O ruchu sprężystego walu wirującego w podatnych łożyskach

In this article the motion is considered of a flexible massless shaft with a statically unbalanced disk, mounted in the centre of its length. The shaft rotates in radially susceptible bearings. It has been assumed that the characteristics of elastic forces of both the shaft and bearing supports are of the character of central forces and are in general nonlinear functions of radial bending. The equations of motion of the rotor have been derived. Analytical and graphical methods have been presented of simplifying the equations of motion by the introduction of the so called generalized characteristic of elasticity. The graphical method of finding the amplitude of resonance vibrations (a steady synchronic precesion of the rotor) has been presented. The proposed analytical methods of obtaining the generalized characteristic of elasticity and the graphical construction might serve as methods of selecting the elasticity characteristic of the shaft and bearing supports of the rotor so that in the range of the working revolutions of the rotor the resonance amplitudes
be minimal. The article has been supplement with an extensive review of literature pertaining the dynamics
of rotors on bearings.