This paper mainly investigates the nonlinear dynamics of a friction-induced self-excited vibration when the coefficient of static friction is larger than that of kinetic friction. First, this system is rewritten by a new theory proposed by Jeffrey, which is different from the Filippov theory. Then, the sliding region is obtained from the theory, which is also verified by the numerical simulation. Furthermore, multiple attractors, such as period-1 orbit and equilibrium point, period-2 orbit and equilibrium point, can coexist if the coefficient of static friction exceeds that of kinetic friction, but it is not true if they are equal. Finally, some sliding bifurcations, such as crossing-sliding bifurcation, switching-sliding bifurcation, and grazing-sliding bifurcation, are also found.

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