轨道不平顺激励下悬浮隧道车隧耦合振动响应分析
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摘要
悬浮隧道是悬浮在水下一定深度的新型封闭式交通结构物。为分析轨道不平顺激励下水中悬浮隧道车隧耦合振动特性,将行驶车辆和悬浮隧道分别抽象为弹簧-质量车和离散弹性支撑梁,并结合Morison方程考虑流体附加惯性效应和阻尼效应,建立悬浮隧道车隧耦合振动微分控制方程。基于MATLAB采用四阶龙格-库塔法求解悬浮隧道在轨道不平顺激励下的车隧耦合振动响应。计算结果表明:悬浮隧道车隧耦合振动同时受到轨道不平顺和流体作用效应的影响。基于数值计算结果,考虑流体作用效应的结构位移响应有3%左右的增加;而在轨道不平顺激励下,考虑耦合振动的结构位移响应平均有5%～10%的增加。其次,锚索刚度对在轨道不平顺激励下结构位移响应具有抑制作用。具有较大锚索刚度的悬浮隧道对轨道不平顺更敏感,局部振动更剧烈。再者,快速行驶车辆在高干扰轨道激励下使耦合系统发生更强烈的振动,可通过控制车辆行驶轨道的平顺度以降低高速通行要求下产生的车隧耦合振动影响。
Submerged floating tunnel( SFT) is a novel closed traffic structure suspended under water. Here,in order to analyze vehicle-tunnel coupled vibration responses of a SFT due to track irregularities,it was simplified as a spatial beam on discrete elastic supports with a spring-mass vehicle moving on it. Considering fluid added inertia effect and damping effect with Morison equation,the governing dynamic differential equations for vehicle-tunnel coupled vibration responses of the SFT due to track irregularities were established. Adopting the fourth-order Runge-Kutta method based on MATLAB,these dynamic differential equations were numerically solved. The results showed that the vehicletunnel coupled vibration responses of the SFT are affected by both track irregularities and fluid effects; the structure displacement responses due to fluid effects increase by about 3%; the structure displacement responses due to track irregularities increase by about 5% to 10%; besides,the tether stiffness can suppress the structure displacement responses under excitation of track irregularities, the SFT with larger tether stiffness is more sensitive to track irregularities,and its local vibration is more acute; furthermore,the fast moving vehicle may cause more intensive vibration of the coupled system under excitation of track with larger irregularities,to control track irregularities can reduce the effects of vehicle-tunnel coupled vibration of the SFT on moving vehicles with high velocity.
Submerged floating tunnel( SFT) is a novel closed traffic structure suspended under water. Here,in order to analyze vehicle-tunnel coupled vibration responses of a SFT due to track irregularities,it was simplified as a spatial beam on discrete elastic supports with a spring-mass vehicle moving on it. Considering fluid added inertia effect and damping effect with Morison equation,the governing dynamic differential equations for vehicle-tunnel coupled vibration responses of the SFT due to track irregularities were established. Adopting the fourth-order Runge-Kutta method based on MATLAB,these dynamic differential equations were numerically solved. The results showed that the vehicletunnel coupled vibration responses of the SFT are affected by both track irregularities and fluid effects; the structure displacement responses due to fluid effects increase by about 3%; the structure displacement responses due to track irregularities increase by about 5% to 10%; besides,the tether stiffness can suppress the structure displacement responses under excitation of track irregularities, the SFT with larger tether stiffness is more sensitive to track irregularities,and its local vibration is more acute; furthermore,the fast moving vehicle may cause more intensive vibration of the coupled system under excitation of track with larger irregularities,to control track irregularities can reduce the effects of vehicle-tunnel coupled vibration of the SFT on moving vehicles with high velocity.
引文
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[18]张嫄,董满生,唐飞.冲击荷载作用下水中悬浮隧道的位移响应[J].应用数学和力学,2016,37(5):483-491.ZHANG Yuan,DONG Mansheng,TANG Fei.Displacement response of submerged floating tunnels under impact loads[J].Applied Mathematics and Mechanics,2016,37(5):483-491.
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[2]项贻强,薛静平.悬浮隧道在国内外的研究[J].中外公路,2002,22(6):49-52.XIANG Yiqiang,XUE Jingping.Study on submerged floating tunnels in the world[J].Journal of China&Foreign highway,2002,22(6):49-52.
[3]REMSETH S,LEIRA B J,OKSTAD K M,et al.Dynamic response and fluid/structure interaction of submerged floating tunnels[J].Computers&Structures,1999,72(4/5):659-685.
[4]麦继婷,杨显成,关宝树.悬浮隧道在波浪作用下的动力响应分析[J].铁道工程学报,2007,24(3):45-49.MAI Jiting,YANG Xiancheng,GUAN Baoshu.Dynamic response analysis of the submerged floating tunnel subjected to wave[J].Journal of Railway Engineering Society,2007,24(3):45-49.
[5]SATO M,KANIE S,MIKAMI T.Structural modeling of beams on elastic foundations with elasticity couplings[J].Mechanics Research Communications,2007,34(5):451-459.
[6]葛斐,惠磊,洪友士.波浪场中水中悬浮隧道动力响应的研究[J].工程力学,2008,25(6):188-194.GE Fei,HUI Lei,HONG Youshi.Research on dynamic response of submerged floating tunnel to regular wave forces[J].Engineering Mechanics,2008,25(6):188-194.
[7]晁春峰,项贻强,杨超.悬浮隧道锚索流固耦合振动试验研究[J].振动与冲击,2016,35(3):158-163.CHAO Chunfeng,XIANG Yiqiang,YANG Chao.Experiments on dynamic fluid-structure coupled response of anchor cables of submerged floating tunnel[J].Journal of Vibration and Shock,2016,35(3):158-163.
[8]TARIVERDILO S,MIRZAPOUR J,SHAHMARDANI M,et al.Vibration of submerged floating tunnels due to moving loads[J].Applied Mathematical Modelling,2011,35(11):5413-5425.
[9]董满生,张嫄,唐飞,等.等间距移动荷载作用下水中悬浮隧道管体的位移响应[J].应用力学学报,2016,33(5):760-765.DONG Mansheng,ZHANG Yuan,TANG Fei,et al.Displacement response of submerged floating tunnel tube due to moving loads of constant intervals[J].Chinese Journal of Applied Mechanics,2016,33(5):760-765.
[10]叶茂,张鹏,傅继阳,等.带弹性支撑多跨连续梁桥的车桥耦合演变随机振动[J].振动与冲击,2014,33(3):76-82.YE Mao,ZHANG Peng,FU Jiyang,et al.Coupled vehiclebridge evolutionary random vibration for a multi-span continuous bridge with elastic bearings[J].Journal of Vibration and Shock,2014,33(3):76-82.
[11]陈健云,王变革,孙胜男.悬浮隧道锚索的涡激动力响应分析[J].工程力学,2007,24(10):186-192.CHEN Jianyun,WANG Biange,SUN Shengnan.Analysis of vortex-induced dynamic response for the anchor cable of submerged floating tunnel[J].Engineering Mechanics,2007,24(10):186-192.
[12]项贻强,晁春峰.悬浮隧道管体及锚索耦合作用的涡激动力响应[J].浙江大学报(工学版),2012(3):409-415.XIANG Yiqiang.CHAO Chunfeng.Vortex-induced dynamic response for combined action of tube and cable of submerged floating tunnel[J].Journal of Zhejiang University(Engineering Science),2012(3):409-415.
[13]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 analysis for a simply-supported bridge under speed-varying loads[J].Journal of Vibration and Shock,2010,29(2):26-30.
[14]孙胜男.悬浮隧道动力响应分析[D].大连:大连理工大学,2008.
[15]JOHN H M,KURTIS D F.Numerical methods using MATLAB[M].Beijing:Publishing House of Electronics Industry,2005.
[16]魏冲锋.轨道不平顺功率谱时域转换及其应用研究[D].成都:西南交通大学,2011.
[17]刘寅华,李芾,黄运华.轨道不平顺数值模拟方法[J].交通运输工程学报,2006,6(1):29-33.LIU Yinhua,LI Fu,HUANG Yunhua.Numerical simulation methods of railway track irregularities[J].Journal of Traffic and Transportation Engineering,2006,6(1):29-33.
[18]张嫄,董满生,唐飞.冲击荷载作用下水中悬浮隧道的位移响应[J].应用数学和力学,2016,37(5):483-491.ZHANG Yuan,DONG Mansheng,TANG Fei.Displacement response of submerged floating tunnels under impact loads[J].Applied Mathematics and Mechanics,2016,37(5):483-491.
[19]晁春峰.悬浮隧道流固耦合动力响应分析及试验研究[D].杭州:浙江大学,2013.
[20]FAGGIANO B,MAZZOLANI F M,LANDOIFO R.Design and modeling aspects concerning the submerged floating tunnel:an application to the Messina Strait crossing[C]∥Strait Crossing 2001.Krobeborg:Swets&Zeitlinger Publishers Lisse,2001.
[21]秦银钢,周生国,周晓军.多跨悬浮隧道合理支撑间距分析[J].铁道工程学报,2008,25(3):78-81.QIN Yingang,ZHOU Shengguo,ZHOU Xiaojun.Analysis of the reasonable support length for multi-spans submerged floating tunnel[J].Journal of Railway Engineering Society,2008,25(3):78-81.