Solitary waves in prestressed elastic tubes |
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Authors: | Hilmi Demiray |
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Institution: | (1) Department of Mathematics, Marmara Research Center, Research Institute for Basic Sciences, Gebze, Kocaeli, Turkey;(2) Present address: Faculty of Sciences, Department of Engineering Sciences, Istanbul Technical University, Maslak-Istanbul, Turkey |
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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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Keywords: | |
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