Mix active control feedback of a continuously rotating shaft's nonlinear oscillations through simultaneous resonance

Abstract

In our consideration, mix active controller negative velocity and acceleration feedback are presented to eliminate the vibration of the nonlinear oscillations of a continuous rotating shaft at one of the worst simultaneous resonance cases Ω=ω1,ω2=ω1 . The system presented by two degree of freedom containing the third order of nonlinear terms and multi external forces. The multiple scale method used to obtain the approximate solution of the vibrating system. The frequency response equation is used to investigated the stability of controlled system. We examined at the system numerically to compare the time histories before and after adding a negative velocity and acceleration feedback controller. We analyzed the performance of several selected parameters of the studied system for response curves. Finally, the numerical solution and the approximate solution obtained from the multiple scale are in good agreement.