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Yayın Modulation of non-linear axial and transverse waves in a fluid-filled thin elastic tube(Pergamon-Elsevier Science, 2000-07) Akgün, Güler; Demiray, HilmiIn the present work, utilizing the non-linear equations of a pre-stressed thin elastic tube filled with an incompressible inviscid fluid the propagation of weakly non-linear waves in such a medium is studied. Considering that the arteries are initially subjected to a large static transmural pressure P-0 and an axial stretch lambda(z) and, in the course of blood flow, a finite time-dependent displacement is added to this initial field, the non-linear equations governing the motion of the tube in the radial and axial directions are obtained. Utilizing the reductive perturbation technique the amplitude modulation of weakly non-linear but strongly dispersive waves is examined. The localized travelling wave solution to the evolution equation is given and the stability condition is discussed.Yayın Nonlinear wave modulation in a fluid-filled linearly tapered elastic tube(Gauthier-Villars/Editions Elsevier, 2003-08) Demiray, HilmiIn the present work, treating the arteries as a thin-walled, linearly tapered, prestressed elastic tube and using the reductive perturbation method, we have studied the amplitude modulation of nonlinear 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 nonlinear Schrodinger equation with variable coefficient. It is shown that this type of evolution equations admit a solitary wave type of solution with variable wave speeds and amplitude. It is observed that, the speed of enveloping wave increases with the scaled time parameter tau for negative tapering angle while it decreases for positive tapering. On the other hand, the speed of harmonic wave increases for positive tapering whereas it decreases for negative tapering.
