Initially deformed dissimilar elastic tubes containing fluid flow. (English) Zbl 0873.76007
The paper starts from a short, but substantial review of achievements in the field of deformed dissimilar elastic tubes containing fluid flow. The main attention is paid to the problem coupled with modeling natural arteries and artificial implants. The authors analyze different types of dissimilar elastic tubes connection. Mathematical simulation is based on a theory of thin membrane by Green and Adkins. The material is supposed to be isotropic, elastic and incompressible.
Using a long wavelength approximation, the authors extend their earlier results on inviscid fluid flows to the case of predeformed elastic tubes. They are able to predict the cut-off predeformation states, besides the cut-off frequency state. The analysis of dispersion equation shows that special regime of transition of running waves into standing waves can take place. The authors recommend to account for this phenomenon by implantation of artificial graft, because such transitions can influence negatively. It is noted that this result agrees qualitatively with results given by other authors and with results of numerical simulation for viscous fluid.
Using a long wavelength approximation, the authors extend their earlier results on inviscid fluid flows to the case of predeformed elastic tubes. They are able to predict the cut-off predeformation states, besides the cut-off frequency state. The analysis of dispersion equation shows that special regime of transition of running waves into standing waves can take place. The authors recommend to account for this phenomenon by implantation of artificial graft, because such transitions can influence negatively. It is noted that this result agrees qualitatively with results given by other authors and with results of numerical simulation for viscous fluid.
Reviewer: O.Limarchenko (Kiev)
MSC:
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 76Z05 | Physiological flows |
Keywords:
natural arteries; artificial implants; theory of thin membrane; long wavelength approximation; cut-off predeformation states; dispersion equation; running waves; standing wavesReferences:
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