Pulse waves in a prestressed elastic tube

Abstract

For a better understanding of the effects of initial stresses on flow in elastic tubes, the propagation of time harmonic waves in an initially inflated and axially stretched thick cylindrical shell is studied. To simplify the mathematical analysis, the fluid is assumed to be inviscid and incompressible while the tube wall is taken to be an incompressible elastic material. Utilizing the theory of small deformations superimposed on large initial deformations, for an axially symmetric perturbed motion the governing differential equations are obtained in cylindrical polar coordinates. Due to variability of the coefficients of the resulting differential equations of solid body, the field equations are solved by a truncated power series method. After employing the boundary conditions the dispersion relations are obtained as a function of inner pressure, axial stretch and thickness ratio.