Bulletin of Mathematical Biology

, Volume 58, Issue 5, pp 939–955 | Cite as

Solitary waves in prestressed elastic tubes

  • Hilmi Demiray
Article

Abstract

In this work, we studied the propagation of non-linear waves in a pre-stressed thin elastic tube filled with an inviscid fluid. In the analysis, analogous to the physiological conditions of the arteries, the tube is assumed to be subject to a uniform pressureP0 and a constant axial stretch ratio λz. In the course of blood flow it is assumed that a large dynamic displacement is superimposed on this static field. Furthermore, assuming that the displacement gradient in the axial direction is small, the non-linear equation of motion of the tube is obtained. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is investigated. It is shown that the governing equations reduce to the Korteweg-deVries equation which admits a solitary wave solution. The result is discussed for some elastic materials existing in the literature.

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Copyright information

© Society for Mathematical Biology 1996

Authors and Affiliations

  • Hilmi Demiray
    • 1
  1. 1.Department of MathematicsMarmara Research Center, Research Institute for Basic SciencesKocaeliTurkey
  2. 2.Faculty of Sciences, Department of Engineering SciencesIstanbul Technical UniversityMaslak-IstanbulTurkey

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