During the last decades, a growing interest has been devoted to periodic structures and metamaterials. One of the most interesting characteristics of this class of materials is that they present a transmission gap for given frequency ranges. This peculiar characteristic has many potential applications: from optics to seismic isolation, from filtering to wave guiding. In literature, different approaches were developed to study such kind of structures. In this paper, using an approach based on transfer matrices of a single unit cell and its invariants, a way to represent in compact form the behavior of a mono-coupled periodic structure is presented. As a result, the wave propagation properties are shown as being dependent both on the frequency range and on some chosen design parameters. Furthermore, the adding of multiphysics materials (in the case of this paper piezoelectric inserts with dedicated electric circuits) inside the structure allows, through the tuning of both the mechanical and the electrical parameters, to actively control the bandgap position. This approach also allows checking the robustness of parameter choices with respect to desired bandgap frequency ranges. Finally, some applications of this method for active control of wave propagation are presented.

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