The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell's nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using four degrees of freedom. The effect of internal dense fluid is studied. The solution is obtained by the Method of Normal Forms. Comparison of a three and a four degree-of-freedom model is performed. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated; specific Normal Forms are developed for this study.
Low-dimensional model for nonlinear vibrations of circular cylindrical shells / Amabili, Marco; Pellicano, Francesco. - 2:(1999), pp. 1217-1222. (Intervento presentato al convegno Proceedings of the 1999 17th International Modal Analysis Conference, IMAC. Part 1 (of 2) tenutosi a Kissimmee, FL, USA, nel 1999).
Low-dimensional model for nonlinear vibrations of circular cylindrical shells
Amabili Marco;Pellicano Francesco
1999
Abstract
The response-frequency relationship in the vicinity of a resonant frequency, the occurrence of travelling wave response and the presence of internal resonances are investigated for simply supported, circular cylindrical shells. Donnell's nonlinear shallow-shell theory is used. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using four degrees of freedom. The effect of internal dense fluid is studied. The solution is obtained by the Method of Normal Forms. Comparison of a three and a four degree-of-freedom model is performed. A water-filled shell presenting the phenomenon of 1:1:1:2 internal resonances is investigated; specific Normal Forms are developed for this study.
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