Nonlinear vibrations of circular cylindrical shells coupled to fluid: Discretization method

The large amplitude 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 (driven and companion modes), plus an axisymmetric mode are employed. 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 by direct integration of the equations of motion.