基于MLP法的磁浮列车非线性系统的稳定性分析  

Stability Analysis of Nonlinear Systems in the Maglev Train Based on MLP Method

作　　者：杨志安 崔佳磊 YANG Zhi-an;CUI Jia-lei(Tangshan Key Laboratory of Structure and Vibration Engineering,Tangshan University,Tangshan 063000,China;School of Mechanical Engineering,North China University of Science and Technology,Tangshan 063210,China)

机构地区：[1]唐山学院唐山市结构与振动工程重点实验室,河北唐山063000 [2]华北理工大学机械工程学院,河北唐山063210

出　　处：《唐山学院学报》2019年第3期1-7,共7页Journal of Tangshan University

基　　金：河北省高等学校科学技术研究项目(ZD2017307)

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50s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.

关 键 词：磁浮列车 拉格朗日-麦克斯韦方程 非线性振动 MLP法 

分 类 号：O322[理学—一般力学与力学基础] U266.4[理学—力学]