Dynamic stability of a stiff-edged cylindrical shell subjected to a follower force

In this paper, the dynamic stability of a completely free cylindrical shell under a follower force is analyzed. Both edges of the shell are assumed to have rings to increase the rigidity of the structure. Hamiltonʹs principle is used to derive the equations of motion, and the finite element method is applied to investigate the dynamic stability of the shell. Numerical analysis is performed for each circumferential wave number by using the orthogonality of the vibration modes of the shell. The kinetic or static analysis is carried out according to whether the circumferential wave number is equal to one or not. Numerical results show that the stiffening ring stabilizes the circumferential higher modes. On the other hand, it is found that the ring may destabilize the beam-like mode.