Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping
(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 .