BENDING A WAVE IN THE SCATTERING BY A CIRCULAR CYLINDRICAL-SHELL - ITS RELATION WITH THE BENDING FREE MODES

The steady-state problem of a plane acoustic wave scattered by an elas tic circular cylindrical shell is considered. The standard resonance s cattering theory (RST) procedure is used for the analysis of modal res onances. The bending waves, namely A and A(0) waves, are investigated in detail. At a fixed order of modal resonance n, it is possible to ob tain either the A wave resonance, or the A(0) wave resonance, but neve r both of them together. The relation between the modal resonances of the peripheral waves A and A(0) and the free modes of vibration of the shell is studied by means of the variation of the density rho of the ambient liquid. When the density of the ambient liquid tends toward ze ro (at unchanged sound velocity in it), the resonance frequency approa ches the one of the free vibration in two different ways. If the wave associated with the free mode has a velocity greater than the sound ve locity in the fluid, the A(0) wave resonance frequency tends to that o f the free mode. If the wave associated with the free mode has a veloc ity lower than the sound velocity in the fluid, the A wave resonance f requency tends to that of the free mode. The A wave, which was up to n ow considered as an external wave, is rather internal at a low frequen cy and becomes more external when the frequency increases.