Dispersion of Axially Symmetric Waves in Cylindrical Shells, immersed in an Acoustic Medium

This paper is devoted to the theoretical study of the dispersion of axially symmetric waves in circular cylindrical shells, immersed in an acoustic medium. The special emphasis has been laid on the investigations of the complex branches of the dispersion spectra particularly because the corresponding dispersion equation provides only one real branch for phase velocities lower than the velocity of sound in the surrounding acoustic medium and no real branch for phase velocities higher than the velocity of sound. Although the lowest branch of the dispersion spectrum is almost unaffected by the presence of the surrounding medium some of the higher branches are affected to a considerable extent. These effects can be, particularly, observed near the cut-off frequencies and also at the frequency minima and maxima of the real and imaginary branches of the corresponding dispersion spectra for a solid cylinder or a shell in the absence of the surrounding fluid. The dispersion curves have been obtained for shells of different wall thicknesses with the solid cylinder as a particular case of the shell. The effect of the surrounding medium on the dispersion spectra is found to increase with the decrease in the wall thickness of the shell.