The universal behaviour of oscillators that undergo low velocity impacts

When the motion of a dynamical system is limited by a stop, the behaviour will be strongly nonlinear due to the impacts that occur. Systems of this type are generally called impact oscillators and a plethora of dynamical states and bifurcations have been found, including subharmonics, period doublings and chaos. The paper studies the effect of nonidealities of impact oscillators. For example, it is thinkable that for oscillators that impact with a yielding stop, the square root singularity of the mapping vanishes, such that the bifurcation scenario changes. This course of events is studied by deriving mappings for more general models. The surprising outcome is that the nonideality of a yielding stop does not change the grazing bifurcations and thus the universality class is even wider than what might have been expected. The theoretical results are corroborated by the results of precise experiments that indeed show the expected bifurcation scenario.