Non-uniqueness in cylindrical shells optimization

When a uniform shell is segmented longitudinally along its axis, the thickness optimization of the segment thicknesses will yield in a segmented shell with varying thickness segments. In this paper, the non-uniqueness in optimum design of cylindrical shells for vibration requirements is presented, and its implications are discussed. Related issues such as the new mode sequence, mode crossing, repeated natural frequencies and stationary modes are also discussed. The numerical results were compared with those obtained analytically. The analytical expressions for the equations of motion for segmented circular cylindrical shells are derived using Donnell-Mushtari. The eigenvalue problem of the analytical solution is then solved using a MATLAB program script to predict the natural frequencies and strain energy distribution for the various mode shapes in the modal spectrum.