Periodic Response Analysis of A Jeffcott-Rotor System By The Integral Equation Method

In this paper, two modified nonlinear saturation-based controllers and negative velocity feedback controllers are integrated to suppress the horizontal and vertical vibrations of a horizontally supported Jeffcott-rotor system at primary resonance excitation and the presence of 1:1 and 1:2 internal resonances. The second order approximations and the amplitude equations are obtained by applying the integral equation method to analyze the nonlinear behavior of this model. The stability of the steady-state solutions is ascertained based on the Floquet theory. The necessity of adding a negative velocity feedback to the main system is stated. The effects of different control parameters on the frequency-response curves and the force-response curves are investigated. Time histories of the whole system are included to show the response with and without control. It is shown that the saturation-based controller can reduce the system response to almost zero and the negative velocity feedback can suppress the transient vibrations and prevent the main system having the large amplitude vibration. The analyses show that analytical solutions are in excellent agreement with the numerical simulations. Finally, a comparison with previously published works is included.