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At present, there are few studies considering both nonlinear and fractional characteristics of suspension in vehicle systems. In this paper, a fractional nonlinear model of a quarter vehicle with two-degree-of-freedom (2-DOF) is innovatively proposed to describe the suspension system containing the viscoelastic material metal rubber. Given the lack of a general calculation scheme for the multi-degree-of-freedom fractional-order incremental harmonic balance method (IHBM), a general calculation scheme for the 2-DOF incremental harmonic balance method for nonlinear systems with fractional order is derived. The nonlinear dynamical properties of the presented model are acquired using this method. The accuracy of the proposed method is verified through a comparison with the power series expansion method. Afterward, the effects of the various parameters on the dynamic performance are analyzed. The vibration peak value of the fractional-order model is significantly higher than that of the integer-order model (IOM). Therefore, the suspension parameters should be designed with a margin when using IOM. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic model of piecewise nonlinear system with fractional-order time delay is simplified. The amplitude frequency response equation of the dynamic model of piecewise nonlinear system with fractional-order time delay under periodic excitation is obtained by using the average method. It is found that the amplitude of the system changes when the external excitation frequency changes. At the same time, the amplitude frequency response characteristics of the system under different time delay parameters, different fractional-order parameters, and coefficient are studied. By analyzing the amplitude frequency response characteristics, the influence of time delay and fractional-order parameters on the stability of the system is analyzed in this paper, and the bifurcation equations of the system are studied by using the theory of continuity. The transition sets under different piecewise states and the constrained bifurcation behaviors under the corresponding unfolding parameters are obtained. The variation of the bifurcation topology of the system with the change of system parameters is given. [ABSTRACT FROM AUTHOR]

The chaotic behavior of a nonlinear vehicle suspension system with a fractional-order derivative is considered. A hysteretic nonlinear model of vehicle suspension with a fractional-order derivative term is established and the analytically necessary condition for heterotopic chaos is derived based on the Melnikov method. The largest Lyapunov exponents are compared. Then, the necessary condition is numerically verified by various simulation factors. The possibility of chaotic motion in vehicles should be higher for larger amplitude of road excitation. It is found that the coefficient and order of the fractional differential term, the stiffness coefficient, and the damping coefficient of the system all affect the necessary condition, and analysis on the effects of these parameters is presented individually. It has been shown that the larger the coefficient of the fractional differential term, or the stiffness and damping coefficients of the system, the lower the possibility of chaos in the system. Meanwhile, without considering the fractional order, the integer order suspension model obviously reduces the actual area where chaos may occur, so designing suspensions according to the fractional order model can avoid chaos more accurately than the integer order model. [ABSTRACT FROM AUTHOR]