DYNAMIC STABILITY OF A COMPLETELY FREE CIRCULAR CYLINDRICAL SHELL SUBJECTED TO A FOLLOWER FORCE

The dynamic stability of a completely free isotropic circular cylindrical shell under a follower force is investigated. First order shear deformation is included and the axial stress is assumed to be uniformly distributed through the thickness. A finite element model of the shell is formulated using a ring element in the circumferential direction and a Lagrangian element in the longitudinal direction. The dynamic stability is studied for various dimensionless lengths and thicknesses. The numerical results for the shells are compared with those of a beam model having equivalent dimensions. The analysis shows that the Rayleigh mode and the Love mode have an effect on instability and that the shell structure can be analyzed with a beam model within only a certain range of shell dimensions.