Introduction to Nonlinear Aeroelasticity

10Finite Wings

10.1 Introduction

All the aeroelastic systems investigated up to this point are two‐dimensional and make use of 2D aerodynamic and structural modelling. There are analytical solutions for the unsteady aerodynamic loads acting on 2D airfoils, which can be easily incorporated into a nonlinear structural model. Furthermore, empirical separated flow aerodynamic models are all two‐dimensional. Despite the fact that the real world is three‐dimensional, 2D models have wide‐ranging applications to slender structures, such as helicopter and wind turbine blades, power cables and bridge decks. Nevertheless, most aircraft wings are less slender and feature sweep and/or taper, so that the airflow around them is significantly three‐dimensional.

There are few analytical solutions for 3D unsteady aerodynamics in the literature. For example, Jones (1939) developped an analytical solution for the impulsively started flow around a 3D elliptical wing. Some authors have extended Prandtl’s lifting line theory to unsteady aerodynamics, usually through coupling with Theodorsen’s work (Drela 1999; Reissner 1947; Reissner and Stevens 1947) but such approaches end up being quasi‐numerical. The standard methods used for finite wing aeroelasticity are numerical unsteady panel formulations, such as the Doublet Lattice (Albano and Rodden 1969) or the Vortex Lattice (Katz and Plotkin 2001; Murua et al. 2012) techniques.

The only widely used analytical method for modelling 3D unsteady aerodynamics ...