Derivation of a solution of dynamic equations of motion for quasicrystals

Yakhno V.

JOURNAL OF ENGINEERING MATHEMATICS, cilt.118, sa.1, ss.63-72, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 118 Sayı: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1007/s10665-019-10014-w
  • Dergi Adı: JOURNAL OF ENGINEERING MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.63-72
  • Anahtar Kelimeler: Analytical method, Equations of motion in quasicrystals, Initial value problem, System of time-dependent partial differential equations of the second order, LINEAR ELASTICITY THEORY, DIFFUSE-SCATTERING, 3-DIMENSIONAL ELASTODYNAMICS, FUNDAMENTAL-SOLUTIONS, PLASTIC-DEFORMATION, DISLOCATIONS
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

The dynamic equations of motion in quasicrystals are written in terms of time-dependent partial differential equations of the second order relative to phonon and phason displacements. A method of derivation of a solution (phonon and phason displacements) of the initial value problem is proposed in this paper. In this method, images of the Fourier transform with respect to the 3D space variable of the given phonon, phason forces, and initial displacements are assumed to be vector functions with components which have finite supports for every fixed time variable. The Fourier images of displacements are computed by matrix transformations and solving ordinary differential equations, coefficients and non-homogeneous terms as well as initial data of which depend on 3D Fourier parameter. Finally, phonon and phason displacements are computed by the inverse Fourier transform to obtained Fourier image.