Comparison of the New Energy-Based Versions of the Stochastic Linearization Technique

  • Isaac Elishakoff
  • Ruichong Zhang
Part of the IUTAM Symposia book series (IUTAM)

Summary

In this study a generalization of the stochastic linearization method is proposed; namely the nonlinear system is suggested to be replaced by a linear system equivalent to the original one in the following sense: The two systems should share common mean-square values of potential energies, as well as have coincident mean square values of energy dissipation function. An example of a system with nonlinear damping and nonlinear stiffness is numerically evaluated, to elucidate the proposed method.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Y. K. Lin, Probabilistic Theory of Structural Dynamics, McGraw Hill, New York, 1967 (Second Edition: Robert Krieger Company, Malabar, FL, 1976)Google Scholar
  2. 2.
    V. V. Bolotin, Random Vibration of Elastic Systems, Martinus Nijhoff Publishers, The Hague, 1984.Google Scholar
  3. 3.
    P. D. Spanos, Stochastic Linearization in Structural Dynamics, Applied Mechanics Reviews, 1981, Vol. 34, No.1, pp 1–8.MathSciNetGoogle Scholar
  4. 4.
    S. H. Crandall, Heuristic and Equivalent Linearization Techniques for Random Vibration of Nonlinear Oscillators, Proceedings of the 8th International Conference on Nonlinear Oscillation, Academia, Prague, 1979, Vol. 1, pp. 211–226.Google Scholar
  5. 5.
    J. B. Roberts and P. D. Spanos, Random Vibration and Statistical Linearization, John Wiley and Sons, Chichester, 1990.MATHGoogle Scholar
  6. 6.
    X. Zhang, I. Elishakoff and R. Zhang, A Stochastic Linearization Technique Based on Minimum Mean Square Deviation of Potential Energies, in “Stochastic Structural Dynamics-New Theoretical Developments” (Y.K. Lin and I. Elishakoff, eds.), Springer Verlag, Berlin, 1991, pp.Google Scholar
  7. 7.
    I. Elishakoff and X. Zhang, An Appraisal of Stochastic Linearization Techniques, Journal of Sound and Vibration, 1991, to appear.Google Scholar
  8. 8.
    G.R. Khabbaz, Power Spectral Density of the Response of a Nonlinear System to Random Excitation, Journal of the Acoustical Society of America, Vol 38, 1964, pp. 847–850.CrossRefADSGoogle Scholar
  9. 9.
    R.W. Glough and J. Penzien, Dynamics of Structures, McGraw Hill, Auckland, 1975.Google Scholar
  10. 10.
    G.Q. Cai and Y.K. Lin, Hysteretic Columns under Random Excitations, Technical Report NCEER-89–0003, Center for Applied Stochastics Research, Florida Atlantic University, Jan. 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Isaac Elishakoff
    • 1
  • Ruichong Zhang
    • 1
  1. 1.Center for Applied Stochastics Research and Department of Mechanical EngineeringFlorida Atlantic UniversityBoca RatonUSA

Personalised recommendations