Introduction to Nonlinear Aeroelasticity

5Bifurcations of Fundamental Aeroelastic Systems

5.1 Introduction

In this chapter we will discuss the concept of bifurcation in more detail, using a simple aeroelastic system with structural nonlinearity. It is a 2D flat plate wing with pitch, plunge and control rotation degrees of freedom and with unsteady aerodynamic forces. The unsteady aerodynamic modelling gives rise to aerodynamic states, sometimes resulting in different bifurcation behaviour than that obtained from quasi‐steady models.

The objective of the chapter is to present a wide range of bifurcations that can affect simple aeroelastic systems and to explain their occurrence using some of the mathematical tools introduced in previous chapters. The point of departure is linear flutter analysis, an indispensable step in every nonlinear analysis. We then explore all the other bifurcations usually encountered in aeroelastic systems, such as folds, tori and period‐doubling. We finally treat the subject of two‐parameter bifurcations. Throughout the chapter, we try to explain the appearance of bifurcations in nonlinear systems in terms of the characteristics of related linear systems. In particular, we relate the flutter, static divergence and internal resonance of the underlying linear system to the bifurcations of the nonlinear one.

Only two nonlinearities are considered in this chapter, polynomial structural stiffness and damping. They are very well suited to the demonstration of many bifurcations but only represent ...