Study on chaos of nonlinear suspension system with fractional-order derivative under random excitation

Abstract The chaotic motion of a suspension system with fractional order differential under random excitation is studied. The critical condition of chaos in the mean square sense of suspension system is derived by using random Melnikov method. The function relationship between the parameters of suspension system and chaos threshold is established. The boundary curve of chaos is obtained. The influence of fractional differential parameters on chaos boundary curve is studied. The numerical simulation of fractional order suspension system is carried out, and the time domain diagram and frequency of the system are calculated the spectrum, phase plane, Poincare section and the maximum Lyapunov exponent were obtained. The results show that there is chaotic motion in the suspension system with fractional differential under random road excitation, and the coefficient and order of fractional differential term will change the boundary conditions of chaos.