic cell; the last architecture consists in smart periodic structures with SSDI multilevel interleaved-interconnected electrical networks, involving wave propagation interaction between the continuous mechanical medium and the multilevel continuous nonlinear electrical medium. Compared with the SSDI interconnected case, more resonant-type band gaps in the primitive pass bands of purely mechanical periodic structures can be induced, and the number of such band-gaps are closely related to the interconnection / interleaved level. Finally, the main works and perspectives of the thesis are summarized in the last chapter.