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Yayın Weakly non-linear waves in a fluid-filled elastic tube with variable prestretch(Pergamon-Elsevier Science Ltd, 2008-11) Demiray, HilmiIn the present work, by utilizing the non-linear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable prestretch both in the axial and the radial directions and the approximate equations of motion of an incompressible inviscid fluid, which is assumed to be a model for blood, we studied the propagation of weakly non-linear waves in such a medium, in the long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient KdV equation as the evolution equation. By seeking a travelling wave solution to this evolution equation, we observed that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations.Yayın Localized travelling waves in a prestressed thick elastic tube(Pergamon-Elsevier Science, 2001-10) Demiray, HilmiIn the present work, by using the exact non-linear equations of an incompressible inviscid fluid contained in a prestressed thick elastic tube, the propagation of localized travelling wave solution in such a medium is investigated. Employing the hyperbolic tangent method and considering the long-wave limit, we showed that the lowest-order term in the perturbation expansion gives a solitary wave equivalent to the localized travelling wave solution of the Korteweg-de Vries equation. The progressive wave type of solution is also sought for the second-order terms in the perturbation expansion. The correction terms in the speed of propagation are obtained as part of the solution of perturbation equations.Yayın Non-linear waves in a viscous fluid contained in an elastic tube with variable cross-section(Elsevier Ltd, 2006-04) Demiray, HilmiIn the present work, treating the large arteries as a thin-walled, long and circularly cylindrical, prestressed elastic tube with variable cross-section and using the reductive perturbation method, we have studied the amplitude modulation of non-linear waves in such a fluid-filled elastic tube. By considering the blood as an incompressible viscous fluid, the evolution equation is obtained as the dissipative non-linear Schrodinger equation with variable coefficients. It is shown that this type of equations admit a solitary wave solution with a variable wave speed. It is observed that, the wave speed increases with distance for narrowing tubes while it decreases for expanding tubes.Yayın The dynamic response of an incompressible non-linearly elastic membrane tube subjected to a dynamic extension(Pergamon-Elsevier Science Ltd, 2004-06) Tüzel, Vasfiye Hande; Erbay, Hüsnü AtaThe dynamic response of an isotropic hyperelastic membrane tube, subjected to a dynamic extension at its one end, is studied. In the first part of the paper, an asymptotic expansion technique is used to derive a non-linear membrane theory for finite axially symmetric dynamic deformations of incompressible non-linearly elastic circular cylindrical tubes by starting from the three-dimensional elasticity theory. The equations governing dynamic axially symmetric deformations of the membrane tube are obtained for an arbitrary form of the strain-energy function. In the second part of the paper, finite amplitude wave propagation in an incompressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. A Godunov-type finite volume method is used to solve numerically the corresponding problem. Numerical results are given for the Mooney-Rivlin incompressible material. The question how the present numerical results are related to those obtained in the literature is discussed.
