Flight dynamics of aeroelastic vehicles

TLDR

The study develops nonlinear equations of motion for an elastic airplane from first principles. Using Lagrange’s equation, the Principle of Virtual Work, and aerodynamic strip theory, the authors derive closed‑form equations, minimize inertial coupling via body‑reference axes, and apply the model to a generic elastic aircraft to parametric study flexibility. Closed‑form analytic expressions reveal how parameter variations affect aerodynamics, and show that residualizing elastic modes improves models only up to moderate flexibility, beyond which even modal residualization yields poor predictions.

Abstract

The nonlinear equations of motion for an elastic airplane are developed from first principles. Lagrange's equation and the Principle of Virtual Work are used to generate the equations of motion, and aerodynamic strip theory is then employed to obtain closed-form integral expressions for the generalized forces. The inertial coupling is minimized by appropriate choice of the body-reference axes and by making use of free vibration modes of the body. The mean axes conditions are discussed, a form that is useful for direct application is developed, and the rigid-body degrees of freedom governed by these equations are defined relative to this body-reference axis. In addition, particular attention is paid to the simplifying assumptions used during the development of the equations of motion. Since closed-form, analytic expressions are obtained for the generalized aerodynamic forces, insight can be gained into the effects of parameter variations that is not easily obtained from numerical models. An example is also presented in which the modeling method is applied to a generic elastic aircraft, and the model is used to parametrically address the effects of flexibility. The importance of residualizing elastic modes in forming an equivalent rigid model is illustrated, but as vehicle flexibility is increased, even modal residualization is shown to yield a poor model.