Dynamic Instability of Rocket-Propelled Flying Bodies

This paper deals with dynamic instability of slender rocket-propelled flying bodies, such as launch vehicle and advances missiles subjected to aerodynamic loads and an end rocket thrust. A flying body is simplified into a uniform free-free beam subjected to an end follower thrust. Two types of aerodynamic loads are assumed in the stability analysis. Firstly, it is assumed that two concentrated aerodynamic loads act on the flying body at its nose and tail. Secondly, to take account of effect of unsteady flow due to motion of a flexible flying body, aerodynamic load is estimated by the slender body approximation. Extended Hamilton's principle is applied to the considered beam for deriving the equation of motion. Application of FEM yields standardeigen-value problem. Dynamic stability of the beam is determined by the sign of the real part of the complex eigen-values. If aerodynamic loads are concentrated loads that act on the flying body at its nose and tail, the flutter thrust decreases by about 10% in comparison with the flutter thrust of free-free beam subjected only to an end follower thrust. If aerodynamic loads are distributed along the longitudinal axis of the flying body, the flutter thrust decreases by about 70% in comparison with the flutter thrust of free-free beam under an end follower thrust. It is found that the flutter thrust is reduced considerably if the aerodynamic loads are taken into account in addition to an end rocket thrust in the stability analysis of slender rocket-propelled flying bodies.