Sound waves dynamics in a tube with elastic walls filled with bubbly liquid

The paper offers a theoretical model describing the dynamics of acoustic waves in two-phase fluid placed in a tube with elastic walls. Radial inertia of the tube walls was considered.
Stop band for the dynamics of acoustic waves in two-phase liquid placed in a tube with elastic walls having radial inertia was found. Phase velocity value in the low-frequency region is less than the phase velocity value for acoustic waves in a bubbly liquid in a tube with rigid walls. The values of frozen velocities in both cases are the same.
In a low-frequency region the value of the phase velocity of acoustic waves in a bubbly liquid in a tube with elastic walls with non-radial inertia is lower. The damping coefficient is almost the same as the one for acoustic waves in a bubbly liquid in a tube with rigid walls. In a high-frequency region phase velocity and damping coefficient of acoustic waves in a tube with elastic walls without radial inertia is much lower than the ones for acoustic waves in a bubbly liquid in a tube with rigid walls.