SH wave scattering by a circular arc-shaped nano-hole located within the half-plane boundary of one-dimensional hexagonal quasicrystals

The scattering characteristics of SH waves enable a deeper understanding of wave propagation, thereby improving the accuracy and reliability of non-destructive testing. By combining with the generalized Young–Laplace equation and the wave function expansion method, the anti-plane problem of SH wave scattering by a circular arc-shaped nano-hole within one-dimensional hexagonal (1DH) quasicrystal (QC) half-plane boundary is studied. Based on the Huygens principle, the Graf’s addition formula and the orthogonal characteristic of trigonometric functions, the analytical solutions for the dynamic stress concentration factors (DSCFs) are obtained. Numerical examples discuss the effects of the surface effects, the wave numbers, and the incident angle on DSCFs with different circular arc-shaped nano-holes. The results indicate that the DSCF of the phonon field decreases gradually with the increasing of the surface effect factors or the incident angle at low frequencies (LFs). The influence of the incident angle and surface effect factors on the DSCFs is irregular at high frequencies (HFs). The arc shape significantly affects the DSCFs as the surface effect factors change. This research enhances understanding of disruption caused by nano-holes to the internal stress field in QCs and provides theoretical support for analyzing their mechanical properties and structural health.