Propagation of weakly nonlinear waves in fluid-filled thick viscoelastic tubes

摘要

In the present work, we studied the propagation of small-but-finite-amplitude waves in a prestressed thick walled viscoelastic tube filled with an incompressible inviscid fluid. In order to include he dispersion, the wall's inertial and shear effects are taken into account in determining the inner pressure-inner cross-sectional area relation. Using the reductive perturbation method, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. After obtaining the general evolution equation in he long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-known evolution equations such as the Burgers, Cortege-devise (KdV), Koteweg-de Vries-Burgers (KdVB) and the generalized Rurgers' equations. By proper re-scaling of the perturbation parameter, the modified form of he evolution equations is also obtained. The variations of the travelling wave profile with initial deformation and he viscosity coefficients are numerically evaluated and the results are illustrated in some figures.