Dynamic Analysis of Redesigned Systems Using an Algebraic Method
-
摘要: 利用矩阵修改理论探讨结构系统再设计问题,以等惯性转换求解动态劲度矩阵的隐根,并导出将特征值定位的计算方法;继而在隐根为已知下探讨隐向量的特质及解法,并确认修改后结构的振型必须区分成驻留性与非驻留性自然频率等两种状况处理.Abstract: Bymatrixm odification,the redesign of as tructural system was investigated.The inertia congruence trans formation was adopted to find the laten troots of a dynamic stiffness matrix,and a method for determining its eigenvalue was proposed.The characteristics of the laten tvector for a known latentroo,tand a method for computing it,were studied.The mode shapes of a redesigned structurem ust be handled differently based on whether the structure exhibits are persistentor non-persistent natural frequencies.
-
Key words:
- congruence transformation /
- latent root /
- latent vector /
- diagonal pivoting
-
[1] Pomazal R J. The effect of local modification on the eigenvalues and eigenvectors of damped linear systems[D]. PhD Dissertation. Michigan: Michigan Technology University, 1969. [2] Pomazal R J. Local modification of damped linear systems[J]. AIAA Journal, 1971, 9(11): 2216-2221. doi: 10.2514/3.50028 [3] Hallquist J O. An efficient method for determining the effects of mass modifications in damped linear systems[J]. Journal of Sound and Vibration, 1974, 44(3): 449-459. [4] Chou C M. Structural dynamics modification of 3D beam elements using a local eigenvalue modification procedure[D]. PhD Dissertation. Massachusetts: University of Lowell, 1984. [5] Aronszajn N, Weinstein A.On the unified theory of eigenvalues of plates and membranes[J]. Amer J Math,1945,64(1): 623-645. [6] Beattie C, Fox D W. Schur complements and Weinstein-Aronszajn theory for modified matrix eigenvalue problem[J]. Linear Algebra and Its Applications, 1988,108: 37-61. doi: 10.1016/0024-3795(88)90178-4 [7] Arbenz P, Golub G H. On the spectral decomposition of the Hermitian matrices modified by low rank perturbations with applications[J]. SIAM Journal of Mat Anal and Appl, 1988, 9(1): 40-58. doi: 10.1137/0609004 [8] Liao J Y, Tse C C. An algebra approach for the modal analysis of synthesized structures[J]. Mechanical System and Signal Processing, 1993,7(1): 89-104. doi: 10.1016/0888-3270(93)90007-J [9] Avitabile P. Twenty years of structural synamic modification—a review[J]. Sound and Vibration, 2003,37: 14-27. [10] Lancaster P. Model-updating for self-adjoint quadratic eigenvalue problem[J]. Linear Algebra and Its Applications, 2008, 428(11/12): 2778-2790. doi: 10.1016/j.laa.2007.12.023 [11] Datta B N, Deng S, Sokolov V O, et al. An optimization technique for damped model updating with measured data satisfying quadratic orthogonality constraint[J]. Mechanical Systems and Signal Processing, 2009, 23(6): 1759-1772. doi: 10.1016/j.ymssp.2008.07.017 [12] Johnson C R, Furtado S. A generalization of Sylvester’s law of inertia[J]. Linear Algebra and Its Application, 2001, 338(1/3): 287-290. doi: 10.1016/S0024-3795(01)00408-6 [13] Wittrick W H, Williams F W. A general algorithm for computing natural frequencies of elastic structures[J]. Quarterly Journal of Mechanics and Applied Mathematics, 1971, 24(3): 263-284. doi: 10.1093/qjmam/24.3.263 [14] Trench W F. Numerical solution of eigenvalue problem for Hermitian Toeplitz matrices[J]. SIAM Journal of Mat Anal and Appl, 1989, 10(2): 135-146. doi: 10.1137/0610010 [15] Brent R P. Algorithms for Minimization Without Derivatives[M]. New Jersey: Prentice-Hall, 1973. [16] Sehmi N S. Large Order Structural Eigenanalysis Techniques[M]. West Sussex: Ellis Horwood Limited, 1989. [17] Turkkila T. Use of LDLT decomposition in solution of eigenproblem[C] Lund E, Olhoff N, Stegmann J. 15th Nordic Seminar on Computational Mechanics. Alborg, Denmark, 2002:151-154. [18] Rayleigh J W S. The Theory of Sound[M]. Vol 1, 2.New York: Dover, 1945. [19] Simpson A. A Newtonian procedure for the solution of Ex=λAx[J]. Journal of Sound and Vibration, 1982, 82(2): 161-170. doi: 10.1016/0022-460X(82)90526-0 [20] Liao J Y, Tse C C. A comparison of error bounds for eigenvalues in structural modification problem[J]. Mechanical System and Signal Processing, 1993, 7(3): 273-279. doi: 10.1006/mssp.1993.1013
点击查看大图
计量
- 文章访问数: 1215
- HTML全文浏览量: 68
- PDF下载量: 891
- 被引次数: 0