Passivity analysis and control of nonlinear oscillations in systems with cubic nonlinearities

In this paper we investigate passivity properties of systems with cubic nonlinear coupling terms. We derive sufficient conditions for a 2-DOF system with general cubic non-linearities to be passive. This is done by showing that the system can be divided into three passive subsystems connected in feedback. In the cases where the passivity conditions are satisfied, the result can be applied e.g. in the design of vibration damping controllers. It is straightforward to extend these results to an arbitrary n-DOF system with cubic nonlinearities.