Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media


Applications of Mathematics, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.21136/am.2024.0045-23
  • Journal Name: Applications of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Compendex, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Keywords: 2D quasicrystals, 35L52, 35Q86, elastodynamic system, inhomogeneous media
  • Dokuz Eylül University Affiliated: Yes


Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. A numerical example is considered for the comparison of the exact solution with the computed solution obtained by using the method.