Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

Details of the frequency response curve of the elastic impact oscillator for stiffness ration β=13 at ξ=0.05, e=1 and f=0.3. Blue, green and red points represent one-parameter grazing (GR), period-doubling (PD) and saddle-node (SN) bifurcation points, respectively. The subscript i, i=1, 2 shows the ith bifurcation point of the same type. The solid and dashed curves represent stable and unstable period-1 solution, respectively. Left-hand upper panel shows the coexisting branches of period-2 orbits.102