Vibration and stability of ring-stiffened thin-walled cylindrical shells conveying fluid

Based on the Flügge shell theory, equations of motion of ring-stiffened thin-walled cylindrical shells conveying fluid are developed with the aid of the Hamiltonʹs principle. Analysis is carried out on the vibration and stability of the ring-stiffened shells conveying fluid, and the effects of fluid velocity, the Young modulus, the size, and the number of the ring stiffeners on the natural frequency and the instability characteristics are examined. It is found that stiffeners can reduce the number of circumferential waves for the fundamental mode, and increase the shellʹs natural frequency, and thus the critical fluid velocity. For the number of longitudinal half waves being equal to one, the natural frequency and the corresponding critical fluid velocity are the largest for the internal-ring stiffened shell and are the smallest for the symmetrical-ring stiffened shell. The natural frequencies and the corresponding critical fluid velocity predicted by the established model increase with the increase in the Young modulus, the size, or the number of the stiffeners.