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Deterministic and Stochastic Oscillations of a Flexible Cylinder in Arrays of Static Tubes

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Abstract

This study concentrates on vortex-induced vibrations of one flexiblecylinder in an array of fixed tubes. To describe approximately thedynamics of this system we generalize a previously developed linearsemi-empirical model that includes memory effects. We choose a cubicdamping term to model adequately vortex-induced oscillations and weobtain thus a nonlinear integro-differential equation governing thedisplacement of the cylinder. We use a two-variable expansion to derivecriteria for the appearance of stable, periodic, nonlinear oscillations.This approach predicts the appearance of a limit cycle and gives acriterion for the stability of the oscillations. In a stochasticoscillation model we apply additive white noise to the otherwisedeterministic oscillator model. For small values of the noise intensitywe can approximately solve the Fokker–Planck equation. A comparison ofthis approximation with numerical simulations shows a satisfactorydegree of agreement.

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Authors and Affiliations

  1. Department of Physics, Universidad Autónoma Metropolitana Iztapalapa, 09340, México D.F., México

    Peter Plaschko

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  1. Peter Plaschko
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Plaschko, P. Deterministic and Stochastic Oscillations of a Flexible Cylinder in Arrays of Static Tubes. Nonlinear Dynamics 30, 337–355 (2002). https://doi.org/10.1023/A:1021224605602

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