1997 **Abstract:** In the present work, we examine the propagation of weakly nonlinear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid. Considering that the arteries are initially subjected to a large static transmural pressure P 0 and an axial stretch λz and, in the course of blood flow, a finite time dependent displacement is added to this initial field, the nonlinear equation governing the motion in the radial direction is obtained. Using the reductive perturbation technique, the pro…

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“…In order to have a differential relation for U in terms of τ n (n > 1), one has to consider the higher order expansion. As a special case of this derivation, if we set τ 1 = τ, g 1 = g in equation (36) and neglect the dependence of U on τ n (n > 1), the resulting evolution equation will be exactly the same with that of obtained by Demiray and Antar [16] (equation (47)). Thus, the classical reductive perturbation method may be considered as a special case of the present method.…”

confidence: 78%

“…In order to have a differential relation for U in terms of τ n (n > 1), one has to consider the higher order expansion. As a special case of this derivation, if we set τ 1 = τ, g 1 = g in equation (36) and neglect the dependence of U on τ n (n > 1), the resulting evolution equation will be exactly the same with that of obtained by Demiray and Antar [16] (equation (47)). Thus, the classical reductive perturbation method may be considered as a special case of the present method.…”

confidence: 78%

“…Thus, the classical reductive perturbation method may be considered as a special case of the present method. Moreover, as pointed out in [16], since the coefficient of (U∂U/∂ξ) is a function of the initial deformation, it may vanish for a set of initial stretches. In this case the evolution equation degenerates into the linear equation and by changing the scaling parameter, the resulting governing equation reduces to the modified evolution equation.…”

confidence: 93%

“…Here we note that the coefficients β 1 , β 2 , β 5 , β 6 , β 7 , β 11 , β 13 , β 15 and β 16 depend on the elastic coefficients, β 4 , β 9 , β 10 , β 12 , β 17 −β 19 characterize the viscoelastic effects and β 3 , β 8 and β 14 are related to the inertial effects. The explicit expressions of these coefficients are given in reference [19].…”

confidence: 89%

“…On the other hand, the propagation of small-but-finite amplitude waves in distensible tubes has been investigated by Johnson [10], Hashizume [11], Yomosa [12] and Demiray [13,14] by employing various asymptotic methods. In all these works [10 -14], depending on the balance between the non-0932-0784 / 06 / 1200-0641 $ 06.00 c 2006 Verlag der Zeitschrift für Naturforschung, Tübingen · http://znaturforsch.com linearity, dispersion and dissipation, the Korteweg-de Vries (KdV), Burgers' or KdV-Burgers' equations are obtained as the evolution equations.…”

confidence: 99%