3D analysis of sonic crystal structures with absorbing scatterers

摘要

Computer simulation of sonic crystals using realistic 3D models is a demanding task. Indeed, most of the published works correspond to 2D problems, and only a few deal with the 3D character of such structures. The present paper presents an efficient method based on the Method of Fundamental Solutions (MFS) 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 comparing its results with those from a FDTD algorithm. Absorbing surfaces are considered by means of imposing impedance surface conditions. A simulation example is presented to evidence the formation of acoustic band-gaps at specific frequency bands associated with the Bragg effect, and to illustrate the effect of scatterer absorption.