留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

阻尼系统重特征对导数的计算

解惠青 戴华

解惠青, 戴华. 阻尼系统重特征对导数的计算[J]. 应用数学和力学, 2007, 28(6): 749-756.
引用本文: 解惠青, 戴华. 阻尼系统重特征对导数的计算[J]. 应用数学和力学, 2007, 28(6): 749-756.
XIE Hui-qing, DAI Hua. Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Damped Systems[J]. Applied Mathematics and Mechanics, 2007, 28(6): 749-756.
Citation: XIE Hui-qing, DAI Hua. Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Damped Systems[J]. Applied Mathematics and Mechanics, 2007, 28(6): 749-756.

阻尼系统重特征对导数的计算

基金项目: 国家自然科学基金会数学天元基金资助项目(10626019)
详细信息
    作者简介:

    解惠青(1976- ),女,山西寿阳人,副教授,博士(联系人.Tel:+86-21-64253243;Fax:+86-21-64252018;E-mail:hqxie@ecust.edu.cn).

  • 中图分类号: O241.6;O325

Derivatives of Repeated Eigenvalues and the Corresponding Eigenvectors of Damped Systems

  • 摘要: 提出了一种计算阻尼系统重特征值及其特征向量导数的方法.该方法利用n维空间的特征向量计算特征对的导数,避免了状态空间中特征向量的使用,从而节省了计算量,提高了计算效率.最后以一个5自由度的非比例阻尼系统对所提方法进行了数值试验,数值结果表明方法是有效的.
  • [1] Arora J S,Huang E J. Methods of design sensitivity analysis in structural optimization[J].AIAA J,1979,17(9):970-974. doi: 10.2514/3.61260
    [2] 张景绘.动力学系统建模[M].北京:国防工业出版社,2000.
    [3] Messina A, Williams E J,Contursi T. Structural damage detection by a sensitivity and statistical-based method[J].J Sound Vibration,1998,216(5):791-808. doi: 10.1006/jsvi.1998.1728
    [4] Andrew A L, Tan R C E.Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors[J].Numer Linear Algebra Appl,2000,7(8):151-167. doi: 10.1002/1099-1506(200005)7:4<151::AID-NLA191>3.0.CO;2-M
    [5] XIE Hui-qing,DAI Hua.Davidson method for eigenpairs and their derivatives[J].AIAA J,2005,43(6):1403-1405. doi: 10.2514/1.12546
    [6] XIE Hui-qing,DAI Hua.Davidson method for eigenpairs and their partial derivatives of generalized eigenvalue problems[J].Communications in Numerical Methods in Engineering,2006,22(2):155-165.
    [7] Zhang O,Zerva A. Accelerated iterative procedure for calculating eigenvector derivatives[J].AIAA J,1997,35(2):340-348. doi: 10.2514/2.98
    [8] Lee I W, Kim D O,Jung G H. Natural frequency and mode shape sensitivities of damped systems: Part Ⅰ,distinct natural frequencies[J].J Sound Vibration,1999,223(3):399-412. doi: 10.1006/jsvi.1998.2129
    [9] Adhikari S. Calculation of derivatives of complex modes using classical normal modes[J].Computers & Structures,2000,77(6):625-633.
    [10] Choi K M, Cho S W,Ko M G,et al.Higher order eigensensitivity analysis of damped systems with repeated eigenvalues[J].Computers and Structures,2004,82(1):63-69. doi: 10.1016/j.compstruc.2003.08.001
    [11] Lancaster P,Markus A S, Zhou F.Perturbation theory for analytic matrix functions: The semisimple case[J].SIAM Journal on Matrix Analysis and Applications,2003,25(3):606-626. doi: 10.1137/S0895479803423792
  • 加载中
计量
  • 文章访问数:  2917
  • HTML全文浏览量:  126
  • PDF下载量:  659
  • 被引次数: 0
出版历程
  • 收稿日期:  2006-05-09
  • 修回日期:  2007-03-29
  • 刊出日期:  2007-06-15

目录

    /

    返回文章
    返回