Abstract
An analytical model is presented to predict the influence of non-linearities associated with fluid flow on the dynamic behaviour of a structure consisting of shells and a surrounding fluid medium. The model requires the use of two linear operators to control the equilibrium of the shell and the velocity potential, a linear boundary condition of impermeability and a non-linear dynamic boundary condition. The method is based on thin shell theory and the non-rotational flow of non-viscous fluids, in combination with finite element analysis. It is applicable to non-uniform thin anisotropic cylinders subjected to different boundary conditions. The displacement functions for the wall and liquid column are derived from Sanders' equations and from the velocity field associated with the column, respectively. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration. The coupled equations are solved for the non-flow problem. For cases of fluid flow, certain analytical modifications are proposed to restore the situation to conventional modal analysis. The non-linear equations of motion are solved by the fourth-order Runge-Kutta numerical method. The frequency variations are then determined with respect to the amplitude of the motion. The trends of the non-linearities are of a softening type.
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