Wiener Chaos Expansion for an Inextensible Kirchhoff Beam Driven by Stochastic Forces

  • Alexander VibeEmail author
  • Nicole Marheineke
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


In this work we study the feasibility of the Wiener Chaos Expansion for the simulation of an inextensible elastic slender fiber driven by stochastic forces. The fiber is described as Kirchhoff beam with a 1d-parameterized, time-dependent curve, whose dynamics is given by a constrained stochastic partial differential equation. The stochastic forces due to a surrounding turbulent flow field are modeled by a space-time white noise with flow-dependent amplitude. Using the techniques of polynomial chaos, we derive a deterministic system which approximates the original stochastic equation. We explore the numerical performance of the approximation and compare the results with those obtained by Monte-Carlo simulations.



This work has been supported by German DFG, project 251706852, MA 4526/2-1 and by the German BMBF, project OPAL 05M13.


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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department MathematikFAU Erlangen-NürnbergErlangenGermany

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