Wave propagation in a viscous fluid contained in a prestressed viscoelastic thin tube

Abstract

In this work a theoretical analysis is presented for the wave propagation in a thin walled prestressed viscoelastic tube filled with a viscous fluid. The fluid is assumed to be incompressible and Newtonian, whereas the tube material is considered to be incompressible, isotropic and viscoelastic. Considering the physiological conditions that the arteries are subjected to, such a tube may be treated to be initially stressed under the effect of inner pressure P i and the axial stretch λ z. Assuming that in the course of blood flow, a small incremental disturbance is added onto this initial field, the governing equations of this incremental motion are obtained for a fluid and viscoelastic tube. A harmonic wave type of solution is sought for these field equations and the dispersion relation is obtained. Some special cases, as well as the general case, are thoroughly discussed and the present formulation is compared with some previous works on the same subject.