Solitary waves in prestressed elastic tubes

Demı́ray, Hilmi

doi:10.1007/bf02459491

Cited by 82 publications

(30 citation statements)

References 18 publications

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“…In general, it is quite difficult to study a nonlinear problem by use of the constitutive relation given in (13). Assuming that the memory of the material under consideration is short, the viscoelastic coefficients λ ν (t * ) and µ ν (t * ) may be approximated as…”

Section: Nonlinear Waves In An Inviscid Fluid 329mentioning

confidence: 99%

“…The propagation of finite amplitude waves in fluid-filled elastic or viscoelastic tubes has been examined, for instance, by Rudinger [6], Anliker et al [7] and Moodie and Swaters [8], by using the method of characteristics, in studying the shock formation. On the other hand, the propagation of small-but-finite amplitude waves 326 H. Demiray and N. Antar ZAMP in distensible tubes has been investigated by Johnson [9], Hashizume [10], Yomosa [11], Erbay et al [12] and Demiray [13] by employing various asymptotic methods.…”

Section: Introductionmentioning

confidence: 99%

“…Erbay et al [12] examined the propagation of weakly nonlinear waves in a fluid filled viscoelastic thin tube and obtained the governing equations as KdV, Burgers and KdVB, depending on the order of certain parameters. Demiray [13] studied the propagation of weakly nonlinear waves in a thin elastic tube filled with an incompressible inviscid fluid and obtained the KdV equation as the governing equation.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube

Demı́ray

Antar

1997

Z. angew. Math. Phys.

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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 propagation of weakly nonlinear waves in the long-wave approximation is studied. After obtaining the general equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-know nonlinear evolution equations. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained.Mathematics Subject Classification (1991). 76B25, 73D35, 73G25.

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Section: Nonlinear Waves In An Inviscid Fluid 329mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube

Demı́ray

Antar

1997

Z. angew. Math. Phys.

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“…The first assumption, that the tube can be modeled as a thin-walled membrane, is well established and has been used in studies by [1][2][3][4], and [5]. The second assumption, that the fluid in the tube is inviscid and can be considered in an averaged sense (i.e.…”

Section: Introductionmentioning

confidence: 99%

The validity of the long-wave approximation for solitary waves in fluid-filled elastic tubes

Johnston

Epstein

2010

Z. Angew. Math. Phys.

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Studies of solitary waves commonly apply the long-wave approximation, which unnecessarily rigidifies the behavior of the tube, but permits the problem to be solved using certain approximate numerical techniques. In this study, an approach was developed where approximating the contribution of the axial strain as a linear function of the radial strain reduced the system of exact governing differential equations to a single equation of a single dependent variable. The approximated solution was found to agree with the exact solution to within 3%. This approach would be useful for considering more complex problems where the exact solution technique may not be reasonably applied. (2000). Primary 74J35; Secondary 76Z05. Mathematics Subject Classification

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“…The propagation of small-but-finite amplitude waves in distensible tubes has been investigated by Johnson [9], Hashizume [10], Yomosa [11], Erbay et al [12] and Demiray [13] by employing various asymptotic methods. In [12] and [13], they took the inertia effect of the tube wall but used the uniform inner pressure-area relation, which is valid for a the cross-sectional area independent of the axial coordinate. However, in substituting this pressure-area relation into the fluid equations they artificially introduced the dependence of inner area on the axial coordinate z.…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation of nonlinear waves in a thick elastic tube filled with an inviscid fluid

Demı́ray¹

1999

Z. angew. Math. Phys.

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In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thick tube and the approximate equations of an incompressible inviscid fluid, and then utilizing the reductive perturbation technique the amplitude modulation of weakly nonlinear waves is examined. It is shown that the amplitude modulation of these waves is governed by a nonlinear Schrödinger(NLS) equation. The range of modulational instability of the monochromatic wave solution with the initial deformation, material and geometrical characteristics is discussed for some elastic materials.Mathematics Subject Classification (1991). 76B25, 73D35, 73G05.

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Solitary waves in prestressed elastic tubes

Cited by 82 publications

References 18 publications

Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube

Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube

The validity of the long-wave approximation for solitary waves in fluid-filled elastic tubes

Amplitude modulation of nonlinear waves in a thick elastic tube filled with an inviscid fluid

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