A study on free vibration of a ring-stiffened thin circular cylindrical shell with arbitrary boundary conditions
The vibration of ring-stiffened cylinders associated with arbitrary boundary conditions is investigated. Displacements of cylinders can be easily described by trigonometric functions when the cylinders are shear diaphragms supported at both ends. As to other boundary conditions, exponential functions are used and axial factors are introduced. An eighth-order algebraic equation for this axial factor is derived. The physical meaning of the axial factor is studied. Both analytical and numerical studies prove that, when the axial factor is a pure imaginary number, the cylinder appears to have a certain length with shear diaphragm boundary conditions. The effects of shell parameters and hydrostatic pressure on the axial factor are determined in the analysis.
Abstract Degenerate Rayleigh-Schrodinger perturbation theory is treated by expansions in unperturbed eigenfunctions. The results of seventh order perturbation are presented for the cases in which the degeneracy can be totally removed in the first and second orders.