Waves in initially stressed fluid-filled thick tubes

In this paper, treating the artery as a thick walled cylindrical shell made of an incompressible, clastic and isotropic material and the blood as an incompressible inviscid fluid, by taking the inertia of the wall into account, the propagation of harmonic waves in an initially stressed tube, filled with an inviscid fluid, is studied. Utilizing inner-pressure-inner-cross-sectional-area relation in the linear momentum equation of the fluid, together with the continuity equation, we obtained two nonlinear equations governing the axial velocity and the cross-sectional area of the tube. Assuming that the dynamical motion superposed on large initial static deformation is small, a harmonic wave type of solution to incremental equations is sought and the dispersion relation is obtained as a function of transmural pressure, axial stretch, thickness ratio and the wave number. The wave speed is evaluated numerically for various materials and thickness/radius, and the results are depicted in graphical forms. The result indicates that, due to the inertial component of pressure, the wave is dispersive. The present formulation is compared with some previously published works.