Prediction of non-linear aeroelastic instabilities

Abstract

This paper describes part of an investigation into the use of Normal Form Theory to predict and characterise Limit Cycle Oscillations (LCO) in non-linear aeroelastic systems. Starting with the coupled aeroelastic integro-differential equations of a system with non-linearities, it is shown how to reduce the order of the system and then compute the normal forms using a class of the period-averaging method. The stability of the LCO can then be characterised by considering the behaviour around the linear flutter condition. Such an approach does away with the need for numerical simulation of the system. The methodology is demonstrated upon a simple two-degrees-of-freedom aeroelastic wing model with cubic stiffness. A good agreement is obtained between analytical and simulation results.