Nonlinear waves in a prestressed thick elastic tube filled with an inviscid fluid

In this work, we study the propagation of nonlinear waves in a prestressed thick-walled elastic tube filled with an incompressible inviscid fluid. In order to include geometric dispersion in the analysis, the tube wall inertia effects are taken into account in the pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long-wave approximation is investigated. It is shown that, in contrast to thin tube theories, for thick tubes it is possible to have solitary waves in a Mooney-Rivlin material. The variation in the solitary wave speed and wave profile with inner pressure for some elastic materials are evaluated and depicted graphically. The results indicate that the solitary wave for biological material is steeper than that of the Mooney-Rivlin material. Moreover, the speed of solitary wave for biological tissues decreases with increasing inner pressure whereas for a Mooney-Rivlin material the speed gradually increases with inner pressure. This is due to difference of internal structure of the Mooney-Rivlin material and biological tissues. Copyright (C) 1996 Elsevier Science Ltd