二轴列车行经序列等跨桥时车辆共振响应分析
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摘要
采用解析方法推导了二轴车通过序列等跨桥梁时车辆共振机理和条件,进而运用列车与桥梁动力分析模型及数值模拟方法来验证共振条件。结合重载铁路实例分析,以研究车辆共振对车桥系统影响规律。由研究结果得到以下几点结论:车辆出现共振现象是由车轮下规则的等跨梁重复性振频与车辆频率(车体点头或沉浮频率)一致而引起,就当前运营的重载列车而言,主共振车速常在正常运营速度之上,而次共振车速会落在列车运行速度范围之内;在车辆发生沉浮和点头主共振和次共振条件下,车辆动力响应和轮轨力将会被明显地放大;尽管车辆共振对桥梁动力响应的影响要比桥梁共振对车辆响应的影响要小,但对于短跨度桥梁而言,车辆共振也会显著加剧桥梁振动响应;当各节车辆均同时达到共振速度时,则会出现整列车出现全体性共振现象,是值得注意之处。
The vehicle resonance mechanism and conditions during a two-axle train passing through sequential equal-span bridges were derived analytically. Then, a simplified planar train-bridge dynamic analysis model and the numerical simulation method were employed to verify resonance conditions. A heavy haul railway system was taken as an example to study the effect laws of vehicle resonance on the vehicle-bridge system. The results showed that vehicle resonance phenomena are caused by the repetitive vibration frequency of sequential equal-span bridges being consistent with vehicle vibration frequency(train body nod or float frequency), for current heavy haul trains, the vehicle speed corresponding to the main resonance is often above the normal train operating speed, while that corresponding to the sub-resonance is within the train running speed range; when the vehicle has the float main resonance and the nod sub-resonance, its dynamic response and the wheel-rail force are amplified significantly; although the effect of vehicle resonance on bridge dynamic response is smaller than that of bridge resonance on vehicle dynamic response, for a short span railway bridge, the vehicle resonance can significantly intensify bridge dynamic response; when each vehicle of a train simultaneously reaches the resonant speed, the whole train resonance phenomenon occurs.
The vehicle resonance mechanism and conditions during a two-axle train passing through sequential equal-span bridges were derived analytically. Then, a simplified planar train-bridge dynamic analysis model and the numerical simulation method were employed to verify resonance conditions. A heavy haul railway system was taken as an example to study the effect laws of vehicle resonance on the vehicle-bridge system. The results showed that vehicle resonance phenomena are caused by the repetitive vibration frequency of sequential equal-span bridges being consistent with vehicle vibration frequency(train body nod or float frequency), for current heavy haul trains, the vehicle speed corresponding to the main resonance is often above the normal train operating speed, while that corresponding to the sub-resonance is within the train running speed range; when the vehicle has the float main resonance and the nod sub-resonance, its dynamic response and the wheel-rail force are amplified significantly; although the effect of vehicle resonance on bridge dynamic response is smaller than that of bridge resonance on vehicle dynamic response, for a short span railway bridge, the vehicle resonance can significantly intensify bridge dynamic response; when each vehicle of a train simultaneously reaches the resonant speed, the whole train resonance phenomenon occurs.
引文
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[2] 李慧乐, 夏禾, 郭薇薇. 移动荷载作用下简支梁共振与消振机理研究[J]. 工程力学, 2013,30(7):47-54. LI Huile,XIA He,GUO Weiwei. Study on mechanism of resonance and vibration cancellation for simply-supported beam under moving loads[J]. Engineering Mechanics,2013, 30(7): 47-54.
[3] 王少钦, 夏禾, 郭薇薇, 等. 变速移动荷载作用下简支梁桥的动力响应及共振分析[J]. 振动与冲击, 2010,29(2):26-30. WANG Shaoqin,XIA He,GUO Weiwei,et al. Dynamic response and resonance analyses for a simply-supported bridge under speed-varying loads[J]. Journal of Vibration and Shock, 2010,29(2):26-30.
[4] YANG Y B, YAU J D. Vertical and pitching resonance of train cars moving over a series of simple beams[J]. Journal of Sound and Vibration, 2015,337:135-149.
[5] 王英杰, 时瑾, 魏庆朝. 单车过桥下弹性车体共振与消振现象分析[J]. 振动与冲击, 2015,34(2):1-8. WANG Yingjie,SHI Jin,WEI Qingchao. Resonance and vibration cancellation analysis of a vehicle with flexible car body moving over multi-span bridge[J]. Journal of Vibration and Shock, 2015,34(2):1-8.
[6] YANG Y B, LIN C W. Vehicle-bridge interaction dynamics and potential applications[J]. Journal of Sound and Vibration, 2005,284(1/2):205-226.
[7] 翟婉明, 王少林. 桥梁结构刚度对高速列车—轨道—桥梁耦合系统动力特性的影响[J]. 中国铁道科学, 2012,33(1):19-26. ZHAI Wanming, WANG Shaolin. Influence of bridge structural stiffness on dynamic characteristics of high speed train track bridge coupling system[J]. China Railway Science, 2012, 33(1): 19-26.
[8] 欧阳冲, 陈应波, 谢伟平, 等. 基于梁段单元法轨道连续箱梁的车桥耦合动力响应分析[J]. 振动与冲击, 2016,35(17):88-94. OUYANG Chong,CHENG Yingbo,XIE Weiping. Dynamic responses of a vehicle-bridge coupled railway box girder system based on beam segment model[J]. Journal of Vibration and Shock, 2016,35(17):88-94.
[9] 夏禾, 张楠, 郭薇薇. 车桥耦合振动工程[M]. 北京: 科学出版社, 2014.
[10] 夏禾, 郭薇薇, 张楠. 车桥系统共振机理和共振条件分析[J]. 铁道学报, 2006,28(5):52-58. XIA He, GUO Weiwei, ZHANG Nan. Resonance mechanism and resonance condition analysis of vehicle bridge system[J]. Railway Transaction, 2006, 28(5): 52-58.
[11] 蔡超勋, 刘吉元, 肖祥淋, 等. 30 t轴重重载货车作用下常用跨度预应力混凝土简支梁动力响应的试验分析[J]. 铁道建筑, 2015(1):1-6. CAI Chaoxun, LIU Jiyuan, XIAO Xianglin, et al. Experimental analysis of dynamic response of prestressed concrete simple supported beam under 30 t axle load heavy haul freight train[J]. Railway Engineering, 2015(1): 1-6.
[12] 梅山, 徐升桥, 沈平, 等. 蒙西至华中地区铁路常用跨度简支梁设计方案比选[J]. 铁道勘察, 2014(2):117-121. MEI Shan, XU Shengqiao, SHEN Ping, et al. Monsey to central China common span simple supported beam railway design scheme comparison[J]. Railway Investigation and Surveying, 2014(2): 117-121.
[13] YANG Y B, YAU J D. Resonance of high-speed trains moving over a series of simple or continuous beams with non-ballasted tracks[J]. Engineering Structures, 2017,143:295-305.