Flutter and Forced Response of Mistuned Turbomachinery

Abstract

This report reviews the mathematical analysis of mistuned aeroelasticity in turbomachines, avoiding excessive mathematical complexity, and putting the emphasis on the physical interpretation of the mathematics. The aeroelastic behaviour can be analysed either by considering the motion of individual blades or by considering a sum of travelling wave modes. The modal viewpoint is shown to be most suitable when the degree of mistuning is small. On the other hand, the blade viewpoint is more natural when the structural mistuning is larger than the aerodynamic coupling, resulting in highly localised eigenmodes. Asymptotic analyses are used to enlighten the physical mechanisms through which structural mistuning affects flutter and forced response, and their accuracy is assessed by comparison with the exact solution obtained by direct numerical computation. Numerical results illustrate the transition from travelling wave modes to localised vibration as the degree of mistuning increases, demonstrate the stabilising effect of mistuning on blade flutter and help explaining the dependence of the peak blade response on the order of the excitation in mistuned rotors. Monte Carlo simulations are carried out for randomly mistuned blades to draw conclusions on the expected effects of the mistuning.

This research was supported by Rolls-Royce plc and EPSRC and this report is an expanded version of a paper presented at the ISUAAAT 2000 Conference in Lyon, France on September 4-8, 2000