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

The nonlinear free and forced vibrations of a simply supported, circular cylindrical shell incontact with an incompressible and inviscid, quiescent and dense ßuid are investigated.DonnellÕs shallow-shell theory is used, so that moderately large vibrations are analysed. Theboundary conditions on radial displacement and the continuity of circumferential displacementare exactly satisÞed, while axial constraint is satisÞed on the average. The problem is reduced toa system of ordinary di¤erential equations by means of the Galerkin method. The mode shape isexpanded by using three degrees of freedom; in particular, two asymmetric modes (driven andcompanion modes), plus an axisymmetric mode are employed. The time dependence of eachterm of the expansion is general and the axisymmetric mode is obtained from a series involvingall axisymmetric linear modes. Di¤erent tangential constraints can be imposed at the shell ends.E¤ects of both internal and external dense ßuid are studied. Internally, the shell is consideredcompletely Þlled, while externally, an unbounded ßuid domain is considered around the shell inthe radial direction. The solution is obtained both numerically and by the Method of NormalForms. Numerical results are obtained for both free and forced vibrations of empty andwater-Þlled shells.