Coupled Shaft-Torsion and Blade-Bending Vibrations of a Rotating Shaft–Disk–Blade Unit

A new approach to analyzing the dynamic coupling between shaft torsion and blade bending of a rotating shaft–disk–blade unit is introduced. The approach allows the shaft to vibrate freely around its rotation axis instead of assuming a periodic perturbation of the shaft speed that may accommodate the shaft flexibility only to a limited extent. A weighted residual method is applied, and the receptances at the connections of blades and shaft–disk are formulated. Numerical examples are given for cases with between two and six symmetrically arranged blades. The results show not only coupling between the shaft, disk, and blades, but also coupling between individual blades where the shaft acts as a rigid support and experiences no torsional vibration. The blade-coupling modes occurred only in repeated frequencies. Finally, the effect of shaft speed on the modal frequencies was investigated. Plots illustrating the occurrence of critical speeds and flutter instabilities are presented.