Dynamics of a cubic nonlinear vibration absorber

We study the dynamics of a nonlinear active vibration absorber. We consider a plant model possessing curvature and inertia nonlinearities and introduc e a second-order absorber that is coupled with the plant through user-defin ed cubic nonlinearities. When the plant is excited at primary resonance and the absorber frequency is approximately equal to the plant natural frequen cy, we show the existence of a saturation phenomenon. As the forcing amplit ude is increased beyond a certain threshold, the response amplitude of the directly excited mode (plant) remains constant, while the response amplitud e of the indirectly excited mode (absorber) increases. We obtain an approxi mate solution to the governing equations using the method of multiple scale s and show that the system possesses two possible saturation values. Using numerical techniques, we perform stability analyses and demonstrate that th e system exhibits complicated dynamics, such as Hopf bifurcations, intermit tency, and chaotic responses.