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http://dx.doi.org/10.12989/sem.2004.18.3.331

The standard deviations for eigenvalues of the closed-loop systems with random parameters  

Chen, Su Huan (Department of Mechanics, Jilin University, Nanling Campus)
Liu, Chun (Department of Mechanics, Jilin University, Nanling Campus)
Chen, Yu Dong (Department of Mechanics, Jilin University, Nanling Campus)
Publication Information
Structural Engineering and Mechanics / v.18, no.3, 2004 , pp. 331-342 More about this Journal
Abstract
The vibration control problem of structures with random parameters is discussed, which is approximated by a deterministic one. A method for calculating the standard deviations of eigenvalues of the closed-loop systems is presented by using the random perturbation. The method presented in this paper will not require the distribution function of the random parameters of the systems other than their means and variances. Similarly, the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the stability robustness. The present method is applied to a vibration control system to illustrate the application. The numerical results show that the present method is effective.
Keywords
uncertain systems; vibration active control; random parameters; standard deviations of eigenvalues of the closed-loop systems;
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1 Meirovitch, L. (1990), Dynamics and Control, Wiley, New York.
2 Rachid, A. (1989), "Robustness of discrete systems under structural uncertainties", Int. J. of Control, 50, 1563-1566.   DOI   ScienceOn
3 Sobld, K.M., Banda, S.S. and Yeh, H.M. (1989), "Robust control for linear systems with structural state space uncertainty", Int. J. of Control, 50, 1991-2004.   DOI   ScienceOn
4 Chen, Y.D., Chen, S.H. and Liu, Z.S. (2001), "Modal optimal control procedure for near defective systems", J. Sound Vib., 245, 113-132.   DOI   ScienceOn
5 Chen, S.H. (1992), Vibration Theory in Structural with Random Parameters, Jilin Science and Technology Press (in Chinese).
6 Chen, Y.D., Chen, S.H. and Liu, Z.S. (2001), "Quantitative measures of modal controllability and observability for the defective and near defective systems", J. Sound Vib., 248, 413-426.   DOI   ScienceOn
7 Juang, Y.T., Kuo, T.S. and Hsu, C.F. (1987), "Root-Locus approach to the stability analysis of interval matrices", Int. J. of Control, 46, 817-822.   DOI   ScienceOn
8 Liu, W.K. and Mani, A. (1986), "Probabilistic finite elements for nonlinear structural dynamics", Comput. Methods Appl. Mech. Eng., 56, 61-81.   DOI   ScienceOn
9 Lyengow, R.N. and Manohar, C.S. (1989), "Probability distribution of the eigenvalues of the random string equation", Tran of the ASME, J. Applied Mechanics, 56, 202-220.   DOI
10 Mori, T. and Kokame, H. (1987), "Convergence property of interval matrices and interval polynomials", Int. J. of Control, 45, 481-484.   DOI   ScienceOn
11 Porter, B. and Crossley, R. (1972), Modal Control Theory and Applications, Taylor & Francis, London.
12 Inman, Daniel J. (1989), Vibration with Control, Measurement, and Stability, Prentice-Hall, New Jersey.
13 Contreras, M. (1980), "The stochastic finite element method", Comput. Struct., 12, 341-348.   DOI   ScienceOn
14 Liu, W.K., Belytsohko, T. and Mani, A. (1980), "Random filed finite elements", Int. J. Numer. Meth. Eng., 23, 1831-1845.   DOI   ScienceOn
15 Argoun, M.B. (1987), "Stability of a hurwitz polynomial under coefficient perturbations: necessary and sufficient conditions", Int. J. of Control, 45, 739-744.   DOI   ScienceOn