Structural Engineering and Mechanics

  • 제18권3호
  • /
  • Pages.331-342
  • /
  • 2004
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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)
  • 투고 : 2003.09.18
  • 심사 : 2004.06.16
  • 발행 : 2004.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Argoun, M.B. (1987), "Stability of a hurwitz polynomial under coefficient perturbations: necessary and sufficient conditions", Int. J. of Control, 45, 739-744. https://doi.org/10.1080/00207178708933765
  2. 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. https://doi.org/10.1006/jsvi.2000.3481
  3. 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. https://doi.org/10.1006/jsvi.2000.3826
  4. Chen, S.H. (1992), Vibration Theory in Structural with Random Parameters, Jilin Science and Technology Press (in Chinese).
  5. Contreras, M. (1980), "The stochastic finite element method", Comput. Struct., 12, 341-348. https://doi.org/10.1016/0045-7949(80)90031-0
  6. Inman, Daniel J. (1989), Vibration with Control, Measurement, and Stability, Prentice-Hall, New Jersey.
  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. https://doi.org/10.1080/00207178708547394
  8. Liu, W.K. and Mani, A. (1986), "Probabilistic finite elements for nonlinear structural dynamics", Comput. Methods Appl. Mech. Eng., 56, 61-81. https://doi.org/10.1016/0045-7825(86)90136-2
  9. Liu, W.K., Belytsohko, T. and Mani, A. (1980), "Random filed finite elements", Int. J. Numer. Meth. Eng., 23, 1831-1845. https://doi.org/10.1002/nme.1620231004
  10. 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. https://doi.org/10.1115/1.3176047
  11. Meirovitch, L. (1990), Dynamics and Control, Wiley, New York.
  12. Mori, T. and Kokame, H. (1987), "Convergence property of interval matrices and interval polynomials", Int. J. of Control, 45, 481-484. https://doi.org/10.1080/00207178708933746
  13. Porter, B. and Crossley, R. (1972), Modal Control Theory and Applications, Taylor & Francis, London.
  14. Rachid, A. (1989), "Robustness of discrete systems under structural uncertainties", Int. J. of Control, 50, 1563-1566. https://doi.org/10.1080/00207178908953449
  15. 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. https://doi.org/10.1080/00207178908953478

피인용 문헌

  1. Interval eigenvalues of closed-loop systems of uncertain structures vol.84, pp.3-4, 2006, https://doi.org/10.1016/j.compstruc.2005.08.004
  2. Interval finite element method for complex eigenvalues of closed-loop systems with uncertain parameters vol.26, pp.2, 2007, https://doi.org/10.12989/sem.2007.26.2.163