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

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 adequatel...

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Bibliographic Details
Published in:Nonlinear dynamics 2002-12, Vol.30 (4), p.337-355
Main Author: Plaschko, Peter
Format: Article
Language:English
Subjects:
Arrays
Computer simulation
Cylinders
Differential equations
Fokker-Planck equation
Mathematical analysis
Oscillations
Tubes
Vortex-induced vibrations
White noise
Online Access:Get full text
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Summary: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.
ISSN:0924-090X
1573-269X
DOI:10.1023/A:1021224605602