Layered Acoustic Structures with Equally Phased Elements

It is often required to control the acoustic transmission across layered structures in order to favor or, more frequently, limit it in prescribed energy ranges. The selection of the materials and layer thicknesses needed to achieve a given objective is not straightforward, and it is often performed empirically. This is connected with the lack of simple models that dictate the frequency behavior of the layered structure. In this work, we present an approach to the systematic design of layered media, based on an assumption that allows us to obtain simple analytical expressions for the occurrence of bandgaps in the frequency response of ideally infinite periodic structures. Correspondingly low-transmission frequency ranges are then analyzed and discussed in finite-thickness realizations of the designed periodic structures.