Nonlinear and Nonstationary Random Vibration of Hysteretic Systems with Application to Vehicle Dynamics

  • S. Narayanan
Conference paper
Part of the IUTAM Symposium book series (IUTAM)


The nonstationary response of a nonlinear multi-degree of freedom vehicle model is obtained. The suspension is of hysteretic nonlinear type and nonstationarity is due to variable velocity traverse. The road excitation is modelled as the response of a time variant filter to modulated white noise. Equivalent linearization method is adopted and response statistics are obtained by numerical integration of matrix differential equations.


Rear Wheel Random Vibration Road Profile Matrix Differential Equation Road Roughness 
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  1. 1.
    Virchis, V.J. and Robson, J.D. Response of an accelerating vehicle to random road undulation. Journal of Sound and Vibration 18 (3), 1971,pp 423–427.CrossRefADSGoogle Scholar
  2. 2.
    Sobczyk, K. and Macvean, D.B. Nonstationary random vibrations of systems travelling with variable velocity. Proc.IUTAM Symposium on Stochastic Problems in Dynamics, Ed.B.L.Clarkson,Pitman (1976).Google Scholar
  3. 3.
    Yadav,D. and Nigam,N.C. Ground induced nonstationary response of vehicles. Journal of Sound and Vibration, 61 (1), 1978,pp 117–126.CrossRefzbMATHADSGoogle Scholar
  4. 4.
    Hammond,J.K, and Harrison,R.F., Nonstationary response of vehicles on rough ground–A state-space approach. ASME.Journal of Dynamic Systems,Measurement and contro1. 103, 1981 pp 245–250.CrossRefGoogle Scholar
  5. 5.
    Schiehlen,W.O, Nonstationary random vibrations. Proc.IUTAM Symposium on Random Vibrations and Reliability. Ed.K.Hennig. Akademie Verlag. Berlin(GDR) 1983,pp 295–301.Google Scholar
  6. 6.
    Harrison,R.F.and Hammond,J.K. Approximate time domain nonstationary analysis of stochastically excited nonlinear systems with particular reference to the motion of vehicles on rough ground. Journal of Sound and Vibration, 105 (3), 1986, pp. 361–371.Google Scholar
  7. 7.
    Harrison,R.F., and Hammond,J.K. Analysis of the nonstationary response of vehicles with multiple wheels.ASME. Journal of Dynamic Systems, Measurement and control. 108, 1986,pp. 69–73.Google Scholar
  8. 8.
    Harrison,R.F. and Hammond,J.K. Evolutionary (Frequency/Time) spectral analysis of the response of vehicles on rough ground by using ‘Covariance equivalent’ modelling. Journal of Sound and Vibration. 107 (1), 1986,pp. 29–38.CrossRefADSGoogle Scholar
  9. 9.
    Foster.E.T. Semilinear random vibration in discrete systems. Trans.ASME. Journal of Applied Mechanics, 35, 1968,pp 560–564.CrossRefzbMATHADSGoogle Scholar
  10. 10.
    Iwan,W.D. and Yang,I. Application of statistical linearization techniques to nonlinear multidegree of freedom systems. Trans.ASME. Journal of Applied Mechanics. 39, 1972, pp 545–550.CrossRefADSGoogle Scholar
  11. 11.
    Iwan,W.D. A generalisation of the method of equivalent linearization. Int.Journal of nonlinear mechanics. 8, 1973, pp 279–287.CrossRefzbMATHADSMathSciNetGoogle Scholar
  12. 12.
    Atalik.T.S. and Utku.S. Stochastic linearization of multidegree of freedom nonlinear systems. Int.Journal of Earthquake Engineering and Structural Dynamics. 4, 1976, pp 41–420.Google Scholar
  13. 13.
    Iwan,W.D. and Mason.A.B. Equivalent linearization for systems subjected to nonstationary random excitation. Int.Journal of Nonlinear Mechanics. 15, 1980, pp 71–82.CrossRefzbMATHADSMathSciNetGoogle Scholar
  14. 14.
    Wen,Y.K. Equivalent linearization for hysteretic systems under random excitation. Trans.ASME.Journal of Applied Mechanics. 47, 1980, pp 150–154.CrossRefzbMATHADSGoogle Scholar
  15. 15.
    Tsao.Y.H. and Hammond.J.K. Nonstationarity in acoustic fields. Journal of Acous. Soc. of America. 74 (3), 1983, pp 827–839.Google Scholar
  16. 16.
    Dahlberg.T. Optimization criteria for vehicles travelling on a randomly profiled road-a survey. Vehicle system Dynamics Journal. 8, 1979,pp 239–252.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • S. Narayanan
    • 1
  1. 1.Machine Dynamics Laboratory Department of Applied MechanicsIndian Institute of Technology, MadrasMadrasIndia

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