5.7.1 Natural frequencies and excitation frequencies
The vibration characteristics of turbine machine blades, as measured under operating conditions, are usually found to be extremely complex and often quite different from theoretical predictions. There are several reasons for this.
First, in spite of the advances in finite element computation in recent years, the intricate geometry of a blade, which is demanded for aerodynamic performance, makes it a very difficult component to analyse theoretically. Consequently, predictions for the modes and frequencies of a single cantilevered blade may not always be very accurate. Then, a second factor which compounds the problem, is the existence of multiple interactions between each blade and all the other blades in the same stage due to coupling through the disc and shrouds or lacing wires linking adjacent blades. These interactions lead to the prediction of a multiplicity of modes in the working frequency range, where for a single blade there are only two or three. The vibration of a fully-bladed disc is therefore much more complicated than is suggested by the characteristics of a single cantilever blade.
An individual blade, cantilevered at its root, has a set of natural frequencies in the operating range which are classified in three groups: 'flap' modes, 'edgewise' modes and torsion modes. The disc carrying a set of such blades itself possesses several natural frequencies within the same range, each one of these being associated with a mode mode shape having n nodal diameters (and possibly one or two nodal circles as well). The complete bladed disc has a very large number of modes of vibration in the same frequency range, and each of these will constitute a unique mix of the individual blade and disc modes. Some of these assembly modes will be identified as being 'predominantly disc' modes, while others will be immediately associated with one of the blade cantilever modes, in both cases by virtue of the respective natural frequencies.
Other modes exist which are associated with the fully-bladed wheel assembly and are quite distinct from disc or blade modes. When there is additional inter-blade coupling provided by some form of shrouding either at the tip or part-span, then most of the modes of the complete structure will tend to be wheel modes, and small modifications to the shrouding or lacing can result in significant changes in the pattern of wheel natural frequencies.