NONLINEAR VIBRATIONS OF SIMPLY SUPPORTED, CIRCULAR CYLINDRICAL SHELLS, COUPLED TO QUIESCENT FLUID

Abstract

The nonlinear free and forced vibrations of a simply supported, circular cylindrical shell in contact with an incompressible and inviscid, quiescent and 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 of freedom; in particular, two asymmetric modes (drivenandcompanionmodes), 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 series involving all axisymmetric linear modes. Different tangential constraints can be imposed at the shell ends. Effects of both internal and external dense fluid are studied. Internally, the shell is considered completely filled, while externally, an unbounded fluid domain is considered around the shell in the radial direction. The solution is obtained both numerically and by theMethod of Normal Forms. Numerical results are obtained for both free and forced vibrations of empty and water-filled shells.