Internal resonances and travelling waves in a submerged structure

In the present paper the dynamic behaviour of a circular cylindrical shell submerged in a heavy quiescent fluid is studied with particular attention to realistic boundary conditions and to the modal interactions between resonant modes. Donnell's shallow shell theory is used, therefore the study is limited to moderately large amplitudes of vibration (the more realistic conditions). The Galerkin procedure is employed to perform the spatial discretization of the problem, and suitable assumed modes are used in order to capture the main phenomena present in the problem and to enhance the assumed mode shapes proposed in the literature. The resulting set of ordinary differential is studied using an efficient perturbation technique, the Method of Normal Forms. The use of perturbation methods is justified by the upper limits in the amplitude of vibration required by the Donnell shallow shell theory. The method is developed for systems having an arbitrary number of degrees of freedom. The numerical results are compared with experimental and analytical results available in the literature to test the expansion used in the paper. Moreover, new results concerning the combined effect of fluid structure interaction and nonlinearity are presented.