Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping

Figure 3

(a) Bifurcation diagrams constructed for the mass displacement under varying forcing frequency calculated at ,  ,  ,  ,  . Black and blue dots mark the mass displacement which is swept in the increasing and decreasing directions, respectively. The magenta dots show the unstable period-1 orbit with one impact. Additional windows demonstrate the trajectories of the attractors on the phase plane obtained for ,  ,  ,  , ,  ,  , and (stable impacting period-1 orbit in black, unstable impacting period-1 orbit in magenta, stable nonimpacting period-1 orbit in blue). Green solid lines indicate the location of the discontinuity boundaries and , and the red points show the Poincaré sections. (b) The corresponding amplitude frequency curve showing the maximum of the absolute values of the mass displacement as a function of the forcing frequency . Blue, green, and red dots represent one-parameter grazing (GR), period-doubling (PD), and saddle-node (SN) bifurcations, respectively. Solid and dotted lines denote stable and unstable solutions, respectively. The dashed horizontal line denotes .