General Solutions of Plane Problem in One-Dimensional Hexagonal Quasicrystals

Abstract

A theory of general solutions of plane problem is developed for the coupled equations in plane elasticity of one-dimensional (1D) hexagonal quasicrystals (QCs), and three general solutions are presented by an operator method. These solutions are expressed in terms of a displacement function, which satisfies a sixth-order partial differential equation. By utilizing a theorem, a decomposition and superposition procedure is taken to replace the sixth-order function with three second-order displacement functions, and the general solution is simplified in terms of these functions. In consideration of different cases of three characteristic roots, the general solution possesses three cases, but all are in simple forms that are convenient to be used.