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.

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Hollow cylinders often exhibit backward propagation modes whose group and phase velocities have opposite directions, and these exhibit a minimum possible frequency at which the group velocity vanishes at a nonzero wavenumber. These zero-group-velocity (ZGV) points are associated with resonant conditions in the medium. On the basis of ZGV resonances, a non-contact and laser ultrasound technique has been developed to measure elastic constants of hollow pipes. This paper provides a theoretical and numerical investigation of the influence of the contained liquid on backward waves and associated ZGV modes, in order to explore whether this ZGV technique is suitable for in-service non-destructive evaluations of liquid-filled pipes. Dispersion spectra and excitation properties have been analyzed. It is found that the presence of the liquid causes an increased number of backward modes and ZGVs which are highly excitable by a point source. In addition, several guided modes twice undergo a change of sign in the slopes of their dispersion curves, leading to two ZGV points. This phenomenon of double ZGVs in one backward wave, which is caused by strong mode repulsions, has not been found in isotropic hollow cylinders, but it can be observed in a fluid-filled thin-walled pipe.