Nonlinear vibration control of a horizontally supported Jeffcott-rotor system

A positive position feedback (PPF) controller is proposed to control the nonlinear vibrations of a horizontally supported Jeffcott-rotor system. A nonlinear restoring force and the rotor weight are considered in the system model. The controller is coupled to the system with 1:1 internal resonance. A second order approximate solution to the system governing equations is constructed by applying the multiple scales perturbation technique (MSPT). The bifurcation analyses of the Jeffcott-rotor system before and after control are conducted. The effects of the different controller parameters on the system frequency-response curves are investigated. Optimum working conditions of the controlled system are extracted to be used in the design of such systems. Numerical simulations demonstrated a good agreement with the approximate results that obtained by MSPT. A comparison is provided with already published work.