二维准晶平面问题中的Hamilton体系求解方法

李彤; 屈建龙; 王炜; 王晨龙; 徐新生

doi:10.21656/1000-0887.450204

二维准晶平面问题中的Hamilton体系求解方法

doi: 10.21656/1000-0887.450204

大连理工大学力学与航空航天学院，辽宁大连 116023

详细信息

作者简介:
李彤（1998—），女，博士(E-mail: litong1998@mail.dlut.edu.cn);徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

通讯作者:
徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

中图分类号: O343.1
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- 文章访问数: 68
- HTML全文浏览量: 19
- PDF下载量: 25
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-10
- 修回日期: 2024-08-16
- 网络出版日期: 2024-12-02

A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

摘要

摘要: 针对二维准晶平面问题，该文通过导入Hamilton体系，将问题转化为Hamilton体系下的辛本征值和辛本征解问题，即问题的解可由辛本征解组成的级数表示.利用辛本征解之间的辛共轭正交关系，可将满足边界条件的解问题归结为代数方程组的求解问题，从而形成一种解析求解方法.这种方法可直接推广到求解混合边界条件及分段边界条件问题中.
- 二维准晶 /
- Hamilton体系 /
- 辛共轭正交 /
- 辛方法 /
- 平面问题
Abstract: Aimed at the planar problem of 2D quasicrystals, the problem was transformed into one of symplectic eigenvalues and symplectic eigensolutions through introduction of the Hamiltonian system. In the Hamiltonian system, the solution to this problem was expressed by a series of symplectic eigensolutions. With the symplectic conjugate orthogonality relationship between symplectic eigensolutions, the solving problem satisfying boundary conditions can be reduced to a problem of solving algebraic equations, thus to form an analytical solution method. The proposed method can be directly extended to solve the problems of mixed boundary conditions and segmented boundary conditions.
- 2D quasicrystal /
- Hamiltonian system /
- symplectic conjugate orthogonality /
- symplectic method /
- planar problem

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参考文献(30)

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二维准晶平面问题中的Hamilton体系求解方法

doi: 10.21656/1000-0887.450204

作者简介:
李彤（1998—），女，博士(E-mail: litong1998@mail.dlut.edu.cn);徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

通讯作者:
徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

计量

A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

计量

目录

留言板

二维准晶平面问题中的Hamilton体系求解方法

doi: 10.21656/1000-0887.450204

作者简介: 李彤（1998—），女，博士(E-mail: litong1998@mail.dlut.edu.cn);徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

通讯作者: 徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

计量

出版历程

A Hamiltonian System Solution Method for Planar Problems of 2D Quasicrystals

计量

出版历程

目录

作者简介:
李彤（1998—），女，博士(E-mail: litong1998@mail.dlut.edu.cn);徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).

通讯作者:
徐新生（1957—），男，教授，博士，博士生导师(通讯作者. E-mail: xsxu@dlut.edu.cn).