Saturation-based active absorber for a non-linear plant to a principal external excitation

The use of active non-linear absorber to control the high-amplitude vibration of the non-linear plant subjected to primary external excitation is investigated. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities and a two-to-one internal resonance. The dynamic behaviour of the plant is described by an oscillator, which includes velocity-dependent damping forces, polynomial and differential-polynomial non-linearities. First, the approximate solutions to the governing equations are obtained by using the method of multiple scales. Then a bifurcation analysis is conducted to examine the stability of the system and the performance of the control strategy is studied. A parametric investigation is carried out to see the effects of changing the damping ratio of the absorber, the value of the feedback gain and the detuning frequency of the absorber on the responses of the plant and absorber. The instantaneous power of the control law is also calculated. Finally, the numerical simulations are performed to demonstrate and validate the saturation control method.