Nonstationary Resonant Oscillations of a Gyroscopic Rigid Rotor with Nonlinear Damping and Non-ideal Energy Source

Abstract

The article is concerned with the effect of nonlinear cubic damping of an elastic support on unsteady resonant vibrations of a gyroscopic rigid rotor when interacting with a non-ideal energy source. It is confirmed that nonlinear cubic damping can suppress not only the maximum amplitude, but also the amplitude of unsteady oscillations behind the rotation speed corresponding to the amplitude peak. It shifts the control parameter corresponding to the maximum amplitude, downward with a rigid nonlinear elastic characteristic of the support material, and upward with a soft nonlinear elastic characteristic of the support material. An increase in the nonlinear cubic damping coefficient can significantly weaken the Sommerfeld effect with a nonlinear jump in unsteady oscillations, up to its complete elimination. The difference in the values of the maximum amplitude and in the corresponding values of the control parameter in the resonance curves with an increasing and decreasing control parameter is explained by the difference in the values of the same parameters relating to the jumping effects during the acceleration and runout of the rotary machine.