 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Y.F. Qiao, "Hamiltonian System for Two-Dimensional Decagonal Quasicrystal Plates and Its Analytical Solutions," Mech. Solids. 59 (1), 363-378 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
1 |
Pages |
363-378 |
| DOI |
10.1134/S0025654423602549 |
| Title |
Hamiltonian System for Two-Dimensional Decagonal Quasicrystal Plates and Its Analytical Solutions |
| Author(s) |
Y.F. Qiao (Inner Mongolia University, Hohhot, 010021 China; School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021 China, yanfenqiao@mail.imu.edu.cn) |
| Abstract |
This paper deals with the three-dimensional (3D) elasticity problem of two-dimensional
(2D) decagonal quasicrystal (QC) plates by an analytical symplectic approach. Based on the elasticity
theory of QCs, a system of Hamiltonian governing equations for a 2D decagonal QC plate is constructed with the fundamental mechanical quantities as the symplectic variables, such that the symplectic eigenvalue problem is formed. Combined with the properties of trigonometric functions of two
variables, the adjoint symplectic orthogonality relations among the eigenvectors of the Hamiltonian
operator are derived, and the expansion theorem of the double Fourier trigonometric series is proven.
The symplectic analytical solutions of stresses and displacements in the phonon and phason fields of
the 2D decagonal QC plate with four lateral simply supported edges are given without any assumptions. Furthermore, the numerical results are plotted to verify the correctness of the analytical solutions by comparison with those acquired by the pseudo-Stroh formalism. The proposed approach has
broad applicability and high precision and can be extended to the 3D elasticity analysis of more QCs. |
| Keywords |
symplectic approach, decagonal quasicrystal, three-dimensional elasticity, analytical solution, Hamiltonian system |
| Received |
05 December 2023 | Revised |
13 January 2024 | Accepted |
21 January 2024 |
| Link to Fulltext |
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