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．Abstract: A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems.The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system and the use of rather undesirable state space representation is avoided.Hence the cost of computation is greatly reduced.The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.
-
[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 -
计量
- 文章访问数: 3075
- HTML全文浏览量: 168
- PDF下载量: 660
- 被引次数: 0
下载:
渝公网安备50010802005915号