Propagation of weakly nonlinear waves in fluid-filled thin elastic tubes

Abstract

In the present work, we study the propagation of nonlinear waves in a prestressed thin elastic tube filled with an incompressible inviscid fluid. Considering the physiological conditions under which the arteries function, in the analysis the tube is assumed to be subjected to a uniform inner pressure P-0 and the axial stretch ratio lambda(z). In the course of blood flow, a dynamical displacement field is superimposed on this static deformation. Treating the blood as an incompressible inviscid fluid, the nonlinear equations of motion of both the tube and the fluid are obtained. Employing the reductive perturbation method, the propagation of weakly nonlinear waves in the longwave approximation is investigated and the Korteweg-de Vries equations are obtained as the governing equation. It is observed that the present formulation gives two solitary waves associated with dilatational and shear motions of the tube. The results are also discussed for some elastic materials existing in the current literature.