Low-frequency propagation of plane scalar waves through a periodic array of arbitrary volumetric obstacles - Scarpetta, E.; Sumbatyan, M.A. (Нелінійні коливання, 2003)
In the context of wave propagation through gratings of periodically distributed obstacles, we use analytical approaches to derive explicit formulas for the scattering parameters in the low-frequency approximation. The geometric shape of the obstacles is arbitrary. Numerical solution of the main integral equations for assigned shapes will provide some graphs, and comparison with previous results will show that some of these are incorrect or hold under very restrictive conditions.