Dynamic Analysis of Complex Structural Systems

  • L. Faravelli
Part of the International Centre for Mechanical Sciences book series (CISM, volume 340)


Attention is focused on the characterization of the stochastic response of nonlinear complex systems subjected to stochastic external excitations. Non-linearity arises from geometrical considerations and/or material properties. Since exact analytical solutions can be found only in the case of systems idealized by one or few degrees of freedom, approximate methods have been developed. For practical applications in structural engineering the techniques of the stochastic equivalent linearization and of the response surface appear as the most suitable. These methods are illustrated in this Chapter.


Response Surface Random Vector Joint Probability Density Function Equivalent Linearization Random Vibration 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Wen Y.K.: Methods of Random Vibration for Inelastic Structures, Applied Mechanics Review, 42, 2, 1989, 39–52CrossRefGoogle Scholar
  2. [2]
    Socha L. and Soong T.T.: Linearization in Analysis of Nonlinear Stochastic Systems, Applied Mechanics Review, 44, 10, 1991, 399–422CrossRefMathSciNetGoogle Scholar
  3. [3]
    Caughey T.K.: Response of a Nonlinear String to Random Loading, Journal of Applied Mechanics, 26, 1959, 341–344MATHMathSciNetGoogle Scholar
  4. [4]
    Caughey T.K.: Equivalent Linearization Technique, Journal of Acoustical Society of America, 35, 1963, 1706–1711CrossRefMathSciNetGoogle Scholar
  5. [5]
    Atalik T.S. and Utku S.: Stochastic Linearization of Multi-Degree-of-Freedom Non-Linear Systems, Earthquake Engineering and Strctural Dynamics, 4, 1976, 411–420CrossRefGoogle Scholar
  6. [6]
    Faravelli L., Casciati F., and Singh M.P.: Stochastic Equivalent Linearization Algorithms and Their Applicability to Hysteretic Systems, Meccanica, 23 (2), 1988, 107–112CrossRefMATHMathSciNetGoogle Scholar
  7. [7]
    Iwan W.D. and Yang I-M.: Application of Statistical Linearization Techniques to Non-Linear Multidegree of Freedom Systems, Journal of Applied Mechanics, 39, 1972, 545–550CrossRefMATHGoogle Scholar
  8. [8]
    Spanos P.D. and Iwan W.D.: On the Existence and Uniqueness of Solution Generated by Equivalent Linearization, Int. Journal of Non-Linear Mechanics, 13, 1978, 71–78CrossRefMATHMathSciNetGoogle Scholar
  9. [9]
    Bouc R.: Forced Vibrations of a Mechanical System with Hysteresis, Proc. of 4th. Conf. on Non-linear Oscillations, Prague, 1967Google Scholar
  10. [10]
    Wen Y.K.: Equivalent Linearization for Hysteretic Systems Under Random Excitation, Journal of Applied Mechanics, 47, 1980, 150–154CrossRefMATHGoogle Scholar
  11. [11]
    Casciati F. and Faravelli L.: Fragility Analysis of Complex Structural Systems, Research Studies Press, Taunton, 1991MATHGoogle Scholar
  12. [12]
    Casciati F.: Stochastic Dynamics of Hysteretic Media, Structural Safety, 6, 1989, 259–269CrossRefGoogle Scholar
  13. [13]
    Casciati F. and Faravelli L.: Stochastic Equivalent Linearization for Dynamic Analysis of Continuous Structures, in Computational Probabilistic Methods, AMD, 93, 1988, 205–210Google Scholar
  14. [14]
    Casciati F. and Faravelli L.: Stochastic Linearization for 3-D Frames, J. of Engineering Mechanics, ASCE, 114 (10), 1988, 1760–1771Google Scholar
  15. [15]
    Bartels R.H. and Stewart G.W.: Solution of the Matrix Equation AX+BX = C, Algorithm 432, Comm. ACM, 15, 9, 1972, 820–826CrossRefGoogle Scholar
  16. [16]
    Casciati F., Faravelli L., and Venini P.: Neglecting Higher Complex Modes in Nonlinear Stochastic Vibration, Proc. 4th Int. Conf. on Recent Advances in Structural Dynamics, Elsevier 1991, 865–874Google Scholar
  17. [17]
    Casciati F., Faravelli L., and Venini P • Frequency Analysis in Stochastic Linearization, submitted for publication, 1993Google Scholar
  18. [18]
    Elishakoff I. and Zhang R.: Comparison of New Stocastic Linearization Criteria, in Nonlinear Stochastic Mechanics ( Bellomo N. and Casciati F. eds.), Springer-Verlag, Berlin, 1992, 201–212CrossRefGoogle Scholar
  19. [19]
    Casciati F., Faravelli L., and Hasofer M.: A New Philosophy for Stochastic Equivalent Linearization, Probabilistic Engineering Mechanics, 1993Google Scholar
  20. [20]
    Ditlevsen O.: Principle of Normal Tail Approximation, Journal of Engineering Mechanics Division, ASCE, 107, 1981, 1191–1208Google Scholar
  21. [21]
    Lin Y.K.: Probabilistic Theory of Structural Dynamics, R.E. Krieger, 1976Google Scholar
  22. [22]
    Roberts J.B. and Spanos P.D.: Random Vibration and Statistical Linearization, John Wiley zhaohuan Sons Ltd., 1989Google Scholar
  23. [23]
    Roberts J.B.: Averaging Methods in Random Vibration, Report 245, Dept. of Structural Engineering, Technical University of Denmark, Lyngby, 1989Google Scholar
  24. [24]
    Stratonovich R.L.: Topics in the Theory of Random Noise, Vol. 1, Gordon zhaohuan Breach, New York-London, 1981Google Scholar
  25. [25]
    Breitung, K., Asymptotic approximations for multinormal integrals, Journal of Engineering Mechanics Division, ASCE 110, 1984, 357–366Google Scholar
  26. [26]
    Nakagiri S. and Hisada T.: Stochastic Finite Elements: an Introduction (in Japanese), Baifiu-kan, Tokyo, 1985Google Scholar
  27. [27]
    Faravelli L.: Finite Element Analysis of StochasticNonlinear Continua, in Computational Mechanics of Probabilistic and Reliability Analysis (Liu W.K. and Belitschko T. eds. ), Elme Press Int., 1989, 263–280Google Scholar
  28. [28]
    Faravelli L.: A Response Surface Approach for Reliability Analysis, Journal of Eng. Mechanics, ASCE, 115 (12), 1989 b, 2763–2781Google Scholar
  29. [29]
    Faravelli L.: Response Variables Correlation in Stochastic Finite Element Analysis, Meccanica, 22 (2), 1988, 102–106CrossRefMathSciNetGoogle Scholar
  30. [30]
    Petersen R.G.: Design and Analysis of Experiments,M.Decker Inc., New York, 1985Google Scholar
  31. [31]
    Bohm F. and Bruckner-Foit A.: On Criteria for Accepting a Response Surface Model, Probabilistic Eng. Mechanics, 7 (3), 1992, 183–190Google Scholar
  32. [32]
    Veneziano D., Casciati F., and Faravelli L.: Method of Seismic Fragility for Complicated Systems, 2nd CSNI Meeting on Prob. Meth. in Seismic Risk Assessment for Nuclear Power Plants, Livermore, 1983, 67–88Google Scholar
  33. [33]
    Hohenbichler M. and Rackwitz R., Non-normal Dependent Vectors in Structural Safety, Journal of Engineering Mechanics Division, ASCE, 107, 1981, 1227–1241Google Scholar
  34. [34]
    Breitung K. and Faravelli L.: Log-likelihood Maximization and Response Surface in Reliability Assessment, Nonlinear Dynamics, 1993Google Scholar
  35. [35]
    Breitung K.: Probability Approximations by Log Likelihood Maximization, Journal of Engineering Mechanics, ASCE 117, 1991, 457–477Google Scholar
  36. [36]
    Breitung K.: Parameter Sensitivity of Failure Probabilities, in Reliability and Optimization of Structures ‘80 (Der Kiureghian A. and Thoft-Cristensen P. eds.), Lecture Notes in Engineering 61, Springer, Berlin, 1990, 43–51Google Scholar
  37. [37]
    Faravelli L.: Structural Reliability via Response Surface, in Nonlinear Stochastic Mechanics (Bellomo N. and Casciati F. eds. ), Springer Verlag, 1992, 213–224CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • L. Faravelli
    • 1
  1. 1.University of PaviaPaviaItaly

Personalised recommendations