Stochastic Stability

  • Heinz Parkus
Part of the International Centre for Mechanical Sciences book series (CISM, volume 9)


We turn now to the investigation of differential equations whose coefficients are random functions (“parametric excitation”). Such equations occur frequently in applications: flutter of aircraft wings in turbulent atmosphere, instruments on shaking ground or shaking suspensions, wave propagation in inhomogeneous media etc. In this connection, the question of stability or instability of the motion is of fundamental importance.


White Noise Asymptotic Stability Random Function Image Point Parametric Excitation 
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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  1. [1]
    W.W. Bolotin: Kinetische Stabilität elastischer Systeme. VEB Deutscher Verlag der Wissenschaften, Berlin 1961.MATHGoogle Scholar
  2. [2]
    F. Kozin: A survey of stability of stochastic systems. Automatica 5 (1969), 95.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    F. Kozin: On almost sure stability of linear sys tems with random coefficients. J.Math.Phys. 42 (1963), 59.MATHMathSciNetGoogle Scholar
  4. [4]
    E.F. Infante:On the stability of some linear non-autonomous random systems. J.Appl. Mech. 35 (1968), 7.CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    A.H. Gray, Jr.: Behavior of linear systems with random parametric excitation. J.Acoust.Soc.America 37 (1965), 235.CrossRefGoogle Scholar
  6. [6]
    P.W.U. Graefe: On the stabilization of unstable linear systems by white noise coefficients. Ing.-Arch. 35 (1966), 276.CrossRefMATHGoogle Scholar
  7. [7]
    J.L.Bogdanoff and F.Kozin: Moments of the output of linear random systems. J.Acoust. Soc.America 34 (1962), 1063.Google Scholar
  8. [8]
    J.B. Keller: Stochastic equations and wave propaga tion in random media. Proc.Symposia Appl. Math., vol.XVI, 1964,p. 145.Google Scholar
  9. [9]
    W.E. Boyce: A “dishonest” approach to certain stochastic eigenvalue problems. SIAM J. Appl. Math. 15 (1967), 143.MATHMathSciNetGoogle Scholar
  10. [10]
    M.J. Beran: Statistical Continuum Theories. Inter science Publishers, New York 1968.MATHGoogle Scholar
  11. [11]
    J.M. Richardson: The application of truncated hi erarchy techniques in the solution of a stochastic linear differential equation.Proc.Symposia Appl.Math., vol. XVI, 1964,p. 290.CrossRefGoogle Scholar
  12. [12]
    Helga Bunke: Stabilität bei stochastischen Diffe rentialgleichungssystemen. Z.ang. Math. Mech. 43 (1963), 63.MATHMathSciNetGoogle Scholar
  13. [13]
    M. Kac: Probability theory. Proc. 1-st Symposium on Engineering Applications of Random Function Theory and Probability (J.L. Bogdanoff and F. Kozin, editors). J. Wiley and Sons, New York 1963, p. 37.Google Scholar
  14. [14]
    H. Parkus and J.L. Zeman: Some stochastic problems of thermoviscoelasticity. Proc. IUTAM Symposium on Thermoinelasticity. Glasgow 1968 (under press)Google Scholar
  15. [15]
    V.V. Bolotin:Statistical aspects in the theory of structural stability. Proc.Int.Conf. on Dynamic Stability of Structures. ( G.Herrmann, editor) Pergamon Press, New York 1967, p. 67.Google Scholar
  16. [16]
    J.R. Rice and F.P. Beer: First-occurrence time of high-level crossings in a continuous random process. J.Acoust.Soc.Ameri ca 39 (1966), 323.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1969

Authors and Affiliations

  • Heinz Parkus
    • 1
  1. 1.Technical University of ViennaAustria

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