When grazing bifurcation and smooth bifurcation take place simultaneously, one kind of co-dimensional-two grazing bifurcation will occur. The co-dimensional-two bifurcation of a two-degree-of-freedom vibro-impact system and its dynamic behavior near the co-dimensional-two grazing bifurcation points were studied. Firstly, the existence conditions of grazing periodic motion were discussed. The global Poincaré mapping for the 1/n impact period motions was constructed by using the discontinuous mapping method, and the bifurcation conditions for the 1/n impact period motions were obtained. Then, an analytical expression satisfied for grazing bifurcation and smooth bifurcation was derived by combining the conditions of periodic grazing bifurcation and periodic impact bifurcation. Based on the expression, the distribution of co-dimensional-two bifurcation points of the system under different periods was analyzed by numerical simulation. Finally, the effectiveness of theoretical analysis was verified by comparing the bifurcation diagrams obtained by the global Poincaré map and the differential system.
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