DYNAMIC STABILITY OF SHALLOW SHELLS SUBJECTED TO FOLLOWER FORCES

Dynamic stability of cylindrically curved shallow shells subjected to follower forces is presented. The shell analysis uses a two-field variable variational principle with the transverse displacement and Airy stress function as field variables. Starting from the variational equation of the problem, the Euler-Lagrange equations governing the problem and the boundary conditions on the transverse displacement and the Airy stress function are obtained. A finite element formulation that preserves C-1 continuity is used for the solution of the problem. Numerical results are given and the results obtained are discussed. It is shown that the use of the two-field variable variational principle permits, through static condensation, a reduction in the effort needed for the solution of the stability problem to that of a flat plate. Similarity between the response of a flexible structure to a follower force and the aerodynamic supersonic panel nutter is discussed. Practical applications of the problem are large space structures, such as solar power stations, which can undergo nutter or divergence instabilities due to their low rigidity when thrusted by follower forces.