Influence of the curvature on the dispersion curves of a submerged cylindrical shell

Abstract

The free vibration of a thin-walled fluid-loaded cylindrical shell is discussed. The Timoshenko–Mindlin-type theory of thin plates and shells that includes the effects of shear deformation and rotatory inertia is used to describe the motion of the structure. A classical approach of the Watson transformation applied to the normal mode solution makes it possible to solve the problem in a series of different circumferential waves. The coordinates of the poles in a complex wave number plane provide the phase velocities and attenuation of different wave field components, and the study of the corresponding dispersion curves helps to classify the circumferential waves. However, it is not always straightforward to associate propagation types in a fluid-loaded shell with those of a ‘‘dry’’ shell, since additional roots appear. In the case of a fluid-loaded aluminum shell, the phase velocity curve that asymptotically approaches the Rayleigh wave velocity for the elastic half-space at high frequencies, is attributed to the A0 Lamb-type wave in a submerged shell. This wave is considerably influenced by the curvature of the structure surface at low frequencies where strong interaction with the Franz waves takes place. As a result of this interaction, the A0 wave characteristics become very close to those of the Franz family waves. The position of the A0 wave dispersion curve between the Franz curves depends on the radius of curvature of the shell.