| Suspension is one of the most important parts of the vehicle,which directly affects the comfort of passengers and the driving safety of the vehicle.Optimizing the performance of suspension is one of the important ways to improve the ride comfort of the vehicle.In the modeling and analysis of air suspension system,fractional calculus as the new mathematical tool can establish more accurate mathematical model to analyze the dynamic characteristics of air suspension system.It provides theoretical guidance for the design and optimization of air suspension system.The main contents are as follows:(1)Based on the fractional-order Viscoelastic characteristics,the fractional-order model of air suspension is established.The air spring in the air suspension system has obvious fractional viscoelastic characteristics.The traditional modeling method only considers the elasticity of the air spring,and can not fully reflect the constitutive relationship of the air spring.Using fractional-order model to simulate the air suspension is closer to reality.(2)The bifurcations and chaos of fractional-order model of air suspension is studied.The equivalent stiffness and equivalent damping is used to deal with the fractional-order derivative,which is equivalent to the form of trigonometric function and exponential function.Then,Melnikov method is used to analyze the necessary conditions for the bifurcation and chaos generation of the fractional-order model of air suspension.And the approximate analytical solution is obtained.The comparison between the analytical solution and the numerical solution is investigated,and the accuracy of the analytical result is proved.Finally,The influences of fractional order and coefficient on the necessary condition of chaos are studied by simulation.Additionally,it is found that there exsit bistability in fractional-order system of air suspension.Starting from the two steady-state solutions,the system can reach the chaos through the period-doubling bifurcation with the change of external excitation parameter.This phenomenon is verified by analyzing the dynamic response of the system.(3)The influence of semi-active control strategy on the resonance of air suspension system is studied.The approximate analytical solution of the air suspension system with fractional delay feedback control is solved by the average method,and the correctness of the analytical method is proved by numerical method.Then,the semi-active control strategy is introduced into the air suspension system,and the approximate solution of the control system is obtained by the average method.After the accuracy is verified by numerical simulation,the influence of the semi-active control strategy and control parameters on the control effect is studied by the analytical results.(4)The bifurcation and chaotic characteristics of air suspension system with fractional delay feedback control is studied.The fractional-order delayed feedback control is equivalent to the approximate integer-order control.The analytically necessary condition for generating chaos in air suspension system with fractional delay feedback control is obtained by Melnikov method.The accuracy of the analytical results is verified by the power series method.From the analysis of the numerical simulation results,it could be found that there are two paths leading to the chaos after period-doubling bifurcations due to different initial values in air suspension system with fractional delay feedback control.Finally,the influence of the parameters of the fractional-order delayed feedback control on bifurcation and chaos is analyzed. |
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