Periodic solutions of a multi-DOF beam system with impact

The steady state behaviour is analyzed of a periodically driven multi-DOF beam system which has an elastic stop at its middle. The elastic stop is modelled in a continuous way by using the contact law of Hertz. The beam is modelled by using finite elements and subsequently reduced by using a component mode synthesis method. The steady state behaviour of the system reduced to one, two and four DOF's is investigated by calculating periodic solutions at varying excitation frequency. Periodic solutions are calculated by solving two-point boundary value problems by the multiple shooting method in combination with a path-following technique. It is shown that models with more than one DOF are required for a good assessment of the long-term behaviour of the system.