The analysis of wave propagation in complex structures and its application for the semi-active control of smart structures and health monitoring of these structures are dealt with in this thesis. The design of composite structures with shunted piezoelectric patches is one of the main objectives of all the investigations. This kind of smart composite structures is equipped with periodically distributed shunted piezoelectric patches. Former studies have shown the great interest of such a configuration for the active damping of structural modes at low frequencies. This thesis is focused on the extension of all these interesting characteristics of the smart structures to a larger frequency band: low and medium frequencies. The mastering of the propagation parameters and energy diffusion characteristics is targeted. In this context, the proposed work is based on techniques specifically developed in the research team "Dynamics of Systems and Structures"(D2S): the Wave Finite Element (WFE) method and Diffusion Matrix Model(DMM). The WFE approach is constructed via the finite element model of a unit cell, representative of the waveguide structure. It enables the calculation of essential wave propagation parameters like wavenumbers. The DMM, associated with the WFE approach, enables the calculation of energy diffusion characteristics like reflection and transmission coefficients of specific wave modes. These approaches are extended to consider shunted piezoelectric elements and then to evaluate the performance of shunted piezoelectric patches on the control of wave propagation in the aforementioned smart composite structures. Intensive optimizations can be carried out, with these tools, so as to obtain optimal geometric and electric parameters in the design of these smart structures. The present work is integrated in the CALIOP project in cooperation with the Laboratory of Applied Mechanics R.Chaléat at FEMTO-ST Institute and the G.W. Woodruff School of Mechanical Engineering of Georgia Institute of Technology.
