Non-Linear Model for the Longitudinal Dynamics of a Hypersonic Air- breathing Vehicle

摘要

A non-linear, physics-based model of the longitudinal dynamics for an air-breathing hypersonic vehicle is developed. The model is derived from first principles and captures the complex interactions between the propulsion system, aerodynamics, and structural dynamics. Unlike conventional aircraft, hypersonic vehicles require that the propulsion system be highly integrated into the airframe. Furthermore, hypersonic aircraft tend to have very lightweight, flexible structures that have low natural frequencies. Therefore, the first bending mode of the fuselage is important as its deflection affects the amount of airflow entering the engine, thus influencing the performance of the propulsion system. The equations of motion for the flexible aircraft are derived using Lagrange's Equations. The equations-of-motion capture inertial coupling effects between the pitch and normal accelerations of the aircraft and the structural dynamics. The linearized aircraft dynamics are shown to be unstable, and in most cases, exhibit non-minimum, phase behavior. The linearized model also indicates that there is an aeroelastic mode that has a natural frequency more than twice the frequency of the fuselage bending mode. Furthermore, the short-period mode is very strongly coupled with the bending mode of the fuselage.