Consistent Structural Linearization in Flexible Aircraft Dynamics with Large Rigid-Body Motion

Abstract

This paper investigates the linearization, using perturbation methods, of the structural deformations in the nonlinear flight dynamic response of aircraft with slender, flexible wings. The starting point is the coupling of a displacement-based geometrically nonlinear flexible-body dynamics formulation with a three-dimensional unsteady vortex lattice method. This is followed by a linearization 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 still be arbitrarily large. The resulting system preserves all couplings between rigid and elastic motions and 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 can be approximated on a fixed lattice defined by the deformed static geometry. Numerical studies on a representative high-altitude long-endurance aircraft are presented to illustrate the approach. The results show an improvement compared to those obtained using the mean-axes approximation.