The Effect of a Residual Stress on Wave Propagation in a Fluid-Filled Thick Elastic Tube

Abstract

The propagation of harmonic waves in an elastic tubes filled fluid is presented in this study. The tube material is considered to be incompressible, homogeneous, isotropic, initially axially stretched, inflated and thick elastic like human arteries. The viscous fluid is assumed to be incompressible and Newtonian. The differential equations of both materials are obtained in cylindrical coordinates. The analytical solutions of the equations of motion for the fluid, numerical solutions of the equations of motion for the tube have been found. The residual circumferential strain in the unloaded state of artery causes opening angle. The dispersion relation is presented as a function of the axial stretch, opening angle, internal pressure and material parameters. The effects of these parameters are shown and discussed on graphics.