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Yayın Forced KdV equation in a fluid-filled elastic tube with variable initial stretches(Pergamon-Elsevier Science Ltd, 2009-11) Demiray, HilmiIn this work, by utilizing the nonlinear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable initial stretches 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 have studied the propagation of nonlinear waves in such a medium under the assumption of long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient forced KdV equation as the evolution equation. By use of proper transformations for the dependent field and independent coordinate variables, we have shown that this evolution equation reduces to the conventional KdV equation, which admits the progressive wave solution. The numerical results reveal 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. We further observed that, the wave amplitude gets smaller and smaller with increasing time parameter along the tube axis.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 Propagation of weakly nonlinear waves in fluid-filled thin elastic tubes(Elsevier Science, 2002-11-25) Demiray, HilmiIn the present work, we study the propagation of nonlinear waves in a prestressed thin elastic tube filled with an incompressible inviscid fluid. Considering the physiological conditions under which the arteries function, in the analysis the tube is assumed to be subjected to a uniform inner pressure P-0 and the axial stretch ratio lambda(z). In the course of blood flow, a dynamical displacement field is superimposed on this static deformation. Treating the blood as an incompressible inviscid fluid, the nonlinear equations of motion of both the tube and the fluid are obtained. Employing the reductive perturbation method, the propagation of weakly nonlinear waves in the longwave approximation is investigated and the Korteweg-de Vries equations are obtained as the governing equation. It is observed that the present formulation gives two solitary waves associated with dilatational and shear motions of the tube. The results are also discussed for some elastic materials existing in the current literature.
