Characteristics of group velocities of backward waves in a hollow cylinder.

It is known that modes in axially uniform waveguides exhibit backward-propagation characteristics for which group and phase velocities have opposite signs. For elastic plates, group velocities of backward Lamb waves depend only on Poisson's ratio. This paper explores ways to achieve a large group velocity of a backward mode in hollow cylinders by changing the outer to inner radius ratio, in order that such a mode with strong backward-propagation characteristics may be used in acoustic logging tools. Dispersion spectra of guided waves in hollow cylinders of varying radii are numerically simulated to explore the existence of backward modes and to choose the clearly visible backward modes with high group velocities. Analyses of group velocity characteristics show that only a small number of low order backward modes are suitable for practical use, and the radius ratio to reach the highest group velocity corresponds to the accidental degeneracy of neighboring pure transverse and compressional modes at the wavenumber k = 0. It is also shown that large group velocities of backward waves are achievable in hollow cylinders made of commonly encountered materials, which may bring cost benefits when using acoustic devices which take advantage of backward-propagation effects.