Solitary Waves in a Prestressed Thick Elastic Tube Containing an Inviscid Fluid

Abstract

AbstractIn the present work, employing the nonlinear equations of an incompressible, isotropic, and elastic body and the exact equations of an incompressible inviscid fluid, the propagation of weakly nonlinear waves in an elastic thick tube filled with an inviscid fluid is studied. The tube is initially assumed to be subjected to a large inner pressure P0 and the axial stretch λz, and, in the course of blood flow a large time dependent radial displacement is superimposed on this static field. The nonlinear equation governing the radial motion of the tube is obtained. Utilizing a reductive perturbation technique, the propagation of weakly nonlinear waves is studied and the KdV equation is obtained as the evolution equation. Due to the dependence of the coefficients of the nonlinear evolution equation on initial deformation and the geometrical characteristics it is shown that the solution profile changes with initial deformation and the thickness ratio.