The method of fundamental solutions for the analysis of infinite 3D sonic crystals

Abstract

[EN] The use of periodic structures in acoustic applications has interested the scientific community in the last two decades. Although in-depth research has been thoroughly performed, many issues have still not been solved. Computational analysis of sonic structures using realistic 3D models still poses significant problems, and most of the published results correspond to 2D problems. Analysing 3D problems of such structures using conventional methods demands large computational resources, which may be prohibitive. This paper proposes a new approach for such 3D problems making use of a highly efficient Method of Fundamental Solutions (MFS) approach to deal with sonic crystals made of 3D scatterers, infinitely repeated with constant spacing along one direction. The method makes use of a special form of the acoustic fundamental solutions which can be highly efficient in such analysis, while allowing just the cell that is repeated to be effectively modelled. Verification of the model is provided by first comparing its results with those from an ACA-MFS model. Results are compared with those from a FDTD algorithm, and a parametric study is presented revealing the 3D character of the computed responses, and evidencing the formation of acoustic band-gaps at specific frequency bands associated with the Bragg effect.