用加速度和位移反馈修正无阻尼振动系统的一种迭代法

Abstract

Abstract: In this paper, an iterative method for simultaneously updating mass and stiffness matrices is presented. By the method, the required control gain matrices of acceleration and displacement feedback are determined, and thus the optimal approximation mass and stiffness matrices which satisfies the required eigenvalue equation are found under the Frobenius norm sense and the large number of unmeasured and unknown eigeninformation of the original model is preserved. Two numerical examples show that the proposed method is reliable and attractive.

Key words: Model updating, Iterative algorithm, Partially prescribed spectral information, No spill-over, Undamped structural system, Optimal approximation

CLC Number:

O241

Zhang Qian, Yuan Yongxin. An Iterative Updating Method for Undamped Vibration Systems Using Acceleration and Displacement Feedback[J].Acta mathematica scientia,Series A, 2018, 38(2): 358-371.

Trendmd

References

[1] Friswell M I, Mottershead J E. Finite Element Model Updating in Structural Dynamics. Dordrecht:Kluwer Academic Publishers, 1995
[2] Baruch M. Optimization procedure to correct stiffness and flexibility matrices using vibration tests. AIAA Journal, 1978, 16:1208-1210
[3] Baruch M, Bar-Itzhack I Y. Optimal weighted orthogonalization of measured modes. AIAA Journal, 1978, 16:346-351
[4] Berman A, Nagy E J. Improvement of a large analytical model using test data. AIAA Journal, 1983, 21:1168-1173
[5] Wei F S. Structural dynamic model improvement using vibration test data. AIAA Journal, 1990, 28:175-177
[6] Wei F S. Mass and stiffness interaction effects in analytical model modification. AIAA Journal, 1990, 28:1686-1688
[7] Dai H. Optimal approximation of real symmetric matrix pencil under spectral restriction. Numer Math J Chin Univ, 1990, 12:177-187
[8] Carvalho J, Datta B N, Gupta A, Lagadapati M. A direct method for model updating with incomplete measured data and without spurious modes. Mechanical Systems and Signal Processing, 2007, 21:2715-2731
[9] Mao X B, Dai H. A quadratic inverse eigenvalue problem in damped structural model updating. Applied Mathematical Modelling, 2016, 40:6412-6423
[10] Yuan Y, Dai H. On a class of inverse quadratic eigenvalue problem. Journal of Computational and Applied Mathematics, 2011, 235:2662-2669
[11] Bai Z J, Chu D, Sun D. A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure. SIAM Journal on Scientific Computing, 2007, 29:2531-2561
[12] Kuo Y C, Lin W W, Xu S F. New model updating method for quadratic eigenvalue problems using a symmetric eigenstructure assignment. AIAA Journal, 2005, 43:2593-2598
[13] Carvalho J B, Datta B N, Lin W W, Wang C S. Symmetry preserving eigenvalue embedding in finite-element model updating of vibrating structures. Journal of Sound and Vibration, 2006, 290:839-864
[14] Saad Y. Projection and deflation method for partial pole assignment in linear state feedback. IEEE Trans Automatic Control, 1988, 33:290-297
[15] Xu S F, Qian J. Orthogonal basis selection method for robust partial eigenvalue assignment problem in second-order control systems. Journal of Sound and Vibration, 2008, 317:1-19
[16] Cai Y F, Qian J, Xu S F. Robust partial pole assignment problem for high order control systems. Automatica, 2012, 48:1462-1466
[17] Cai Y F, Xu S F. A new eigenvalue embedding approach for finite element model updating. Taiwanese Journal of Mathematics, 2010, 14:911-932
[18] Brahma S, Datta B. An optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures. Journal of Sound and Vibration, 2009, 324:471-489
[19] Datta B N, Lin W W, Wang J N. Robust partial pole assignment for vibrating systems with aerodynamic effects. IEEE Trans Automatic Control, 2006, 51:1979-1984
[20] Datta B N. Finite element model updating, eigenstructure assignment and eigenvalue embedding for vibrating structures. Mechanical Systems and Signal Processing, 2002, 16:83-96
[21] Bai Z J, Datta B N, Wang J. Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems:A new optimization approach. Mechanical Systems and Signal Processing, 2010, 24:766-783
[22] Cai Y F, Qian J, Xu S F. The formulation and numerical method for partial quadratic eigenvalue assignment problems. Numer Linear Algebra Appl, 2011, 18:637-652
[23] Zhang J F, Ouyang H, Yang J. Partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback. Journal of Sound and Vibration, 2014, 333:1-12
[24] Yuan Y X, Zhao W H, Liu H. Analytical dynamic model modification using acceleration and displacement feedback. Applied Mathematical Modelling, 2016, 40:9584-9593
[25] Lancaster P, Tismenetsky M. The Theory of Matrices. London:Academic Press, 1985
[26] Aubin J P. Applied Functional Analysis. New York:John Wiley & Sons, 1979
[27] Ben-Israel A, Greville T N E. Generalized Inverses. Theory and Applications. New York:Springer, 2003
[28] Mitra S K. A pair of simultaneous linear matrix equations A₁XB₁=C₁, A₂XB₂=C₂ and a matrix programming problem. Linear Algebra and Its Applications, 1990, 131:107-123

Metrics

Viewed

Full text

110

HTML			PDF

Just accepted	Online first	Issue	Just accepted	Online first	Issue
0	0	0	0	0	110

From	Others	local

Times	13	97
Rate	12%	88%

Abstract

Just accepted	Online first	Issue

0	0	88

From	Others	local

Times	84	4
Rate	95%	5%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

An Iterative Updating Method for Undamped Vibration Systems Using Acceleration and Displacement Feedback

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 13

Metrics

Comments

Recommended 10

[1]	Yuan Yongxin, Zhao Wenhua, Liu Hao. An Effective Iterative Updating Method for Undamped Structural Systems [J]. Acta mathematica scientia,Series A, 2016, 36(5): 886-900.
[2]	Liu Yuanxing, Zhou Haiyun, Wang Peiyuan, Zhou Yu. Three Kinds of Iterative Algorithms for Solving the Constrained Split Common Fixed Point Problem in Hilbert Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1115-1126.
[3]	QIAN Tao, WANG Jin-Xun, YANG Yan. MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES [J]. Acta mathematica scientia,Series A, 2014, 34(3): 660-672.
[4]	TIAN Xiao-Hong, ZHANG Kai-Yuan. Iterative Method for Centro-symmetric Solution of the Linear Matrix Equations [J]. Acta mathematica scientia,Series A, 2011, 31(6): 1526-1536.
[5]	SHANG Li-Na, ZHANG Kai-Yuan. An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F [J]. Acta mathematica scientia,Series A, 2010, 30(3): 776-783.
[6]	YUAN Yong-Xin, DAI Hua. Inverse Problems for Generalized Reflexive Matrices on a Linear Manifold [J]. Acta mathematica scientia,Series A, 2009, 29(6): 1547-1560.
[7]	GUAN Li, ZHANG Zhong-Zhi, XIE Dong-Xiu. Optimal Approximation Problem of Antireflexive Matrices under the Spectral Restriction [J]. Acta mathematica scientia,Series A, 2009, 29(2): 316-323.
[8]	Peng Zhuohua;Hu Xiyan;Zhang Lei. The Centrosymmetric Solutions of Matrix Equation A1X1B1+A2X2B2+…+AlXlBl=C and its Optimal Approximation [J]. Acta mathematica scientia,Series A, 2009, 29(1): 193-207.
[9]	Gong Lisha; Hu Xiyan; Zhang Lei. The Inverse Problem of Hermitian-Hamiltonian Matrices with a Submatrix Constraint [J]. Acta mathematica scientia,Series A, 2008, 28(4): 694-700.
[10]	Peng Xiangyang; Hu Xiyan. The Part Hermitian Solutions of Matrix Equation A^HXA=B on Subspace [J]. Acta mathematica scientia,Series A, 2007, 27(2): 374-384.
[11]	Yu Lei; Zhang Kaiyuan; Shi Zhongke. Least-Squares Solutions of Inverse Problems for Anti-Symmetric Ortho-Symmetric Matrices on the Linear Manifold [J]. Acta mathematica scientia,Series A, 2006, 26(6): 1031-.
[12]	Zhang Zhongzhi;Hu Xiyan; Zhang Lei. On the Hermitian Generalized Anti-Hamiltonian Semi-definite Solutions of Linear Matrix Equations [J]. Acta mathematica scientia,Series A, 2006, 26(4): 612-620.
[13]	DENG Yuan-Bei, HU Xi-Yan, ZHANG Lei. The Skew symmetric Solutions of Linear Matrix Equation B^TXB=D on Some Linear Manifolds [J]. Acta mathematica scientia,Series A, 2004, 24(4): 459-463.