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Solitary waves in prestressed elastic tubes

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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 pressureP 0 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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Author notes

  1. Hilmi Demiray

    Present address: Faculty of Sciences, Department of Engineering Sciences, Istanbul Technical University, Maslak-Istanbul, Turkey

Authors and Affiliations

  1. Department of Mathematics, Marmara Research Center, Research Institute for Basic Sciences, Gebze, Kocaeli, Turkey

    Hilmi Demiray

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  1. Hilmi Demiray
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Demiray, H. Solitary waves in prestressed elastic tubes. Bltn Mathcal Biology 58, 939–955 (1996). https://doi.org/10.1007/BF02459491

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  • DOI: https://doi.org/10.1007/BF02459491

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