Identification of the Hysteresis Parameters of a Nonlinear Vehicle Suspension Under Random Excitation

  • S. Bellizzi
  • R. Bouc
Part of the IUTAM Symposium book series (IUTAM)


We present a recursive procedure for the identification in the frequency domain of the hysteresis parameters of a non linear suspension, solving the model via iterative applications of a multiharmonic Galerkin method briefly presented. This procedure, susceptible to be carried out “online”, is the first step in the study of “semi-active” non linear suspension control systems.


Galerkin Method Excitation Level Random Excitation Stationary Stochastic Process Input Acceleration 
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.
    R. Bouc, Forced vibration of mechanical system with hysteresis. Proc. 4° Conf. ICNO, Prague (summary) (1967).Google Scholar
  2. 2.
    R. Bouc, Modèle mathématique d’hystérésis. Acustica, 24, (1971) 16–25.MATHGoogle Scholar
  3. 3.
    Y.K. Wen, Method for random vibration of hysteretic systems. J.Eng.Mech.Division, Proc. ASCE, 102, N° EM2, (1976) 249–265.Google Scholar
  4. 4.
    T.T. Baber and Y.K. Wen, Random Vibration of Hysteretic Degrading Systems, J. of the engineering Mechanics Division, ASCE, vol. 107, n° EM6 pp 1069, dec. 1981.Google Scholar
  5. 5.
    R. Bouc et M. Defilippi, Galerkin method for nonlinear random vibration, an example from truck dynamics. Int. workshop on Stochastic Methods in Structural Mechanics, Pavie, Août 1985, Edited by E. Casciati and L. Faravelli, SEAG - Pavia.Google Scholar
  6. 6.
    R. Bouc et M. Defilippi, A Galerkin Multiharmonic Procedure for Nonlinear Multidimensional Random Vibration. International Journal of Engineering Sciences, to appear.Google Scholar
  7. 7.
    M. Urabe, Galerkin procedure for nonlinear periodic systems. Archs ration. Mech. Analysis, 20, (1965) 120–152.MATHMathSciNetGoogle Scholar
  8. 8.
    J.S. Bendat, A.G. Piersol, Random Data: Analysis and measurement procedures. John Wiley 00000 Sons, Inc. (1971).Google Scholar
  9. 9.
    M. Fariss, “ Identification de paramètres de suspensions non linéaires par filtrage multiple et linéarisation stochastique”. Thèse 3° cycle. Lab. de Mecanique et d’Acoustique, Marseille (1984).Google Scholar
  10. 10.
    R. Bouc, Vibrations aléatoires non linéaires multidimensionnelles. Application industrielle. Actes du 8 ième Congrés français de Mécanique. Nantes (France), Sept. 1987.Google Scholar
  11. 11.
    M. Hoshiya and E. Sarro, Structural Identification by Extended Kalman Filter, J. of Engineering Mechanics, Vol 110, n° 12, (dec. 1984 ), 1757–1770.CrossRefGoogle Scholar
  12. 12.
    Y. K. Wen, Equivalent linearization for hysteretic systems under random excitation. J. of Applied Mechanics, Trans. of ASME, 47, n° 1, (1980) 150–154.CrossRefGoogle Scholar
  13. 13.
    P. S. Maybeck, Stochastic models, estimation, and control. In Math. in Sciences and Engineering, Academic Press, Vol 141–2, 1982.Google Scholar
  14. 14.
    A. Papoulis, Probility, random variables and stochastic processes, Mc. Graw-Hill Book, 1965.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • S. Bellizzi
    • 1
  • R. Bouc
    • 1
  1. 1.Laboratoire de Mecanique et d’AcoustiqueCNRSMarseilleFrance

Personalised recommendations