对边简支十次对称二维准晶板弯曲问题的辛分析

范俊杰; 李联和; 阿拉坦仓

doi:10.21656/1000-0887.430267

对边简支十次对称二维准晶板弯曲问题的辛分析

doi: 10.21656/1000-0887.430267

范俊杰^{1, 2, 3,},
李联和^{1, 2, 3,},
阿拉坦仓^{1, 2, 3, ,}

1.
内蒙古师范大学数学科学学院，呼和浩特 010022
2.
内蒙古自治区应用数学中心，呼和浩特 010022
3.
无穷维哈密顿系统及其算法应用教育部重点实验室，呼和浩特 010022

基金项目:

国家自然科学基金项目 11962026

国家自然科学基金项目 12002175

国家自然科学基金项目 12162027

国家自然科学基金项目 62161045

内蒙古自然科学基金项目 2020MS-01018

内蒙古自然科学基金项目 2021MS01013

内蒙古自然科学基金项目 2022ZD05

内蒙古自然科学基金项目 2023QN01007

内蒙古自治区高等学校科学技术研究项目 NJZY22519

详细信息

作者简介:
范俊杰(1987—)，男，讲师，博士生(E-mail: tracyfan2432@126.com)

李联和(1978—)，男，教授，博士，博士生导师(E-mail: nmglilianhe@163.com)

通讯作者:
阿拉坦仓(1963—)，男，教授，博士，博士生导师(通讯作者. E-mail: alatanca@imu.edu.cn)

中图分类号: O343
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- 文章访问数: 495
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- PDF下载量: 72
- 被引次数: 0
出版历程
- 收稿日期: 2022-08-29
- 修回日期: 2022-10-21
- 刊出日期: 2023-07-01

Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

FAN Junjie^{1, 2, 3
,},
LI Lianhe^{1, 2, 3
,},
ALATANCANG^{1, 2, 3
, ,}

1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China
3.
Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education, Hohhot 010022, P.R.China

摘要

摘要: 该文讨论了对边简支十次对称二维准晶中厚板弹性问题的辛方法. 将十次对称二维准晶弹性理论基本方程转化为Hamilton对偶方程，采用分离变量方法，获得了相应Hamilton算子矩阵的辛特征值及辛特征函数系. 证明了Hamilton算子矩阵的辛特征函数系在Cauchy主值意义下的完备性，在此基础上，基于Hamilton系统的辛特征函数展开，给出了十次对称二维准晶板弯曲问题的解析表达式.
- 十次对称二维准晶 /
- 辛方法 /
- Hamilton正则方程 /
- 完备性
Abstract: The symplectic method for the elastic problem of decagonal symmetric 2D quasicrystal plates with 2 opposite edges simply supported, was discussed. The basic equations of the elastic theory for decagonal symmetric 2D quasicrystals were transformed into the Hamilton dual equations. With the method of separation of variables, the symplectic eigenvalues of the corresponding Hamilton operator matrix and the symplectic eigenfunction system were obtained. The completeness of the symplectic eigenfunction system of the Hamilton operator matrix in the sense of the Cauchy principal value was proved. Based on the symplectic eigenfunction expansion of the Hamilton system, the analytical solution to the bending problem of the decagonal symmetric 2D quasicrystal plate was given.
- decagonal symmetric 2D quasicrystal /
- symplectic method /
- Hamilton canonical equation /
- completeness

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图 1 矩形准晶中厚板示意图

Figure 1. Schematic diagram of a rectangular quasicrystal medium thickness plate

下载: 全尺寸图片幻灯片

表 1 不同宽度和厚度比下中点处的挠度

Table 1. Deflections at the midpoint under different width-to-thickness ratios

b/a	h/a	n	u_z(qa⁴K₁/η₂)
1.0	0.2	5	0.004 846 34
		15	0.004 842 8
		25	0.004 843 01
		35	0.004 842 96
		45	0.004 842 98
		55	0.004 842 97
		65	0.004 842 97
1.5	0.2	5	0.008 795 16
		15	0.008 791 62
		25	0.008 791 83
		35	0.008 791 78
		45	0.008 791 8
		55	0.008 791 79
		65	0.008 791 79
2.0	0.2	5	0.011 338 6
		15	0.011 335 1
		25	0.011 335 3
		35	0.011 335 2
		45	0.011 335 3
		55	0.011 335 2
		65	0.011 335 2

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参考文献(34)

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对边简支十次对称二维准晶板弯曲问题的辛分析

doi: 10.21656/1000-0887.430267

作者简介:
范俊杰(1987—)，男，讲师，博士生(E-mail: tracyfan2432@126.com)

李联和(1978—)，男，教授，博士，博士生导师(E-mail: nmglilianhe@163.com)

通讯作者:
阿拉坦仓(1963—)，男，教授，博士，博士生导师(通讯作者. E-mail: alatanca@imu.edu.cn)

计量

Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

计量

目录

留言板

对边简支十次对称二维准晶板弯曲问题的辛分析

doi: 10.21656/1000-0887.430267

作者简介: 范俊杰(1987—)，男，讲师，博士生(E-mail: tracyfan2432@126.com) 李联和(1978—)，男，教授，博士，博士生导师(E-mail: nmglilianhe@163.com)

通讯作者: 阿拉坦仓(1963—)，男，教授，博士，博士生导师(通讯作者. E-mail: alatanca@imu.edu.cn)

计量

出版历程

Symplectic Analysis on the Bending Problem of Decagonal Symmetric 2D Quasicrystal Plates With 2 Opposite Edges Simply Supported

计量

出版历程

目录

作者简介:
范俊杰(1987—)，男，讲师，博士生(E-mail: tracyfan2432@126.com)

李联和(1978—)，男，教授，博士，博士生导师(E-mail: nmglilianhe@163.com)

通讯作者:
阿拉坦仓(1963—)，男，教授，博士，博士生导师(通讯作者. E-mail: alatanca@imu.edu.cn)