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Rotor systems with the shaft weakened by a notch is possible to investigate on the basis of theoryfor rotors with a non-circular cross-section of the shaft , because the stiffness of the shaft with a notchcan be formulated in two perpendicular directions. The investigated problem is very similar to rotorsystems with the shaft containing a fatigue crack. It is known, that the crack can open and close during one shaft rotation or it can be opened or closed, and The influence of an open crack anda non-circular cross-section of the shaft on dynamical behaviour of a rotor are qualitatively the same, because in both cases the stiffness of the shaft changes periodically during rotation.