Vibration of an Asymmetrically Mounted Rotor With Gyroscopic Effects

The equations of motion for the asymmetrically mounted rotor with gyroscopic effects contain periodic coefficients. These periodic coefficients which arise from the system asymmetries cannot be eliminated by transformation into rotating coordinates. The parametrically excited vibrations are studied by referring to the natural frequencies of a generating system consisting of a symmetric rotor on asymmetric supports. First the equations of motion are transformed into normal coordinates of the generating system by application of the Bulgakov normalization technique. The assumed small inertia asymmetry introduces coupling terms with periodic coefficients which are evaluated as generalized forces acting on the generating system. Then the final equations are solved by the approximate perturbation—variation method of Hsu. Formulae for parametric instability speed ranges are derived for the assumed small inertia asymmetry.