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Yayın Interactions of nonlinear acoustic waves in a fluid-filled elastic tube(Pergamon-Elsevier Science, 2001-03) Akgün, Güler; Demiray, HilmiIn the present work, the nonlinear interactions of two acoustical waves propagating in a fluid-filled elastic tube with different wave numbers, frequencies and group velocities are examined. Employing the multiple-scale expansion method, expanding the field quantities into asymptotic series of the smallness parameter and solving the resulting differential equations of various orders of the same parameter, we obtained two coupled nonlinear Schrodinger equations. The nonlinear plane wave solutions to these equations are also given for some special cases.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.
