Free Vibration Characteristics of a Finite Ring-Stiffened Elliptic Cylindrical Shell

A theoretical method is employed to study the free vibration characteristics of a finite ring-stiffened elliptic cylindrical shell. Vibration equations of the elliptic cylindrical shell are derived based on Flugge shell theory, and the effects of the ring stiffeners are evaluated via "smeared" stiffener theory whereby the properties of the stiffeners are averaged over the shell surface. The displacements of the shell are expanded in double Fourier series in the axial and circumferential directions, and the circumferential curvature is expanded in single Fourier series in the circumferential direction. The partial differential characteristic equations with variable coefficients are converted into a set of linear equations with constant coefficients which couple with each other about the circumferential modal parameters. Then, the natural frequencies of the finite ring-stiffened cylindrical shell are obtained. To verify the accuracy of the present method, the finite ring-stiffened elliptic cylindrical shell is degenerated into two models: one of which is a ring-stiffened circular cylindrical shell and the other of which is an elliptic cylindrical shell without ring stiffeners. The present results of the two degenerated shells show good agreements with available results from the literature. The effects of main parameters, including the ellipticity, the shell length ratio, the stiffener's interval, the stiffener's depth, and the stiffener's eccentricity, on the free vibration of the ring-stiffened elliptic cylindrical shell are examined in detail. The ellipticity makes the difference between the symmetric and anti-symmetric modal frequencies of the shell. The stiffeners have a greater influence on the free vibration at relatively higher order circumferential modal parameters. The circumferential modal parameters corresponding to the fundamental frequency are affected by the ellipticity, shell length, stiffeners' interval, and depth. The eccentricity of the ring stiffeners has a weak effect on the vibration of the structure.