Nonlinear Vibrations of Partially Fluid-Filled Cylindrical Shells

Abstract

The present work investigates the nonlinear dynamic behavior and instabilities of partially fluid-filled cylindrical shell subjected to lateral pressure. Donnell shallow shell theory is employed to model the shell. The fluid is modeled as non-viscous and incompressible and its irrotational motion is described by a velocity potential which satisfies the Laplace equation. A discrete low-dimensional model for the nonlinear vibration analysis of thin cylindrical shells is derived to study the shell vibrations. First, a general expression for the nonlinear vibration modes that satisfy all the relevant boundary, continuity and symmetry conditions is derived using a perturbation procedure validated in previous studies and then the Galerkin method is used to discretize the equations of motion. The same modal solution is used to derive the hydrodynamic pressure on the shell wall. The influence played by the height of the internal fluid on the natural frequencies, nonlinear shell response and bifurcations is examined.