Time-delayed control of a continuous flexible rotor via the saturation phenomenon

Abstract

This paper aims to analyze and control nonlinear vibrations of a continuous spinning shaft, including a nonlinear saturation-based controller with time delays near the major critical speed and the presence of 2:1 internal resonance. The nonlinear modal interactions between the rotor and controller modes, as well as the primary and internal resonances, cause an energy bridge between the rotor and controller, so energy is transferred from the rotor to the controller, and a saturation phenomenon occurs. The nonlinear delay equations of motion are touched on analytically using the perturbation technique. Using the NSC gain coefficients, the saturation region and the frequency resonance bandwidth of the rotor are controlled. It is shown that, for negative values of the detuning parameter, as the internal detuning parameter increases, lower energies from the rotor are transferred to the controller, and the controller will be activated sooner. However, for positive values of the detuning parameter, by increasing the internal detuning parameter, the controller amplitude is increased, and the NSC will be later activated. Moreover, the stable zone of the rotor and NSC is studied.