Bubbles effect on sound dispersion in thin-walled tube with polymeric liquid and elastic central rod

The present study is devoted to the investigation of fine air bubbles effect on sound propagation in thin-walled elastic tube with compressible polymeric liquid and cylindrical elastic rod in the central part of the tube. The problem formulation and solution method follow the previous paper of the authors (S.P. Levitsky, R.M. Bergman, J. Haddad, Sound dispersion in deformable tube with polymeric liquid and elastic central rod, Journal of Sound and Vibration 275 (1–2) (2004) 267–281). In order to account for the bubblesʹ influence on sound dispersion and attenuation, dynamic equation of state of the mixture, formulated within homogeneous approximation, is used. It is assumed that the volume gas concentration is small. The resulting dispersion equation for the waveguide with viscoelastic liquid–gas mixture is studied in a long-wave range. Results of simulations illustrate the influence of free gas concentration, bubble radius and rheological properties of the liquid on sound dispersion and attenuation in the system.