Wave propagation in a prestressed elastic tube filled with a viscous fluid

Abstract

For a better analysis of the effects of initial stresses on flow in elastic tubes, the propagation of harmonic waves in an initially inflated and axially stretched thick cylindrical shell is studied. Considering the initial field is static, the fluid is treated as an incompressible Newtonian fluid while the tube wall is taken to be an incompressible, isotropic, elastic material. Employing the theory of small deformation superimposed on large initial deformations, for an axially symmetric perturbed motions, the governing differential equations are obtained in the cylindrical polar coordinates. Because of the variable character of the coefficients of the resulting differential equations of the solid body, the field equations are solved by the method of truncated power series. After using the boundary conditions, the dispersion relations are obtained as a function of inner pressure, axial stretch and the thickness ratio. Various special cases, as well as the general case are discussed by numerical means.