TY - JOUR
T1 - Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube
AU - Demiray, Hilmi
AU - Antar, Nalan
PY - 1997/3
Y1 - 1997/3
N2 - 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 P0 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.
AB - 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 P0 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.
KW - Inviscid fluid
KW - Solitary waves
KW - Viscoelasticity
UR - http://www.scopus.com/inward/record.url?scp=0031522540&partnerID=8YFLogxK
U2 - 10.1007/s000330050034
DO - 10.1007/s000330050034
M3 - Article
AN - SCOPUS:0031522540
SN - 0044-2275
VL - 48
SP - 325
EP - 340
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
IS - 2
ER -