Effect of an interior viscous fluid on the propagation of torsional waves in an elastic pipe

Abstract

The paper theoretically deals with the effects of the interior viscous fluid on the speed and attenuation of torsional waves propagating in an elastic pipe. Expressions for the phase speed and attenuation are obtained as functions of the viscosity and mass density of the adjacent fluid by exact and asymptotic analyses. Exact solutions with transcendental equations lead to an implicit relationship between the quantities of interest. In order to relate explicitly the parameters with physical meaning, asymptotic solutions are derived by the perturbation method. The approximate solutions are in good agreement with the exact solutions for a wide range of parameter values. The results provide quantitative information of the reduction of phase speed and the increase of attenuation affected by the fluid viscosity.