| 有限长周期结构的密集特征值 |
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| 引用本文： | 吴锋,高强,钟万勰.有限长周期结构的密集特征值[J].应用数学和力学,2013,34(11):1119-1129. |
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| 作者姓名： | 吴锋 高强 钟万勰 |
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| 作者单位： | 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 |
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| 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） |
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| 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．
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| 关 键 词： | 周期结构 密集特征值 能带 辛 |
| 收稿时间： | 2013-07-31 |
Close Eigenvalues of Periodic Structures With Finite Unit Cells |
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| Affiliation: | State Key Laboratory of Structural Analysis of Industrial Equipment; Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China |
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| 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. |
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