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Design Sensitivity Random Eigenvalue Problem in Dynamics and Buckling of Structures

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Probabilistic Structural Mechanics: Advances in Structural Reliability Methods

Abstract

In the paper, the problem of the sensitivity of the probabilistic characteristics of the eigenvalue problem and buckling is considered. Using the linearization method, relationships defining the sensitivity of the expected values of eigenvalues and eigenvectors and of the covariance and the standard deviation of eigenvalues to changes in structural parameters and in the probabilistic characteristic of these parameters are derived.

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References

  1. Frank P. M., Introduction to system sensitivity theory, Acad. Press, New York 1978.

    MATH  Google Scholar 

  2. Haug E. J., Choi, K. K. & Komkov, V., Design sensitivity analysis of structural systems, Acad. Press 1985,

    Google Scholar 

  3. Socha L., The sensitivity analysis of stochastic non-linear dynamical systems, Jour. of Sound and Vibr., 110(2) (1986) 271–288,

    Article  MathSciNet  Google Scholar 

  4. Soong T. T. & Chen Y. Q., Stochastic response sensitivity of secondary systems to primary structural uncertainties, Structural Safety, 6 (1989) 311–321,

    Article  Google Scholar 

  5. Madsen H.O., Krenk S., & Lind N. C., Methods of structural safety, 1986, Prentice-Hall, Inc. Englewood Cliffs.

    Google Scholar 

  6. Der Kiureghian A. & Ke J. B., The stochastic finite element method instructural reliability, Probabilistic Engin. Mech. 3(2) (1988) 83–91,

    Article  Google Scholar 

  7. Collins J.D., & Thompson W.T.,The eigenvalue problem for structural systems with statistical properties, AIAAJ, 7(4) (1969,) 642–648,

    Article  MATH  Google Scholar 

  8. Shinozuka M. & Astil J., Random eigenvalue problems in structural analysis, AIAAJ, 10(4) (1972) 456–462,

    Article  MATH  Google Scholar 

  9. Hisada T. & Nakagiri S., Role of the stochastic finite element method in structural safety and reliability, 4th ICOSSAR, 1985, I385-I394,

    Google Scholar 

  10. Mironowicz W. & Śniady P., Dynamics of machine foundations with random parameters, Joum. of Sound and Vibr., 112(1) (1987) 23–30,

    Article  Google Scholar 

  11. Iyengar R.N. & Manohar C.S., Probability distribution of the eigenvalues of the random string equation, Jour. of Applied Mech. 56(3) (1989) 202–207.

    Article  MathSciNet  MATH  Google Scholar 

  12. Vanmarcke E., Shinozuka M., Nakagiri S., Schueller G. & Grigoriu M., Random fields and stochastic finite elements, Struc. Safety, 3 (1986) 143–166,

    Article  Google Scholar 

  13. Nakagiri S., Takopatake H. & Tani S., Uncertain eigenvalue analysis of composite laminated plates by the stochastic finite element method, Jour. of Engineering for Industry, 109 (1987) February, 9–12.

    Article  Google Scholar 

  14. Ibrahim R.A., Structural dynamics with parameter uncertainties, Appl. Mech. Rev. 40, 3 (1987) 309–328.

    Article  Google Scholar 

  15. Benaroya H., Random eigenvalues and structural dynamic models in “Stochastic structural Dynamics 1”, ed. YK. Lin, I. Elishakoff, SpringerVerlag 1990, 11–32.

    Google Scholar 

  16. Śniady P. & Zukowski S., Safety estimation of the rod structures due to loss of stability (in polish), Arch. of Civ. Engineering, XXXVII, 2 (1991) 165

    Google Scholar 

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© 1994 Springer-Verlag, Berlin Heidelberg

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Śniady, P., Żukowski, S. (1994). Design Sensitivity Random Eigenvalue Problem in Dynamics and Buckling of Structures. In: Spanos, P.D., Wu, YT. (eds) Probabilistic Structural Mechanics: Advances in Structural Reliability Methods. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85092-9_31

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  • DOI: https://doi.org/10.1007/978-3-642-85092-9_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-85094-3

  • Online ISBN: 978-3-642-85092-9

  • eBook Packages: Springer Book Archive

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