Stability and bifurcation analysis of two-degrees-of-freedom vibro-impact system with fractional-order derivative

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. •We studied the stability and bifurcation of the fractional-order 2DOF vibro-impact system.•The analytical approximation is obtained by averaging method and its equivalent system.•The stability of n-1 periodic motion of the 2DOF vibro-impact system is analyzed.•The bifurcation behaviors of the 2DOF vibro-impact system are analyzed in detail.