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Amplitude Bounds of Stochastic Nonlinear Multibody Systems

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IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 47))

Abstract

For evaluation of the boundedness of stochastic nonlinear multi-body systems, amplitude bounds with respect to the initial conditions are introduced in this paper. The amplitude bounds of stochastic nonlinear systems are analyzed based on the simulations using the Monte Carlo method. Simulations are available for systems with arbitrary finite dimensions and nonlinearities. By comparing the distribution of the random amplitude bounds, the boundedness of the system can be evaluated quantitatively in a statistical sense.

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References

  • Benettin, G., Galgani, L. and Giorgolli, A. (1980), Ljapunov characteristic exponents for dynamical systems and for Hamiltonian systems: a method for computing all of them, Meccanica 15, 9-30.

    Article  MATH  Google Scholar 

  • Hu, B., Schaub, S. and Schiehlen, W. (1995) Boundedness Evaluation of Structural systems with Randomly Distributed Initial Conditions, submitted to J. of Nonlinear Mechanics.

    Google Scholar 

  • Kozin, F. (1972) Stability of the linear stochastic systems, In: Curtain, R.F. (ed.): Stochastic Stability, Lecture notes in Mathematics No. 294, Springer-Verlag, Berlin, pp. 186 - 229.

    Chapter  Google Scholar 

  • Kushner, H.J. (1967) Stochastic Stability and Control, Academic Press, New York and London.

    MATH  Google Scholar 

  • Lin, Y.K. and Cai, G.Q. (1993) Stability in probability of some nonlinear stochastic systems. In: Schuëller, G.I., Shinozuka, M and Yao, J.T.P. (eds.), Structural Safety and Reliability, ICOSSAR’93, Vol. 1, A. A. Balkema Publishers, Rotterdam, pp. 165-172.

    Google Scholar 

  • Ljapunov, A.M. (1966) Stability of Motion, Academic Press, London. (English translation of the in 1893 published original work in Russian)

    Google Scholar 

  • Müller, P.C. and Schiehlen, W. (1985) Linear Vibration, Kluwer, Dordrecht.

    Google Scholar 

  • Pradlwarter, H.J., Schuëller, G. I. and Melnik-Melnikov, P.G. (1994) Reliability of MDOF-systems. Probabil. Engng. Mech. 9(4), 235–243.

    Article  Google Scholar 

  • Schiehlen, W. (1993) Nonlinear Oscillations in Multibody Systems -Modeling and Stability Assessment-, In: Kreuzer, E. and Schmidt, G. (eds): 1st European Nonlinear Oscillation Conference, Academic-Verlag, Berlin, pp. 85–106.

    Google Scholar 

  • Shampine, L.F. and Gordon, M.K. (1975) Computer Solution of Ordinary Differential Equations, Freeman, San Francisco.

    MATH  Google Scholar 

  • Shinozuka, M and Deodatis, G. (1991) Simulation of stochastic processes by spectral representation. Appl. Mech. Rev. 44(4), 191–203.

    Article  MathSciNet  Google Scholar 

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© 1996 Kluwer Academic Publishers

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Schiehlen, W., Hu, B., Schaub, S. (1996). Amplitude Bounds of Stochastic Nonlinear Multibody Systems. In: Naess, A., Krenk, S. (eds) IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. Solid Mechanics and its Applications, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0321-0_35

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  • DOI: https://doi.org/10.1007/978-94-009-0321-0_35

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6630-3

  • Online ISBN: 978-94-009-0321-0

  • eBook Packages: Springer Book Archive

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