Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid

The nonlinear free and forced vibrations of a simply supported, circular cy lindrical shell in contact with an incompressible and inviscid, quiescent a nd dense fluid are investigated. Donnell's shallow-shell theory is used, so that moderately large vibrations are analysed. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied, while axial constraint is satisfied on the average. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using three degrees o f freedom; in particular, two asymmetric modes (driven and companion modes) , plus an axisymmetric mode are employed. The time dependence of each term of the expansion is general and the axisymmetric mode is obtained from a se ries involving all axisymmetric linear modes. Different tangential constrai nts can be imposed at the shell ends. Effects of both internal and external dense fluid are studied. Internally, the shell is considered completely fi lled, while externally, an unbounded fluid domain is considered around the shell in the radial direction. The solution is obtained both numerically an d by the Method of Normal Forms. Numerical results are obtained for both fr ee and forced vibrations of empty and water-filled shells. (C) 1998 Academi c Press.