The 2.5D MST for sound propagation through an array of acoustically rigid cylinders perpendicular to an impedance surface

In this work a study of sound propagation through arrays of semi-infinitely long cylinders placed perpendicular to an impedance surface has been carried out. The cross sections of the structures are assumed to be invariant along the main axis of the cylinders, and the cylinders are considered rigid. It is further assumed that the structures are insonified by a monopole source placed above the impedance surface. To study such configurations, we introduce the two-and-a-half-dimensional multiple scattering theory (2.5D MST), which essentially solves the pressure in a three-dimensional domain by post-processing a set of precomputed solutions obtained in a two-dimensional domain. The total pressure can then be obtained by complex addition of four contributions: source-to-receiver, source-to-array-to-receiver, image source-to-receiver, and image source-to-array-to-receiver. The proposed method is validated using both analytical and numerical tools, showing very good agreement for all studied cases. Among other things, we show that a cylinder array placed on top of flat rigid ground can deteriorate the ground interference dips that exist without the array. In addition, we show that the characteristic response of the cylinder array, i.e. in terms of pass and stop bands, may be shifted up in frequency due to a projection phenomenon, which happens when the source or receiver is elevated along the main axis of the cylinders