System Mode Shapes in the Flutter of Compressor Blade Rows

The problems associated with the prohibitive number of possible system modes for a fluttering compressor or turbine blade row are eliminated by the development that comprises the present report. The existence and uniqueness of extremely simple system flutter modes are proved for blade rows consisting of identical blades equally spaced about a common rotor. These simple system modes, if properly interpreted, have the effect of reducing by a factor of n the number of degrees of freedom necessary to analyze an w-bladed configuration. Stated differently, the system of n blades may be considered, with no loss of generality whatsoever, in terms of a single equivalent blade. The proof holds under any type of flow and any and all types of interblade coupling, so long as a linear analysis is permissible. Moreover, since it is the flutter-inception point that is of interest in predicting critical velocity or rotational speed, it may well be that the conclusions developed apply even to the onset of stall flutter. Practical application of the method to stall-flutter calculations would, of course, require the availability of aerodynamic stallflutter coefficients. The development is carried out first under the assumption of infinite rotor inertia or, in other words, constant rotor velocity. This restriction is then relaxed, and the treatment is expanded to permit torsional oscillations of the rotor itself. I t is proved that under certain conditions the assumption of infinite rotor inertia introduces no error whatsoever.