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.