Dynamic stability of free-free beam subjected to end rocket thrust and carrying a heavy payload at its nose

The present paper deals with the dynamic stability of a flexible flight body accommodated with a heavy payload at its nose and subjected to end rocket thrust. The thrust acts on the flexible flight body as a follower load, thus the flight body may lose its stability by body-divergence or body-flutter. The intended aim of the paper is to reveal the effect of heavy payload on dynamic stability of slender flight bodies under rocket thrust. It is assumed that a payload is a rigid body, but not a mass point. The slender flight body is simplified into a uniform free-free beam having a spherical rigid body at its nose. A large rigid body at the nose of the beam applies a lumped inertia force on the nose, in addition to a distributed inertia force along the axis of the beam. Extended Hamilton's principle is applied to the considered beam for driving the equations of motion. Application of finite element method yields a standard eigen-values. It is shown that a large rigid body at the tip lowers the flutter bound considerably, As extreme cases, the free-free beam having no payload can be simplified into Feodosiev's beam, while the beam having an infinitely large rigid sphere leads to Beck's column. Thus the proposed beam can be the missing link between Feodosiev's beam and Beck's column.