有限长周期结构的密集特征值

吴锋; 高强; 钟万勰

doi:10.3879/j.issn.1000-0887.2013.11.001

有限长周期结构的密集特征值

doi: 10.3879/j.issn.1000-0887.2013.11.001

大连理工大学工程力学系,工业装备结构分析国家重点实验室, 辽宁大连 116024

基金项目: 国家重点基础基础研究发展计划（973计划）资助项目（2009CB918501）

详细信息

作者简介:
吴锋(1985—),男,江苏靖江人,博士生(通讯作者. E-mail: wufeng-chn@163.com);高强(1978—),男,内蒙古赤峰人,副教授,博士(E-mail: qgao@dlut.edu.cn);钟万勰(1934—),男,浙江德清人,教授,院士(E-mail: zwoffice@dlut.edu.cn).

中图分类号: O175.9;O327
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出版历程
- 收稿日期: 2013-07-31
- 修回日期: 2013-09-01
- 刊出日期: 2013-11-15

Close Eigenvalues of Periodic Structures With Finite Unit Cells

State Key Laboratory of Structural Analysis of Industrial Equipment; Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2009CB918501）

摘要

摘要: 基于单胞结构的特征值问题，给出了有限长周期结构特征值分布范围的估计，基于固体物理中的能带理论，给出了一维有限长周期结构特征值分布范围的更精细估计．通过分析有限长周期结构特征值的分布范围，阐述了密集特征值出现的原因．分析结果表明，对于有限长周期结构，结构的单胞数目越大，其特征值分布会越密集．数值算例验证了该文的结论．
- 周期结构 /
- 密集特征值 /
- 能带 /
- 辛
Abstract: For a periodic structure with finite unit cells, the range where eigenvalues existed was estimated based on the eigenproblem of the unit cell. A more precise estimate of the eigenvalue distriution range for a one dimensional periodic structure with finite unit cells was presented based on the energy band theory in solid physics. In terms of the estimated range of eigenvalues, the close eigenvalue phenomenon was made clear. The analysis results show that, for a periodic structure with finite unit cells, the larger the number of the unit cells is, the closer the eigenvalues are. Numerical tests demonstrate the correctness of the proposed conclusions.
- periodic structure /
- close eigenvalue /
- energy band /
- symplectic

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