similar to the approach used to classify co-dimension-two bifurcations in smooth systems, co-dimension-two grazing bifurcations can be put into one of the following three types: degenerate gazing point, grazing of degenerate cycles, simultaneous occurrence of two grazings. This paper obtained the existence condition of the second type co-dimension-two grazing bifurcation for a two-degree-of-freedom vibro-impact system with symmetric constraints. First, considering the periodic motion of the double-sided grazing, the existence condition of the periodic motion of the double-sided grazing was deduced theoretically. Using the discontinuous mapping method, the analytical expressions of saddle-node bifurcation and period doubling bifurcation for 1/1/n impact periodic motion are derived. Then, combining the existence condition of the grazing periodic motion and the bifurcation condition of the 1/1 /n impact periodic motion, the analytical expression of co-dimensional-two grazing bifurcation was obtained, and The distribution of co-dimensional-two bifurcation points is analyzed for period one motion.
Key words
Vibro-impact system with symmetric constraints /
the discontinuous mapping method；co-dimensional-two grazing bifurcation
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