Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media

Meltem Altunkaynak

Applications of Mathematics (2024)

  • Volume: 69, Issue: 3, page 289-309
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Altunkaynak, Meltem. "Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media." Applications of Mathematics 69.3 (2024): 289-309. <http://eudml.org/doc/299410>.

@article{Altunkaynak2024,
abstract = {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.},
author = {Altunkaynak, Meltem},
journal = {Applications of Mathematics},
keywords = {2D quasicrystals; inhomogeneous media; elastodynamic system},
language = {eng},
number = {3},
pages = {289-309},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media},
url = {http://eudml.org/doc/299410},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Altunkaynak, Meltem
TI - Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 289
EP - 309
AB - 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.
LA - eng
KW - 2D quasicrystals; inhomogeneous media; elastodynamic system
UR - http://eudml.org/doc/299410
ER -

References

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