Abstract
The dynamic stability of a completely free isotropic circular cylindrical shell under a follower force is investigated. The first-order shear deformation and rotary inertia are included in the kinetic energy and the strain energy. A finite element model of the shell is formulated using the trigonometric ring element in the circumferential direction and the Lagrangian element in the longitudinal direction. Using the eigenvalue curves and the method of multiple scales, the dynamic stability is studied for the case of the follower force with a pulsating part as well as the constant follower force. The effect of the thickness ratio and the length ratio is presented in both cases. The numerical results for the shells are compared with those of a beam model having equivalent dimensions. The numerical results show that the shell under a constant follower force behaves like a beam in a certain range. The analysis of the shell under a pulsating follower force shows that the beamlike modes of the shell have larger unstable regions than the other modes. However, for the case of a pulsating load, the modes of higher circumferential wave number are of importance in that the combination resonance of difference type takes place frequently.
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