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

• Random Melnikov method is used to derive the critical conditions for generating chaos in the mean square sense of suspension system, and the functional relationship between the parameters of suspension system and the chaos threshold is established. • The boundary curve of chaos generated by the system is obtained, and the influence of the parameters of fractional differential term on the boundary curve of chaos is studied. • Numerical simulation was carried out for fractional suspension system, and time domain diagram, spectrum diagram, phase diagram, Poincare section diagram and maximum Lyapunov index of the system were calculated. • The research results reveal that the suspension system with fractional differential has chaotic motion under random road excitation, and the coefficient and order of fractional differential will change the boundary conditions of chaos generation. 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. [ABSTRACT FROM AUTHOR]