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Linear and non-linear pulse propagation in fluid-filled compliant tubes

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Sommario

Si studiano le perturbazioni prodotte da impatto in tubi elastici riempiti di fluidi. Si assume che il diametro del tubo indeformato, lo spessore della parete e il modulo elastico del materiale del tubo siano funzioni della distanza misurata lungo la linea centrale del tubo. La versione linearizzata delle equazioni che governano il fenomeno è risolta con la trasformata di Laplace, invertita con un metodo approssimato. Il sistema originale non lineare delle equazioni è risolto numericamente con il metodo delle caratteristiche. Vengono rappresentate, per valori fissati del tempo e della coordinata assiale, le relazioni tra la velocità assiale del fluido e la coordinata assiale oltre alle relazioni fra velocità e tempo, sia per la teoria lineare sia per quella non lineare.

Summary

Here we study impact-initiated disturbances in fluid-filled elastic tubes. The undeformed tube diameter, wall thickness, and elastic modulus of the tube material are assumed to be functions of the distance along the centre line of the tube. The linearized version of the governing equations are solved by the Laplace transform, which is inverted by means of an approximate method. The original non-linear system of governing equations is solved numerically by the method of characteristics. Relationships between the axial fluid velocity and axial coordinate as well as between velocity and time are displayed for fixed values of time and axial coordinate respectively for the linear and nonlinear theory for ease of comparison.

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Abbreviations

x :

axial coordinate

t :

time variable

v :

axial fluid velocity

A :

cross-sectional area of tube

ρ :

fluid density

D 0,D :

undeformed and deformed tube diameter

p :

fluid pressure

τ ω :

shearing stress

μ :

fluid viscosity

E :

Young's modulus

h :

tube wall thickness

c :

wave speed

L :

phase

Ψ :

confluent hypergeometric function

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Authors and Affiliations

  1. Department of Mathematics and Statics, University of New Brunswick, E3B 5A3, Fredericton, Canada

    D. W. Barclay

  2. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    T. Bryant Moodie & V. P. Madan

Authors
  1. D. W. Barclay
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  2. T. Bryant Moodie
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  3. V. P. Madan
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Barclay, D.W., Moodie, T.B. & Madan, V.P. Linear and non-linear pulse propagation in fluid-filled compliant tubes. Meccanica 16, 3–9 (1981). https://doi.org/10.1007/BF02128301

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  • DOI: https://doi.org/10.1007/BF02128301

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