Stability of mechanical systems under stochastic parametric excitation

  • S. T. Ariaratnam
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 294)


Instability Region Mathieu Equation Freedom System Axial Thrust Liapunov Function 
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. Ariaratnam, S.T. and Graefe, P.W.U., 1965, Int. J. Control, 2, 161.CrossRefGoogle Scholar
  2. Ariaratnam, S.T., 1965. Proc. Int. Conf. on Dynamic Stability of Structures, Ed: G. Herrmann, Pergamon, 1966, 255.Google Scholar
  3. Ariaratnam, S.T., 1967, Proc. Can. Cong. Appl. Math., Vol. III, 163.Google Scholar
  4. Ariaratnam, S.T., 1969, Proc. IUTAM Symp. on Instability of Continuous Systems, Ed: H. Leipholz, Springer-Verlag, 78.Google Scholar
  5. Bogdanoff, J.L. and Kozin, F., 1962, J. Acous. Soc. Am., 34, 1063.MathSciNetCrossRefGoogle Scholar
  6. Bolotin, V.V., 1964, The Dynamic Stability of Elastic Systems, Holden-Day, Inc.Google Scholar
  7. Bolotin, V.V., 1971, Study No. 6, Stability, Ed: H. Leipholz, Solid Mechanics Division, University of Waterloo, 385.Google Scholar
  8. Caughey, T.K. and Dienes, J.K., 1962, J. Math. Phys., 40–41, 300.MathSciNetCrossRefGoogle Scholar
  9. Caughey, T.K. and Gray, A.H. Jr., 1965, J. Appl. Mech., 32, 365.MathSciNetCrossRefGoogle Scholar
  10. Chelpanov, I.B., 1962, PMM, 26, 762, English Translation, 1145.MathSciNetGoogle Scholar
  11. Dimentberg, F., 1961, Flexural Vibration of Rotating Shafts, Butterworths.Google Scholar
  12. Graefe, P.W.U., 1966, Ing. Arch., 35, 202.CrossRefGoogle Scholar
  13. Gray, A.H. Jr., 1967, J. Appl. Mech., 34, 1017.CrossRefGoogle Scholar
  14. Infante, E.T., 1968, J. Appl. Mech., 35.Google Scholar
  15. Kozin, F., 1963, J. Math. Phys., 42, 59.MathSciNetCrossRefGoogle Scholar
  16. Kushner, H.J., 1967, Stochastic Stability and Control, Academic Press.Google Scholar
  17. Man, F.T., 1970, J. Appl. Mech., 37, 541.CrossRefGoogle Scholar
  18. Mettler, E., 1965, Proc. Int. Conf. on Dynamic Stability of Structures, Ed: G. Herrmann, Pergamon, 1966, 169.Google Scholar
  19. Mettler, E., 1967, Proc. Fourth Conf. on Nonlinear Oscillations, Prague, Academia, 1968; 51.Google Scholar
  20. Samuels, J.C., 1960, J. Acoust. Soc. Am., 32, 594.MathSciNetCrossRefGoogle Scholar
  21. Samuels, J.C., 1961, J. Acoust. Soc. Am., 33, 1782.MathSciNetCrossRefGoogle Scholar
  22. Stratonovich, R.L., 1963, Topics in the Theory of Random Noise, Vol. I, Gordon and Breach.Google Scholar
  23. Stratonovich, R.L., and Romanovskii, Yu.M., 1958, Nauchnye doklady vysshei shkoly, Fiziko-mat. nauk., 3, 221, Reprinted in Non-Linear Transformations of Random Processes, Ed: Kuznetsov, P.I., R.L. Stratonovich and V.I. Tikhonov, Pergamon, 1965, 332.Google Scholar
  24. Wedig, W., 1972, Proc. IUTAM Symposium on Stability of Stochastic Dynamical Systems, Springer-Verlag.Google Scholar
  25. Weidenhammer, F., 1964, Ing. Arch., 33, 404.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • S. T. Ariaratnam
    • 1
  1. 1.Solid Mechanics DivisionUniversity of WaterlooWaterlooCanada

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