The influence on coupling vibrations among shaft-torsion and blade-bending coupling vibrations of a multi-disk rotor system was investigated analytically. The natural frequencies and the mode shapes of the system were solved for one- to three-disk cases as examples. First, numerical results showed how the natural frequencies varied with blades in a disk unit. The diagrams of the coupling mode shapes were drawn. From the results, it was found that the inter-blade (BB) modes were of repeated frequencies of (N_b-1) multiplicity for number blades. At multi-disk unit, the shaft-blade (SB) modes added to Nd modes for number disks. The BB modes were of repeated frequencies of [N_d × (N_b-1)] multiplicity for number disks. Numerical calculations also revealed that the natural frequencies were affected by disk distance. In the rotation effect, the times of instability will due to the number of disk. And, the more disk rotor causes instability earlier than the less disk case.
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