The nonlinear dynamics of elastic tubes conveying a fluid

Matthew A. Beauregard; Alain Goriely; Michael Tabor

doi:10.1016/j.ijsolstr.2009.09.022

The nonlinear dynamics of elastic tubes conveying a fluid

Matthew A. Beauregard, Alain Goriely, Michael Tabor

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.

Original language	English (US)
Pages (from-to)	161-168
Number of pages	8
Journal	International Journal of Solids and Structures
Volume	47
Issue number	1
DOIs	https://doi.org/10.1016/j.ijsolstr.2009.09.022
State	Published - Jan 1 2010
Externally published	Yes

Keywords

Dean number
Dynamical instabilities
Elastic tubes
Kirchhoff equations
Pipe flow

ASJC Scopus subject areas

Modeling and Simulation
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Applied Mathematics

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10.1016/j.ijsolstr.2009.09.022

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title = "The nonlinear dynamics of elastic tubes conveying a fluid",

abstract = "The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.",

keywords = "Dean number, Dynamical instabilities, Elastic tubes, Kirchhoff equations, Pipe flow",

author = "Beauregard, {Matthew A.} and Alain Goriely and Michael Tabor",

note = "Funding Information: This material is based in part upon work supported by the National Science Foundation under grants No. DMS-0907773 (AG & MT).",

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AU - Beauregard, Matthew A.

AU - Goriely, Alain

AU - Tabor, Michael

N1 - Funding Information: This material is based in part upon work supported by the National Science Foundation under grants No. DMS-0907773 (AG & MT).

PY - 2010/1/1

Y1 - 2010/1/1

N2 - The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.

AB - The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.

KW - Dean number

KW - Dynamical instabilities

KW - Elastic tubes

KW - Kirchhoff equations

KW - Pipe flow

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EP - 168

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

IS - 1

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The nonlinear dynamics of elastic tubes conveying a fluid

Abstract

Keywords

ASJC Scopus subject areas

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