Fractional-order Modeling And Dynamic Analysis Of Air Spring

Almost simultaneously come up with classical integer-order calculus,fractional-order calculus was advanced in 1695.They have a history of more than 300 years.When describing the problems of complex physical mechanics,fractional-order derivative models have advantages of concise expression,clear physical meaning,and more real response to physical constitutive relation.Through theoretical analysis,experimental research and numerical simulation,this thesis makes fractional-order modeling of viscoelastic material air springs using the unique memory characteristics of fractional-order calculus.The fractional-order differential term is introduced into the nonlinear system,and a series of studies on the complex dynamic behavior of the simultaneous resonance are carried out.The main studies of this thesis are as follows:In Chapter 2,the air spring is loaded by the HT911 hydraulic servo test system and the air compressor.Different parametric conditions(such as pressure,frequency,and amplitude)have been adopted to more experimental data.The nonlinear characteristics of air springs under different parametric are analyzed.A reasonable fractional-order derivative model is carried out.The fractional-order model parameters function expression under the different parametric conditions are established by using Matlab software to fit the experimental data and identify the parameter and the corresponding change rule and detailed analysis can be obtained.In Chapter 3,fractional order model of air spring as a nonlinear term is applied to a linear system differential equations.The dynamical characteristics of super-harmonic and sub-harmonic simultaneous resonance of Duffing oscillator with fractional-order derivative are studied.The first-order approximate analytical solution is obtained by averaging method.The definitions of equivalent linear damping coefficient and equivalent linear stiffness efficient for super-harmonic and sub-harmonic simultaneous resonance are presented.The analytical amplitude-frequency equation for steady-state solution of simultaneous resonance is established.The analytic solution and the numerical solution are compared,and their satisfactory agreement verifies the correctness and the higher-order precision of the approximately analytical results.The effects of fractional-order differential term parameters on the amplitude-frequency curve of the system are studied.In Chapter 4,the dynamical characteristics of super-harmonic and sub-harmonic simultaneous resonance of van der Pol oscillator with fractional-order derivative are studied.The first-order approximate analytical solution is obtained by averaging method.The analytic expression of steady-state solution amplitude-frequency curve of simultaneous resonance is established and the stability criterion of the periodic response is obtained.Finally,the numerical simulation is used to analyze the differences between the super-harmonic and sub-harmonic resonances under single-frequency excitation.The effects of the parameters in fractional-order derivative on the response amplitude,the resonance frequency,the stability of stationary solution,the number of periodic solutions,the resonance region,topological structure of the curve and jump phenomena and other complex dynamic characteristics are analyzed.