Resonant Oscillations of a Vertical Hard Gyroscopic Rotor with Linear and Nonlinear Damping

Abstract

A vertical rigid gyroscopic rotor with linear and cubic nonlinear damping of the support where the disk has a mass imbalance is considered herein. The motion equations in the form of Lagrange equations of the second kind have been composed to describe the motion of the rotor. The expressions have been found to determine the amplitude of the fundamental oscillations harmonic and the amplitude of the dynamic influence moment with the help of the harmonic balance method. Analysis of the results of amplitude-frequency characteristic studies and of the dependence of the dynamic influence moment amplitude on the oscillations frequency for different values of the linear and nonlinear damping coefficients show that both linear damping and cubic nonlinear damping have almost no effect on the amplitude-frequency characteristic in the lower resonant frequencies range, linear and cubic nonlinear damping can significantly suppress the resonance peak of the main harmonic in the resonance region, nonlinear damping, in contrast to linear damping, can slightly suppress the vibration amplitude of the rotor in the region where the velocity is above the critical velocity. The results of the studies can be successfully used to create passive vibration isolators used for damping of rotary machines vibrations.