On spatial aliasing in the phononic band-structure of layered composites

Abstract

The conventional finite element (FE) method has been used to efficiently obtain phononic dispersion relations for a wide range of geometries and materials. The motive of this research is to draw attention to the research community and addressing that special care should be taken in interpreting the FE results of dispersion analysis for some periodic structures whose FE model possesses an artificial periodicity. Layered composites have been investigated as a representative example to study this numerical issue. Despite the simple geometry of layered composites, it is well known that the accuracy of numerical dispersion relations for waves perpendicular to the layers may be highly impaired by the existence of fictitious modes. The spectral distortion stems from an arbitrarily selected unit cell which causes an artificial finite periodicity in the direction parallel to the composite layers, and they are known to be highly dependent on the unit cell configuration. However, this issue has never been thoroughly investigated, and there has been no specific guideline for a proper unit cell configuration for numerical dispersion relations. In this study, using the classical analytical solution for wave motion in the sagittal plane, the authors show that the spectral distortion induced from the artificial finite periodicity are the manifest results of spatial aliasing in the wavevector domain. In order to prevent the spectral distortion in numerical dispersion relations for waves perpendicular to the layers, this study presents a definitive guideline based on an anti-aliasing condition and the effective elastic modulus theory for layered composites and demonstrates its validity.