Resonance vibrations of a gyroscopic rotor with linear and nonlinear damping and nonlinear stiffness of the elastic support in interaction with a non-ideal energy source

•Combined linear and non-linear cubic damping is more efficient.•Combined damping can significantly suppress maximum amplitude.•Combined damping eliminates jump effects.•Combined damping significantly reduces the amplitude of the vibration frequency.•Cubic nonlinear damping significantly narrows the unstable region. The article examines the effect of linear damping and combined linear and nonlinear cubic damping of an elastic support on the dynamics of a gyroscopic rigid rotor with a non-ideal energy source, taking into account cubic nonlinear stiffness of the support material. Analysis of the research results shows that both linear damping and combined linear and nonlinear cubic damping can significantly suppress the resonance peak of the fundamental harmonic, reduce the amplitude of vibration frequency variation and stabilize the shaft rotation speed, but the effect of combined damping is more significant. In non-resonant regions, where the speed is higher than the natural frequency of the rotor system, both types of damping shorten the distance between jumps in nonlinear resonance curves and eliminate them. If linear damping mainly affects the boundaries of the instability region close to the resonant frequency, then nonlinear cubic damping significantly narrows the width of the instability region throughout the entire range beyond the resonant rotation speed. These results can be successfully used for the development of passive vibration isolators used to damp vibrations generated by rotary machines