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有限长周期结构的密集特征值

吴锋 高强 钟万勰

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. doi: 10.3879/j.issn.1000-0887.2013.11.001
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. doi: 10.3879/j.issn.1000-0887.2013.11.001
WU Feng, GAO Qiang, ZHONG Wan-xie. Close Eigenvalues of Periodic Structures With Finite Unit Cells[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1119-1129. doi: 10.3879/j.issn.1000-0887.2013.11.001
Citation: WU Feng, GAO Qiang, ZHONG Wan-xie. Close Eigenvalues of Periodic Structures With Finite Unit Cells[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1119-1129. 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
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

Close Eigenvalues of Periodic Structures With Finite Unit Cells

Funds: The National Basic Research Program of China (973 Program)(2009CB918501)
  • 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.
  • [1] 于岩磊, 高维成, 刘伟, 王兆敏, 孙毅. 密集模态结构模态跃迁分析的简化摄动法[J]. 工程力学,2012, 29(3): 33-40.(YU Yan-lei, GAO Wei-cheng, LIU Wei, WANG Zhao-ming, SUN Yi. Simplified perturbation method for analyzing the mode jumping of close mode structure[J].Engineering Mechanics,2012, 29(3): 33-40.(in Chinese))
    [2] Kushwaha M S, Halevi P, Dobrzynski L, DjafariRouhani B. Acoustic band structure of periodic elastic composites[J].Physical Review Letters,1993, 71(13): 2022-2025.
    [3] 刘玉民, 张帆, 吴蕙. 水轮发电机组结构密集特征值求解新方法[J]. 机械强度, 1996, 18(4): 9-11.(LIU Yu-min, ZHANG Fan, WU Hui. A new method for solving the concentrated eigenvalues of the water trubogenerator [J].Journal of Mechanical Strength,1996, 18(4): 9-11.(in Chinese))
    [4] 徐涛, 陈塑寰, 赵建华. 接近亏损系统的矩阵摄动法[J]. 力学学报, 1998, 30(4): 120-124.(XU Tao, CHEN Su-huan, ZHAO Jian-hua. Perturbation method of near defective systems[J].Acta Mechanica Sinca,1998, 30(4): 120-124.(in Chinese))
    [5] 刘中生, 陈塑寰, 王家林, 赵又群. 密集模态摄动的新方法[J]. 固体力学学报, 1993, 14(1): 1-6.(LIU Zhong-sheng, CHEN Su-huan, WANG Jia-lin, ZHAO You-qun. A new matrix perturbation method for closely spaced eigenvalues of vibration[J].Chinese Journal of Solid Mechanics,1993, 14(1): 1-6.(in Chinese))
    [6] 刘璐. 密集型固有振模电力系统模态不稳定现象的研究[D]. 硕士学位论文. 保定: 华北电力大学, 2009.(LIU Lu. Research on the phenomenon of modes instability in close modes power system[D]. Master Thesis. Baoding: North China Electric Power University, 2009.(in Chinese))
    [7] 周树荃, 戴华. 求解大型对称特征值问题的块Chebyshev-Lanczos方法[J]. 南京航空航天大学学报, 1989, 21(4): 22-28.(ZHOU Shu-quan, DAI Hua. The block Chebyshev-Lanczos method for solving large symmetric eigenvalue problems[J].Journal of Nanjing Aeronautical Institute,1989, 21(4): 2228.(in Chinese))
    [8] 赵又群, 刘中生, 陈塑寰. 密集模态的判断准则[J]. 吉林工业大学学报, 1996, 26(3): 79-82.(ZHAO You-qun, LIU Zhong-sheng, CHEN Su-huan. Judging criterion of closely spaced modes[J].Journal of Jilin University of Technology,1996, 26(3): 7982.(in Chinese))
    [9] 刘中生, 陈塑寰. 频率集聚时模态分析的移位摄动法[J]. 宇航学报, 1993(1): 81-88.(LIU Zhong-sheng, CHEN Su-huan. Perturbation analyses of vibration modes with close eigenvalues by eigenvalue shift[J].Journal of Astronautics,1993(1): 8188.(in Chinese))
    [10] 吕振华. 重特征值及其特征向量摄动重分析方法探讨[J]. 振动工程学报, 1993, 6(4): 327-335.(Lü Zhen-hua. An investigation into the perturbational reanalysis method of repeated eigenvalues and associated eigenvectors[J].Journal of Vibration Engineering,1993, 6(4): 327-335.(in Chinese))
    [11] 陈塑寰, 徐涛, 韩万芝. 线性振动亏损系统的矩阵摄动理论[J]. 力学学报, 1992, 24(6): 747-754.(CHEN Su-huan, XU Tao, HAN Wan-zhi. Matrix perturbation for linear vibration deffective systems[J].Acta Mechanica Sinica,1992, 24(6): 747-754.(in Chinese))
    [12] 陈塑寰. 结构振动分析的矩阵摄动理论[M]. 重庆出版社, 1991.(CHEN Su-huan.The Matrix Perturbation Theory for the Analysis of Structural Vibration [M]. Chongqing Publishing House, 1991.(in Chinese))
    [13] 胡海昌. 参数小变化对本征值的影响[J]. 力学与实践, 1981, 3(2): 29-31.(HU Hai-chang. The influence of parameters of small changes to this eigenvalue[J].Mechanics in Engineering,1981, 3(2): 29-31.(in Chinese))
    [14] 黄昆. 固体物理学[M]. 北京: 高等教育出版社, 1998.(HUANG Kun.Solid State Physics [M]. Beijing: Higher Education Press, 1998.(in Chinese)) [15]Zhong W X, Williams F W. On the localization of the vibration mode of a substructural chaintype structure[J].Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,1991, 205(4): 281-288.
    [15] Zhong W X, Williams F W. Wave problems for repetitive structures and symplectic mathematics[J].Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,1992, 206(6): 371-379.
    [16] 高强, 张腾, 钟万勰. 一维离散结构能带结构与表面态的辛分析方法[J]. 固体力学学报, 2011, 32(4): 372-381.(GAO Qiang, ZHANG Teng, ZHONG Wan-xie. Symplectic method for energy bands and surface states of 1D periodic structure with defects[J].Chinese Journal of Solid Mechanics,2011, 32(4): 372-381.(in Chinese))
    [17] 钟万勰. 应用力学的辛数学方法[M]. 北京: 高等教育出版社, 2005.(ZHONG Wan-xie.Symplectic Solution Methodology in Applied Mechanics [M]. Beijing: Higher Education Press, 2005.(in Chinese))
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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

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