A class of single-degree-of-freedom piecewise smooth mechanical vibration systems was stud-ied.The modes and distribution regions of sub-harmonic vibrations in the two-parameter plane are nu-merically calculated.The bifurcation characteristics,stability and transmigration laws of sub-harmonic vibrations in the sub-harmonic inclusion regions are investigated in detail by using the continuation shooting method.The results show that the grazing bifurcation is continuous in the elastic impact sys-tem.In the sub-harmonic inclusion regions,PD-type grazing bifurcation are prevalent,and SN-type grazing bifurcation and subcritical period-doubling bifurcation cause jumps and hysteresis phenomenon of system response.Multiple attractors coexist in the high-frequency sub-harmonic inclusion regions,and the chaotic attractor ends up at the boundary crisis.
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