Consistent aeroelastic linearisation and reduced-order modelling in the dynamics of manoeuvring flexible aircraft

Abstract

This work proposes a novel reduced-order modelling approach in time domain for the coupled flight dynamics and aeroelastic response of manoeuvring very flexible aircraft. The starting point is the coupling of a displacement-based, geometrically-nonlinear flexible-body dynamics formulation with a 3-D unsteady vortex-lattice method. This is followed by a linearisation of the structural degrees of freedom, which are assumed to be small in a body- fixed reference frame. The translations and rotations of that reference frame and their time derivatives, which describe the vehicle flight dynamics, can be arbitrarily large. As a result, all couplings between the rigid and elastic motions are introduced without the a priori assumptions of the mean axes approximation, traditionally used to decouple the equations in flexible-aircraft dynamics. The resulting system can be projected onto a few vibration modes of the unconstrained aircraft with geometrically-nonlinear static deflections at a trim condition. Equally, the unsteady aerodynamics are approximated on a fixed lattice defined by the deformed static geometry. The resulting high-order aerodynamic system, which defines the mapping between the small number of generalised coordinates and unsteady aerodynamic loads, is then reduced through balanced truncation. This unified description of the flexible aircraft dynamics provides a hierarchy of aeroelastic model fidelities, which will be illustrated on a representative high-altitude, long-endurance aircraft to identify the importance of geometrically-nonlinear wing deformations on the vehicle dynamics. Application of the reduced-order modelling approach further shows a very substantial reduction in model size that leads to model orders (and computational cost) similar to those in conventional frequency-based methods but with higher modelling fidelity to compute manoeuvre loads. Closed-loop results for the Goland wing finally demonstrate the application of this approach in the synthesis of a robust flutter suppression controller.