The general solution of one-dimensional hexagonal quasicrystal

A general solution is given for three-dimensional dynamic problems in 1D hexagonal quasicrystalline material with Laue class 6/mhmm. In the general solution, the phonon and phason displacements and stresses are controlled by two displacement functions Ψ and F, which satisfy a second-order partial differential equation, and a sixth-order partial differential equation, respectively. The general solution for static equilibrium problems is treated as a special case.