A nonlinear mechanical model of a vibro-impact system influenced by double nonsmooth mechanical factors that combine elastic and rigid impact is described. The theoretical solutions to judge the periodic motion stability of the system are presented, and three different “gazing” motions and the corresponding conditions are described. The transition and coupling of periodic motions by the nonsmooth mechanical factors are demonstrated. The formation mechanism of sticking motion, chattering motion, and the periodic cavity by the influence of gazing bifurcation are analyzed. The coexistence of periodic motions and the extreme sensitivity of the initial value within the high frequency region are studied. The distribution of the attractor and the corresponding attracting domain corresponding to different periodic motions are also studied.

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