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New Insights on the Application of Moment Closure Methods to Nonlinear Stochastic 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

The cumulant-neglect closure method is briefly outlined and subsequently applied to two Duffing systems, one exhibiting a unimodal and the other a bimodal response probability density function. The closure results are compared at stationarity to the exact solution over a broad range of parameters, and some connections are drawn between the accuracy of cumulant-neglect closure and the choice of system parameters. Finally, characteristic equations governing all stationary solutions of the closed system of moments equations are obtained, and the stability of the resulting solutions is ascertained. From this analysis, it is determined whether the closure results are physically consistent; that is, if the stationary closure results can be reached by letting the system evolve from arbitrary initial conditions.

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Author information

Authors and Affiliations

  1. Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    S. F. Wojtkiewicz

  2. Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA

    B. F. Spencer Jr.

  3. Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    L. A. Bergman

Authors
  1. S. F. Wojtkiewicz
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  2. B. F. Spencer Jr.
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  3. L. A. Bergman
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Editor information

Editors and Affiliations

  1. Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway

    A. Naess

  2. Division of Mechanics, Lund Institute of Technology, Lund University, Sweden

    S. Krenk

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© 1996 Kluwer Academic Publishers

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Wojtkiewicz, S.F., Spencer, B.F., Bergman, L.A. (1996). New Insights on the Application of Moment Closure Methods to Nonlinear Stochastic 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_43

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  • DOI: https://doi.org/10.1007/978-94-009-0321-0_43

  • 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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