Effect of Follower Forces on Aeroelastic Stability of Flexible Structures
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Missile bodies and wings are typical examples of structures that can be represented by beam models. Such structures, loaded by follower forces along with aerodynamics, exhibit the vehicle's aeroelastic instabilities. The current research integrates a nonlinear beam dynamics and unsteady aerodynamics to conduct aeroelastic studies of missile bodies and wings subjected to follower forces. The structural formulations are based on a geometrically-exact, mixed finite element method. Slender-body theory and thin-airfoil theory are used for the missile aerodynamics, and two-dimensional finite-state unsteady aerodynamics is used for wing aerodynamics. The aeroelastic analyses are performed using time-marching scheme for the missile body stability, and eigenvalue analysis for the wing flutter, respectively. Results from the time-marching formulation agree with published results for dynamic stability and show the development of limit cycle oscillations for disturbed flight near and above the critical thrust. Parametric studies of the aeroelastic behavior of specific flexible missile configurations are presented, including effects of flexibility on stability, limit-cycle amplitudes, and missile loads. The results do yield a significant interaction between the thrust, which is a follower force, and the aeroelastic stability. Parametric studies based on the eigenvalue analysis for the wing flutter, show that the predicted stability boundaries are very sensitive to the ratio of bending stiffness to torsional stiffness. The effect of thrust can be either stabilizing or destabilizing, depending on the value of this parameter. An assessment whether or not the magnitude of thrust needed to influence the flutter speed is practical is made for one configuration. The flutter speed is shown to change by 11% for this specific wing configuration.