The stability and bifurcation behaviors of fractional-order vibro-impact system are investigated, where a two-degrees-of-freedom vibro-impact oscillator excited by external harmonic excitation is considered. The approximate analytical solution of the fractional-order vibro-impact system is acquired based on the approximate equivalent integer-order system of fractional-order system obtained by the averaging method. Poincaré mapping of the system is established, the linearized matrix of Poincaré mapping is obtained according to the approximate analytical solution, and the stability of n-1 periodic motion is analyzed. The bifurcation behaviors of the two-degrees-of-freedom vibro-impact system are investigated by numerical solutions. Under different system parameters, the bifurcation behaviors of the system are analyzed in detail when the excitation frequency and fractional order change. It is found that there are Hopf bifurcation, period doubling bifurcation, quasi periodic motion and chaotic motion in the two-degrees-of-freedom vibro-impact system with fractional-order derivative, and there are two routes to chaos in the system when the excitation frequency changes.

研究了分数阶振动冲击系统的稳定性和分岔行为，其中考虑了由外部谐波激励激发的两自由度振动冲击振荡器。基于通过平均法获得的分数阶系统的近似等效整数阶系统，获取分数阶振动冲击系统的近似解析解。建立系统的庞加莱映射，根据近似解析解求出庞加莱映射的线性矩阵，得到n的稳定性。-1周期性运动被分析。通过数值解研究了两自由度振动冲击系统的分叉行为。在不同的系统参数下，详细分析了当激励频率和分数阶变化时系统的分叉行为。发现在具有分数阶导数的两自由度振动冲击系统中，存在霍普夫分岔，周期加倍分岔，准周期运动和混沌运动，当振动频率为零时，系统中存在两条导致混沌的路径。激发频率变化。