TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green’s function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions (?) and ψ, the original problem is reduced to the determination of Green’s functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green’s function can be obtained by letting the circular frequency approach zero.