基于格林函数法的铁道车辆弹性车体垂向振动分析
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摘要
铁道车辆车体弹性共振机理的确定对车体弯曲频率的设计及车辆运行平稳性的改善有重要意义。为研究车体垂向弹性共振机理,建立包含车体弹性的铁道车辆垂向刚柔耦合系统动力学模型,提出基于格林函数法的车辆系统运动偏微分方程求解方法,计算获得车体振动加速度功率谱及车辆运行平稳性,分析几何滤波与车体弹性共振的关系。结果表明,与传统的模态叠加法相比,格林函数法可以实现车体全模态的"一次运算",并且能够反映出弹性车体全频带的振动特性,这对研究及预测车体高频振动特性极具意义;平稳性指标频率权重在高频处较低,采用模态截断的方法评价车辆运行平稳性是合理的。结果还表明,车体弹性共振与车辆运行速度及几何滤波密切相关,车体的弯曲频率仅依据构架浮沉自振频率设计是不完善的,应该辅以考虑几何滤波现象的影响。
Confirming of resonance mechanism of flexible car body is important for car body bending frequencies design and ride quality improvement of railway vehicle.To research the fundamental reasons of resonance of flexible car body,a vertical rigid-flexible coupling dynamic model of railway vehicle which includes the flexibility of car body is established,Green functions are applied to solve the partial differential equations of the dynamic system,the power spectrum densities of acceleration of car body and ride quality are calculated,the relationship between geometry filtering phenomenon and resonance of flexible car body is studied.Results show that comparing with the conventional mode superposition method,Green functions method can realize ‘one-time calculation’ of the whole modes of car body,and can present the vibrations of flexible car body in whole frequency bands,which is significant for studying and predicting the vibration performance of car body at high frequencies.Since frequency weighting of ride quality index in high frequency is low,it is reasonable to evaluate vertical ride quality by utilizing modal truncation method.Results also show that resonance of flexible car body is closely related to the vehicle running speed and geometry filtering phenomenon,the design of car body vertical bending frequencies only based on the frame bounce frequency is incomplete,it is supposed to take the influences of geometry filtering phenomenon into consideration.
Confirming of resonance mechanism of flexible car body is important for car body bending frequencies design and ride quality improvement of railway vehicle.To research the fundamental reasons of resonance of flexible car body,a vertical rigid-flexible coupling dynamic model of railway vehicle which includes the flexibility of car body is established,Green functions are applied to solve the partial differential equations of the dynamic system,the power spectrum densities of acceleration of car body and ride quality are calculated,the relationship between geometry filtering phenomenon and resonance of flexible car body is studied.Results show that comparing with the conventional mode superposition method,Green functions method can realize ‘one-time calculation’ of the whole modes of car body,and can present the vibrations of flexible car body in whole frequency bands,which is significant for studying and predicting the vibration performance of car body at high frequencies.Since frequency weighting of ride quality index in high frequency is low,it is reasonable to evaluate vertical ride quality by utilizing modal truncation method.Results also show that resonance of flexible car body is closely related to the vehicle running speed and geometry filtering phenomenon,the design of car body vertical bending frequencies only based on the frame bounce frequency is incomplete,it is supposed to take the influences of geometry filtering phenomenon into consideration.
引文
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[2]项彦勇,郭家奇.分布热源作用下裂隙岩体渗流-热传的拉氏变换-格林函数半解析计算方法[J].岩土力学,2011,32(2):333-340.XIANG Yanyong,GUO Jiaqi.A laplace transform andGreen function method for calculation of water flow andheat transfer in fractured rocks[J].Rock and SoilMechanics,2011,32(2):333-340.
[3]NICHOLSON J W,BERGMAN L A.Free vibration ofcombined dynamical systems[J].Journal of EngineeringMechanics,1986,112(1):1-13.
[4]BERGMAN L A,NICHOLSON J W.Forced vibration ofa damped combined linear system[J].Journal ofVibration,Acoustics,Stress,and Reliability in Design,1985,107(3):275-281.
[5]周劲松,宫岛,孙文静,等.铁道客车车体垂向弹性对运行平稳性的影响[J].铁道学报,2009,31(2):32-37.ZHOU Jinsong,GONG Dao,SUN Wenjing,et al.Influence of vertical elasticity of car body of railwaypassenger vehicles on ride quality[J].Journal of the ChinaRailway Society,2009,31(2):32-37.
[6]SUZUKI Y,AKUTSU K.Theoretical analysis of flexuralvibration of car body[J].Quarterly Report of RTRI,1990,31(1):42-48.
[7]ABU-HILAL M.Forced vibration of Euler-Bernoullibeams by means of dynamic green functions[J].Journalof Sound and Vibration,2003,267(2):191-207.
[8]王福天,周劲松,任利惠.用于高速车辆动态仿真的轨道谱分析[J].铁道学报,2002,24(5):21-27.WANG Futian,ZHOU Jinsong,REN Lihui.Analysis ontrack spectrum density for dynamic simulations of highspeed vehicles[J].Journal of the China Railway Society,2002,24(5):21-27.
[9]宫岛,周劲松,孙文静,等.高速列车弹性车体垂向振动控制[J].机械工程学报,2011,47(20):159-164.GONG Dao,ZHOU Jinsong,SUN Wenjing,et al.Verticalvibration control of flexible high-speed railway carbody[J].Journal of Mechanical Engineering,2011,47(20):159-164.
[10]GARG V K,DUKKIPATI R V.Dyanmics of railwayvehicle systems[M].New York:Academic Press,1984.
[11]GONG Dao,ZHOU Jinsong,SUN Wenjing.On theresonant vibration of a flexible railway car body and itssuppression with a dynamic vibration absorber[J].Journalof Vibration and Control,2013,19(5):648-657.
[12]International Union of Railways.UIC 566 Loadings ofcoach bodies and their components[S].3rd ed.Paris:Railway Technical Publications ETF,1990.
[13]European Committee for Standardization.EN12663-1:2010(E)Railway applications-structural requirements ofrailway vehicle bodies[M].London:British StandardsInstitution,2010.
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