On three-dimensional elastodynamic problems of one-dimensional quasicrystals

In this paper, dynamic elasticity equations for one-dimensional (1D) quasicrystals (QCs) with arbitrary system of anisotropy are considered. Fundamental solutions (FSs) of the phonon-phason displacements, displacement speeds, and stresses arising from pulse point sources are computed. New existence, uniqueness and stability estimate theorems are obtained for dynamic elasticity equations in 1D QCs with the initial conditions (ICs). As a computational example, FS components are computed for orthorhombic and triclinic structures in 1D QCs.