Transient growth rates of near-grazing impact velocities: Theory and experiments

In this paper, nonsmooth fold bifurcations associated with the onset of low-relative-velocity (near-grazing) impacts in an oscillatory mechanical system are proposed as a potential operating principle for high-speed limit switches. Specifically, analytical, numerical, and experimental methods are employed to investigate the near-grazing transient behavior in a representative system. It is shown that the rate of growth of successive impact velocities increases beyond all bounds as the threshold parameter value is approached. A limit switch based on the proposed nonsmooth fold scenario would thus be expected to outperform one that relies on a smooth bifurcation, such as the cyclic-fold bifurcation, in terms of switching speed and sensitivity.