Passive control of a two degrees-of-freedom pendulum by a non-smooth absorber

A pendulum, which can oscillate in two directions, is subjected to a generalized external force. A non-smooth absorber is coupled to the pendulum with an arbitrary location and orientation. The equations of the system are derived and are treated with a multiple scale method. At fast time scale, the topology of the slow invariant manifold is described with its stable and unstable zones. The equilibrium and singular points of the system are detected at the first slow time scale. The responses of the main system, given as a function of the frequency of the external force, show reductions of the vibration levels. The analytic predictions are compared by direct numerical time integration of the equations of the system. They illustrate the operationality of the non-smooth absorber in several cases.