Levitsky S., Bergman R., Haddad J.

Propagation of acoustic waves in thin-walled two-layered elastic tube with compressible polymeric liquid is investigated. It is assumed that the waveguide consists of two thin circular cylindrical shells with different thicknesses, made from different isotropic elastic materials. The layers of the shell are supposed to be rigidly jointed. Dynamics of the tube wall in the wave is described within Kirchhoff-Love approximation, formulated for a layered cylindrical shell. Dynamics of polymeric liquid in the tube is treated within quasi-one-dimensional approach; the liquid rheology is described by linear hereditary rheological equation. Solution of the boundary value problem for the complex amplitudes leads to dispersion equation for sound waves in the waveguide, which accounts for viscoelastic effects in the fluid in coupling with inertia and deformations of the tube's wall. This equation is valid in the low frequency range where the sound wave length is greater than the tube radius. Numerical analysis of sound dispersion in different waveguides with viscoelastic liquid (solution of high polymer in pure viscous solvent) has shown a strong influence of the liquid rheological properties and parameters of the layered shell on dispersion and attenuation of pressure signals.