Vibration analysis of ribbed and ring-stiffened FG cylindrical shell under hydrostatic pressure

This paper proposed an energy method, based on the Donnell thin shell theory, to derive the vibration characteristic equations of underwater ribbed and ring-stiffened functionally graded (FG) cylindrical shells, and the characteristic equations are solved by MATLAB to obtain their natural frequencies. Through comparative analysis with the existing literature, the correctness and effectiveness of the calculation method are verified. By using numerical examples, the effects of the shell size, material composition, rib section length to width ratio, and rib arrangement on the natural frequency are analyzed, and it has been proved that the aforementioned parameters are the key parameters influencing natural frequency. It is found that the natural frequency of the FG cylindrical shell increases with the decrease in the length–diameter ratio of the shell, increases with the increase in the shell thickness–diameter ratio, and increases with the decrease in the rib spacing. When the cylindrical shell is short and thin, the addition of longitudinal ribs can significantly change the natural frequency of the cylindrical shell.