Low-Frequency Sound Propagation in a Cylindrical Gap, Filled with a Polymeric Solution

A model of low-frequency sound propagation in a cylindrical gap between two thin coaxial elastic shells is developed. The gap is filled with a polymeric solution, treated as a compressible hereditary liquid, following an integral constitutive equation. The shells are pure elastic, made from different isotropic materials and have different widths. The dissipation in the sound wave is accounted for by a "hydraulic" approximation, based on calculation of shear stresses, emerging in the flow, from the solution of a dynamic problem for incompressible liquid in the same gap, but with rigid boundaries. Dynamics of shells is described within the Kirchhoff-Love approximation. Analytical solution of the formulated boundary value problem leads to a dispersion equation, which is studied numerically. Its analysis has shown that geometrical parameters of the waveguide and material properties of both viscoelastic liquid and elastic shells highly influence sound dispersion and attenuation in the low frequency range. It indicates, in particular, that the waveguide studied can be used as a basis for characterization of the liquids rheology by acoustic means.