Unsteady Aeroelasticity of Generic Transport Model

Abstract

This paper is devoted to unsteady aeroelastic modeling and analysis of the Generic Transport Model (GTM), which is a notional twin-engine transport aircraft introduced by the NASA Langley Research Center. The aircraft is treated as an unstrained, flexible multibody system subject to unsteady aerodynamics. The bodies are fuselage, wing, and horizontal and vertical stabilizers, whose structures are modeled as hollow beams with constant thicknesses. The mass and stiffness distributions of the components are approximated using geometry and cross-sectional properties of the bodies, such as geometric center, cross-sectional area, area moments of inertia etc., at some finite number of stations on the respective components. Each beam is assumed to have one bending and one torsional displacements. The aerodynamic forces and moments are generated using an unsteady state-space theory for the wing, and a quasi-steady theory for the other aircraft bodies. The equations of motion are derived using Lagrange’s Equations in quasi-coordinates, which yield a set of ordinary differential equations for the rigid body translations and rotations of the aircraft as a whole, and partial differential equations for the bending and torsional displacements of the bodies. The partial differential equations are discretized by means of the Galerkin method. The resulting equations are a set of nonlinear ordinary differential equations of relatively high order. The equations are used for aeroelastic analysis. Reliable aeroelastic analysis and control of modern aircraft require an accurate mathematical model. A great deal of accuracy can be gained in the model if both rigid body and elastic degrees of freedom, and their coupling are considered. A comprehensive model with both of these degrees of freedom were presented by the same authors in Refs. 1 and 2. However, the aerodynamics used in these papers were only quasi-steady aerodynamics. The present paper aims to use an unsteady aerodynamics, which significantly improves the accuracy of the model, but at the same time, increases the order of the system of the equations. There are very accurate unsteady aerodynamic theories in the frequency domain that can be used for flutter prediction. However, our interest lies in the development of models that can be used in not only flutter prediction, but also the simulation of the response of flexible aircraft to external excitations and the feedback control design to alleviate the these external effects. Such models require time domain aerodynamics as opposed to frequency domain aerodynamics. An easily implementable theory is given in Refs. 3-5, which will be used in this paper to generate the unsteady aerodynamic loads. Equations of motion of flexible aircraft can conveniently be derived using the Lagrangian equations of motion in quasi-coordinates as described in Refs. 6 and 7. The Lagrangian equations of motion require the knowledge of only three scalar quantities, namely, kinetic energy, potential energy, and the virtual work due to the applied forces. In our modeling approach, we regard the aircraft as a flexible multibody system where the bodies are the fuselage ( f ), wing (w), horizontal stabilizer ( h), and vertical stabilizer ( v). To describe the motion of the aircraft, we first attach a set of body axes xyz to the undeformed aircraft at a convenient point on the fuselage (not necessarily the center of mass of the