Flutter and Forced Response of MistunedTurbomachineryM

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 aeroe-lastic 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 aaects utter 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 eeect of mistuning on blade utter 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 eeects of the mistuning.