Study On Dynamics Behavior Of Vehicle System With Fractional-order Nonlinear Characteristic Suspension

Fractional-order derivative theory has been developed for more than 300 years,and it is a hot topic of research.Fractional-order derivative theory is widely used in the field of science and engineering,because it needs fewer parameters to describe complex physical problems,and it has good memory characteristics,and can accurately reflect the true constitutive relationship of viscoelastic materials.Based on this,this paper introduces fractional-order derivative into nonlinear system to study the dynamics of Duffing system and vehicle suspension system.The main research contents are as follows:(1)Taking the Duffing System of fractional-order derivative as the research object,the approximate analytical solution of steady-state amplitude frequency response of the system is obtained by harmonic balance method,and the results are verified by numerical value.The influence of fractional order differential term parameters on the amplitude frequency response curve is analyzed.It is found that the change of fractional-order derivative term parameters affects the resonance amplitude and resonance frequency of the amplitude frequency response curve of the system.The boundary condition of chaos is studied by Melnikov method,and the correctness of chaos boundary is verified by numerical method,including the Largest Lyapunov exponent,time histories,frequency spectrograms,phase portraits and Poincare maps,and the influence of system parameters on chaotic threshold curve is analyzed.(2)The time delay is introduced into the fractional-order Duffing system,and the Duffing system with fractional-order derivative time delay term is obtained.The analytical solution of the amplitude frequency response of the system is obtained based on the average method,and the influence of the time delay parameter and fractional-order differential term parameter on the amplitude frequency response curve is analyzed.It is found that the time-delay parameter changes the frequency range of the unstable solution.The boundary of chaotic motion is studied by Melnikov method and numerical method.The bifurcation diagram of the system shows that chaos can be achieved through period doubling bifurcation and paroxysmal motion.It is found that the possibility of chaos can be reduced by reducing the time delay parameter and increasing the fractional differential term parameter.(3)In this paper,the random Melnikov method is used to study the chaotic motion boundary of a single degree of freedom suspension system with fractional differentiation under the condition of bounded noise excitation.The influence of system parameters on the chaotic boundary curve and the response of the suspension system under different excitation amplitudes are analyzed.It is found that the parameters of fractional-order differential term affect the boundary curve by changing the stiffness and damping of the system.(4)Taking the suspension system with fractional-order derivative two degrees of freedom as the research object,the amplitude frequency response functions of vehicle acceleration,tire dynamic load and suspension dynamic deflection are obtained by Laplace transform method,and the influence of fractional-order differential term parameters on the amplitude frequency response is analyzed.The response curve of vehicle body vibration amplitude frequency with nonlinear suspension system is calculated by numerical method.It is found that the vibration amplitude decreases with the increase of the parameter value of fractional-order differential term.