Coupled Flight-Dynamic and Low-Order Aeroelastic Model for a Slender Launch Vehicle

Abstract

This paper presents a method to develop a low-order aeroelastic model that qualitatively captures some of the phenomena experienced by launch vehicles, suitable for use in preliminary controller design. Equations of motion for the two-dimensional dynamics are derived by treating the vehicle as a beam with a gimbaled nozzle attached at the aft end. The flexible-body dynamics are kinematically described using a modal representation. An aerodynamic model focuses on flow separations at diameter transitions in the transonic regime that can lead to lengthwise variations in the applied aerodynamic force. Additionally, convective effects are modeled that lead to time lag in the aerodynamic forces. The equations of motion are tenth order when neglecting convective effects and twelfth order when including convective effects. The model demonstrates some of the possible coupling that occurs between rigid-body, flexible-body, and aerodynamic states. For representative parameter values, the aeroelastic coupling can destabilize the flexible-body motion. The resulting linearized model is not fully controllable, however, is stabilizable.