CAJ | 학술논문

根据油气悬架的多相介质力学特点，引入了分数阶微积分理论，在油气悬架运动微分方程基础上建立其分数阶 Bagley-Torvik 方程。设计 Oustaloup 算法低通滤波器进行运算，求得非线性分数阶微分方程数值解。将微分方程中最优阶次的选取转化为单变量最优问题，确立位移差方均值为评价目标进行求解。搭建等比例试验台和建立仿真模型，进行理论、试验、整数阶仿真数据的对比。改变激励频率和振幅观察最优阶次变化及误差变化趋势。结果表明试验油气悬架在激励频率1 Hz，振幅5 mm 下分数阶次取0．912时能更好地反映油气悬架运动特性。最优分数阶次随着激励幅值和频率的增加而减小并最终趋于稳定，在高频振动下分数阶次趋于0．9，在高幅振动下分数阶次为0．86。在多个频率及振幅激励的试验条件下，分数阶结果误差都要小于整数阶结果，论证了分数阶微积分在油气悬架建模上的有效性。
근거유기현가적다상개질역학특점，인입료분수계미적분이론，재유기현가운동미분방정기출상건립기분수계 Bagley-Torvik 방정。설계 Oustaloup 산법저통려파기진행운산，구득비선성분수계미분방정수치해。장미분방정중최우계차적선취전화위단변량최우문제，학립위이차방균치위평개목표진행구해。탑건등비례시험태화건립방진모형，진행이론、시험、정수계방진수거적대비。개변격려빈솔화진폭관찰최우계차변화급오차변화추세。결과표명시험유기현가재격려빈솔1 Hz，진폭5 mm 하분수계차취0．912시능경호지반영유기현가운동특성。최우분수계차수착격려폭치화빈솔적증가이감소병최종추우은정，재고빈진동하분수계차추우0．9，재고폭진동하분수계차위0．86。재다개빈솔급진폭격려적시험조건하，분수계결과오차도요소우정수계결과，론증료분수계미적분재유기현가건모상적유효성。
According to multi-phase medium mechanical characteristics of a hydro-pneumatic suspension,fractional calculus theory was introduced.A fractional Bagley-Torvik equation was established on the basis of the motion differential equation of the hydro-pensumatic suspension.Oustaloup algorithm for low-pass filters was designed to obtain the numerical solutions to the nonlinear fractional differential equations.The selection of optimal order was converted into a univariate optimization problem.The mean square value of displacement differences was taken as an objective function for solving. The thecrectical analysis data,test data,integer order simulation data were compared by building a proportional test bench and a simulation model.Through varying excitation frequency and amplitude the changtrends of optimal order and error were observed.The results showed that the suspension with excitation frequency 1Hz,amplitude 5mm,and fractional order 0.912 can reflect better its dynamic characteristics;the optimal fractional-order decreases with increase in excitation amplitude and frequency and it finally tends to steady;under high-frequency vibration it tends to be 0.9 and under high-amplitude vibration it tends to be 0.86;under multiple excitations of different frequencies and amplitudes,the fractional order results are all less than the integer-order results;the effectiveness of fractional calculus for modeling a hydro-pneumatic suspension is verified.