Flutter in functionally graded conical shell under follower force

Truncated conical shells are essential components of rocket booster nozzles and thrust vector control (TVC) systems for the propulsion of multi-stage launch vehicles. The TVCs assist the ascent of launch vehicles by directing the resultant thrust from the boosters, acting as a follower force that might trigger instability. Previous studies on the instability of aerospace structures have mostly focused on beams, plates, and cylindrical shells. This study analyses a truncated conical shell under a follower force of constant magnitude, considering thickness-wise gradation of material properties employed for thermal management. The governing equations are derived following Hamilton's principle, considering first-order shear deformation theory, and solved using the finite element method. Clamped and free boundaries are assumed at the small and large ends. The influence of mass and stiffness proportional damping is considered. Although strong flutter appears as the dominant instability mode, instances of erratic weak instabilities are also observed for undamped and lightly damped cases. Damping enhances stability, but its effect becomes saturated. The flutter loads are presented for varying non-dimensional parameters, characterizing the shell geometry and material properties.