Sound dispersion in a deformable tube with polymeric liquid and elastic central rod

Sound waves in deformable tubes containing a compressible polymeric liquid are investigated. The central part of the tube is occupied by a coaxial elastic rod. A dispersion equation is derived for this system which accounts for viscoelastic effects in the fluid and elastic deformations of the tube and the rod. The equation is valid in the low frequency range where the sound wavelength is greater than the tube radius. Its analysis has shown that rheological properties of the liquid essentially influence the speed and attenuation of sound in the waveguide. This influence depends on the gap width and elastic properties of both the tube wall and the internal rod.