Wave Propagation in a Viscous Incompressible Fluid Contained in Flexible Viscoelastic Tubes

Abstract

The dispersion attenuation of waves in viscoelastic tubes filled with a viscous incompressible fluid are analyzed, with special attention to two cases: where the constitutive relation of the wall is that (1) of a Voigt material, and (2) of a standard linear solid. Explicit expressions show the dependence of the phase-velocity and damping factor on the various parameters characterizing the fluid and the viscoelastic tube. In comparison with elastic tubes, viscoelastic tubes have a higher phase velocity and attenuation coefficient. Also, as the ratio of the relaxation time of the viscoelastic material to the period of the oscillation increases, there is a marked difference between the behavior of the waves for the two types of materials considered. The frequency equation for a stretched elastic tube is also derived. The analysis is restricted to waves whose amplitude is infinitesimal with the wavelength large and the wall thickness small as compared with the radius of the tube.