基于MLP法的磁浮列车非线性系统的稳定性分析
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摘要
以磁浮列车的垂向运动为研究对象,研究其非线性系统的稳定性。选取气隙值、电流值为磁浮列车悬浮系统的广义坐标,依据拉格朗日-麦克斯韦方程建立磁浮列车非线性悬浮系统的动力学模型,得到的振动方程是三阶的强非线性负刚度微分方程。应用MLP法求得系统的共振永年项条件,并对初始方程进行了数值计算,得到了磁浮列车在空载、满载、过载情况下的悬浮系统振动时间响应曲线和相图,结果表明:随着列车质量的增加,列车初始位移增加,但列车启动后50 s的时间内,系统振动趋于稳定。
With the vertical motion of maglev train as the research object,the stability of its nonlinear system was studied. In the experiment, the air gap value and current value were selected as the generalized coordinates of the suspension system in the maglev train. By the dynamic model of the nonlinear suspension system established based on Lagrange-Maxwell equation, a third-order strongly nonlinear negative stiffness differential equation was obtained. After the amplitude frequency response condition of the system obtained by MLP method and the initial equation calculated numerically, the vibration time response curve and the phase diagram of the suspension system under no-load,full-load and overload conditions were achieved. The results show that with the weight of the train increasing, the initial displacement also increases, but the the vibration of the system tends to be stable in 50 seconds after its starting.
With the vertical motion of maglev train as the research object,the stability of its nonlinear system was studied. In the experiment, the air gap value and current value were selected as the generalized coordinates of the suspension system in the maglev train. By the dynamic model of the nonlinear suspension system established based on Lagrange-Maxwell equation, a third-order strongly nonlinear negative stiffness differential equation was obtained. After the amplitude frequency response condition of the system obtained by MLP method and the initial equation calculated numerically, the vibration time response curve and the phase diagram of the suspension system under no-load,full-load and overload conditions were achieved. The results show that with the weight of the train increasing, the initial displacement also increases, but the the vibration of the system tends to be stable in 50 seconds after its starting.
引文
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[5] 席晓燕,杨志安,李高峰,等.受简谐激励载流导线的强非线性主共振[J].唐山学院学报,2013,26(3):5-7.
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[8] 杨霞,高燕,杨波,等.基于状态空间控制方法的磁悬浮系统稳定性研究[J].组合机床与自动化加工技术,2008(5):40-44.
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[11] 李小保,左鹏,居荣誉.基于MATLAB的机械振动问题的研究[J].科技创新与应用,2016(17):116-116.
[2] 邱家俊.机电分析动力学[M].北京:科学出版社,1992.
[3] YANG Z A,LI W L,QIU J J,et al.Lagrange-Maxwell equation and magnetic saturation parametric resonance of generator set[J].Applied Mathematics & Mechanics,2007,28(11):1545-1553.
[4] 杨志安.基于磁链和电压为广义坐标机电耦合系统动力学方程[J].工程力学,2012,29(5):189-192.
[5] 席晓燕,杨志安,李高峰,等.受简谐激励载流导线的强非线性主共振[J].唐山学院学报,2013,26(3):5-7.
[6] WU L,SU X,SHI P.Fuzzy control of nonlinear electromagnetic suspension systems[J].Mechatronics,2014,24(4):328-335.
[7] 施晓红,龙志强.磁悬浮车轨耦合控制系统的非线性振动特性分析[J].铁道学报,2009,31(4):38-42.
[8] 杨霞,高燕,杨波,等.基于状态空间控制方法的磁悬浮系统稳定性研究[J].组合机床与自动化加工技术,2008(5):40-44.
[9] 陈怀海,贺旭东.振动及其控制[M].北京:国防工业出版社,2015.
[10] 谢元喜.一类强非线性问题的MLP解法[J].湖南人文科技学院学报,2004(2):5-6.
[11] 李小保,左鹏,居荣誉.基于MATLAB的机械振动问题的研究[J].科技创新与应用,2016(17):116-116.