Experimental and numerical analysis of the steady-state behaviour of a beam system with impact

In this paper the steady state behaviour of a beam system with a periodically moving support and an elastic stop is analysed both numerically and experimentally. In the numerical analysis a continuous model for the elastic stop is used based on the contact force law of Hertz. The beam is modelled using finite elements and subsequently reduced using a component mode synthesis method leading to a non-linear six-degree-of-freedom model. The steady state behaviour of this model is investigated by calculating periodic solutions while varying the excitation frequency. This is done by solving two-point boundary value problems using the multiple shooting method in combination with a path-following method. Experimental research concerning periodic solutions is carried out to verify the numerical results. The experimental results correspond very well with the numerical results. It appears that the high eigenfrequencies of the linear beam system strongly influence the low-frequency non-linear steady state response. This means that multi-degree-of-freedom models are important for an accurate representation of the actual system behaviour, although a single-degree-of-freedom model captures important first-order information about a lot of the non-linear phenomena in the low-frequency range