Natural Frequencies of a Free Gyroscope Supported in Gimbals on an Elastic Shaft

Abstract

This paper concerns the free vibrations of a gyroscope supported symmetrically in rigid gimbals on an elastic shaft. Three natural modes involving conical whirling of the rotor axis are shown to exist. The dependence of the three frequencies on rotor speed, moments of inertia and shaft stiffness is discussed in general and illustrated in some numerical cases. The principal results determine (1) the decrease in the frequency of nutation resulting from flexibility of the shaft, (2) the critical speeds of the rotor.