Backward waves with double zero-group-velocity points in a liquid-filled pipe

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.