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Probability Densities of the Response of Non-Linear Structures under Stochastic Dynamic Excitation

  • N. C. Hampl
  • G. I. Schuëller
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 31)

Abstract

An approximate method for determining estimates of response statistics for non-linear oscillators driven by wide-band random excitation is presented. The development is based on the theory of Markov processes. The proposed method is based on non-Gaussian closure procedures where a number of moment differential equations are used to evaluate parameters of non-Gaussian response distributions. The developments are described and illustrated by means of numerical examples. Special attention is given to the choice of types of non-Gaussian distributions. it is shown that some serious shortcomings of series approximations, particularly with respect to negative probability densities can be avoided by using generalized exponential distributions.

Keywords

Probability Density Function Joint Probability Density Function Generalize Exponential Distribution High Excitation Level Hysteretic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T.K. Caughey, Nonlinear theory of random vibrations, Advances in Appliec Mechanics 11, 209–253 (1971).CrossRefGoogle Scholar
  2. 2.
    A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc-Graw Hill, Singapore, 2nd ed. (1984).MATHGoogle Scholar
  3. 3.
    C.V.L Charlier, A new form of the frequency function, Meddelande frår Lands Astronomiska Observatorium,Sen II,Nr.51, (1928).Google Scholar
  4. 4.
    M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, Volume 1, Griffin, London (1963).Google Scholar
  5. 5.
    N.C.Hampl, On the Probability Density of the Response of Nonlinear Systems to Random Excitation (in German), Report 10-87, Institute of Engineering Mechanics, University of Innsbruck, Innsbruck (1987).Google Scholar
  6. 6.
    S.H. Crandall and W.Q. Zhu, Random vibration: a survey of recent developments, Journal of Applied Mechanics 50, 953–962 (1983).CrossRefMATHGoogle Scholar
  7. 7.
    T.S. Atalik and S. Utku, Stochastic linearization of multi-degree-of-freedom non-linear systems, Earthquake Engineering and Structural Dynamics 4, 411–420 (1976).CrossRefGoogle Scholar
  8. 8.
    Y.K Lin, Probabilistic Theory of Structural Dynamics, McGraw—Hill, New York (1967).Google Scholar
  9. 9.
    H. Parkus, Random processes in mechanical sciences, CISM No. 9, Springer, Vienna (1969).Google Scholar
  10. 10.
    J.L. Zeman, Zur Lösung nichtlinearer stochastischer Probleme der Mechanik, Acta Mechanica 14, 157–169 (1972).Google Scholar
  11. 11.
    W.F. Wu and Y.K. Lin, Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations, Int. J Non-Lineal Mechanics 19, 349–362 (1984).CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    R. Bouc, Mod mathématique d’hystérésis, Acustica 24, 16–25 (1971).MATHGoogle Scholar
  13. 13.
    Y.K. Wen, Method for random vibration of hysteretic systems, Journal of the Engineering Mechanics Division, ASCE, 102, 249–263 (1976).Google Scholar
  14. 14.
    T.T. Baber and Y.K. Wen, Stochastic equivalent linearization for hysteretic degrading, multistory structures, Structural Research Series 471, University of Illinois at Urbana-Champaign, Urbana (1979).Google Scholar
  15. 15.
    T.-P. Chang, T. Mochio and E. Samaras, Seismic response analysis of nonlinear structures, Probabilistic Engineering Mechanics 1, 157–166 (1986).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • N. C. Hampl
    • 1
    • 2
  • G. I. Schuëller
    • 3
  1. 1.Getzner Chemie, Bludenz-BürsAustria
  2. 2.Institute of Engineering MechanicsUniversity of InnsbruckAustria
  3. 3.University of InnsbruckAustria

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