Half-plane Green`s function for anti-plane elastic 1D hexagonal QCs

TL;DR

This paper derives an analytical Green's function for 1D hexagonal quasicrystals under anti-plane elastic waves, providing foundational insights and closed-form solutions for wave propagation in these materials.

Contribution

It introduces the first analytical frequency-dependent Green's function for 1D hexagonal quasicrystals under anti-plane strain, advancing theoretical understanding and computational modeling.

Findings

Derived a fundamental Green's function for 1D hexagonal quasicrystals.

Obtained closed-form solutions for shear wave propagation.

Provides a basis for future quasicrystal dynamic analysis.

Abstract

This paper presents an analytical derivation of a frequency-dependent fundamental solution plus a Green's function for the uni-dimensional, hexagonal quasicrystal sheet subjected to elastic waves under anti-plane strain conditions. Furthermore, closed-form solutions for the free-fields developing in this sheet for propagating shear waves are also obtained. The analysis presented here provides a foundation for understanding quasicrystal dynamic behavior and for advancing relevant computational methods.