Analysis of grazing bifurcation from periodic motion to quasi-periodic motion in impact-damper systems

A peculiar discontinuous bifurcation phenomenon that the periodic solution directly jumps to quasi-periodic attractor through grazing bifurcation is reported in this paper. This phenomenon is revealed in the impact damper system by the spectrum of the largest Lyapunov exponent in parameter plane. The origin of the quasi-periodic attractor and coexistence of solutions are analyzed. And the MDCM (multi-DOF cell mapping) method is used to reveal the variety of attraction basins of solutions.