8Low‐Speed Aerodynamic Nonlinearities

8.1 Introduction

The vast majority of the examples presented up to this point feature structural nonlinearity; aerodynamic nonlinearity was only included in the galloping oscillator. The aerodynamic modelling in all the other examples was based on the assumption that the flow remains attached to the body’s surface at all times. Attached flow can feature weak nonlinearity due to the presence of trigonometric functions of the angle of attack and the motion of the wake. As an example, the classical conformal transformation solution of the steady, incompressible and inviscid flow around a 2D flat plate airfoil yields

images

where cl is the 2D lift coefficient and α is the angle of attack (see e.g. Katz and Plotkin, 2001). Theodorsen’s and Wagner’s solutions for the unsteady, incompressible and inviscid flow around a 2D flat plate airfoil also make use of the conformal transformation method but linearise further by assuming that all disturbances are small so that images . Consequently, the aerodynamic models used in the aeroelastic systems presented in Appendix A.2A.5 are completely linear.

In general, solutions to Laplace’s equation are either linear or weakly nonlinear functions of angle of attack and/or motion. Significant nonlinearity can only be obtained ...

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