Anti-plane SH wave scattering by an elliptical nanohole with non-zero surface density

Always in non-destructive evaluations to find defects or cracks in materials at any scale, knowing how to solve the direct wave scattering problem will be the primary requirement for analysis. In this regard, the study of anti-plane wave scattering due to an elliptical hole at the nanoscale has gained special importance today. At this scale, surface effects play a key role. Here, in addition to considering surface tensions, the density of the surface layer has also been added to the boundary equations due to the dynamic nature of the problem. Therefore, by taking these matters into account, noticeable changes will occur in the analyses, of course, in the desired scales and final frequencies, which certainly were not found in classical analysis or analyses without considering the surface layer density. In the elliptical coordinate system, the solution is introduced by expanding it into Mathieu functions to solve the corresponding boundary value problem, and a series solution is obtained for the scattering wave function

Keywords:

Surface effect , Elliptic nanohole scatterer , Anti-plane SH waves , Free surface density , Mathieu functions