Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

doi:10.1088/1674-1056/acfaf3

中国物理B ›› 2024, Vol. 33 ›› Issue (1): 16107-16107.doi: 10.1088/1674-1056/acfaf3

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

Zhiqiang Sun(孙志强), Guolin Hou(侯国林), Yanfen Qiao(乔艳芬), and Jincun Liu (刘金存)^†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

收稿日期:2023-05-08 修回日期:2023-08-06 接受日期:2023-09-19 出版日期:2023-12-13 发布日期:2023-12-29
通讯作者: Jincun Liu E-mail:jcliu@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12261064 and 11861048), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2021MS01004 and 2022QN01008), and the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No. 10000-21311201/165).

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

Zhiqiang Sun(孙志强), Guolin Hou(侯国林), Yanfen Qiao(乔艳芬), and Jincun Liu (刘金存)^†

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received:2023-05-08 Revised:2023-08-06 Accepted:2023-09-19 Online:2023-12-13 Published:2023-12-29
Contact: Jincun Liu E-mail:jcliu@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12261064 and 11861048), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2021MS01004 and 2022QN01008), and the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No. 10000-21311201/165).

摘要/Abstract

摘要： A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

关键词: Hamiltonian system, symplectic elasticity, quasicrystals, analytic solution, state function

Abstract: A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Key words: Hamiltonian system, symplectic elasticity, quasicrystals, analytic solution, state function

中图分类号: (Quasicrystals)

61.44.Br

46.25.-y (Static elasticity) 02.30.Jr (Partial differential equations)

Zhiqiang Sun(孙志强), Guolin Hou(侯国林), Yanfen Qiao(乔艳芬), and Jincun Liu (刘金存). Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions[J]. 中国物理B, 2024, 33(1): 16107-16107.

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Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

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