Acoustic insertion loss due to two dimensional periodic arrays of   circular cylinders parallel to a nearby surface
  The acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane, have been investigated through predictions and laboratory experiments. Semi-analytical predictions based on multiple scattering theory and numerical simulations based on a boundary element formulation have been made. Measurements have been made in an anechoic chamber using arrays of (a) cylindrical acoustically-rigid scatterers (PVC pipes) and (b) thin elastic shells. Insertion loss (IL) spectra due to the arrays have been measured without and with ground planes for several receiver heights. Data and predictions have been compared. The minima in the excess attenuation spectrum i.e., attenuation maxima due to the ground alone resulting from destructive interference between direct and ground-reflected sound waves, tend to have an adverse influence on the band gaps (BG) related to a periodic array in the free field when these two effects coincide. On the other hand, the presence of rigid ground may result in an IL for an array near the ground similar to or, in the case of the first BG, greater than that resulting from a double array, equivalent to the original array plus its ground plane mirror image, in the free field. 
Anton Krynkin, Olga Umnova, Juan Vicente Sanchez-Perez, Alvin Y.B.   Chong, Shahram Taherzadeh and Keith Attenborough
math-ph math.MP