Solitary waves in a thick walled elastic tube

Abstract

In the present work, we studied the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. The efects of wall inertia and shear deformation are taken into account in determining the inner pressure–inner cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long wave approximation is investigated and the Korteweg–de Vries equation is obtained as the evolution equation. Due to dependence of the coefficients of the governing Korteweg–de Vries equation on the initial deformation, the material parameters and the thickness ratio, it is observed that the solution profile changes with these parameters. The numerical calculations indicate that for engineering materials (small α) the wave profile gets steepened with increasing thickness ratio, whereas for soft biological tissues the wave profile is not so sensitive to the thickness ratio but it is quite sensitive to the material nonlinearity characterized by the coefficient α. This shows that for biological tissues the material nonlinearity is more important than the geometrical nonlinearity.