| Summary: | Phononic Crystals (PnCs) are novel synthetic periodic materials for controlling and manipulating the propagation of elastic (or acoustic) waves. In this work, we have considered systems formed by three-dimensional (3D) acoustic rectangular waveguides, which have internal periodic structures. Also, the case of a two-dimensional (2D) rectangular waveguide with a periodic array of circular cylindrical inclusions is exhibited, to carry out a comparative study with the 3D case. Integral numerical methods used to obtain phononic band structures involve a Boundary Element Method, which requires the use of periodic Green’s functions. An interesting detail that resulted from this study was the appearance of band gaps of the proposed structure for different values of the filling fractions. The system considered constitutes itself a PnC whose band structure corresponds in many ways to a conventional one-dimensional PnC. This fact is an alternative to manufacture a PnC that exhibits a double function: acting as a PnC and as an acoustic waveguide. The main result of this work is that discrete modes for some frequency range were obtained, which indicates that Phononic Crystal Waveguides (PnCWs) considered act as unimodal filters when the filling fraction is large. These properties exhibit some interest from a technological point of view. Keywords: Phononic Crystal Waveguide, Periodic Green’s Function Method, Band gap, Discrete mode
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