公路桥梁车桥耦合振动分析
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摘要
研究公路桥梁与车辆耦合振动问题具有重要的理论和现实意义。本文将桥梁和车辆视为两个子系统,车辆采用5个自由度的模型,桥梁采用基于梁单元的有限元模型,通过车轮和桥面接触处的几何协调条件和力的平衡条件将两个子系统联系起来；采用三角级数法模拟按国家标准划分的A、B、C和D级路面的不平顺,作为车桥耦合振动的激励输入,根据桥面不平顺及初始条件,形成作用于车辆上的力；采用Newmark-β算法求解车辆系统振动方程,得出车辆的时间～响应序列,并据此形成作用于桥梁上的力。具体实施时,利用有限元软件Ansys的二次开发APDL语言编写了车桥耦合系统迭代计算的命令流,进行车桥耦合系统动力响应计算。本文分析了路面不平顺、车重、车速、车悬架刚度、车悬架阻尼、轮胎刚度、轮胎阻尼、桥梁抗弯刚度、桥梁阻尼比等因素对桥梁动力响应、车辆动力响应、汽车对桥梁的冲击系数、乘客舒适性等的影响,得到如下结论：
1.随着路面等级的降低,桥梁动力响应、车辆动力响应、汽车对桥梁的冲击系数都增大,而乘客的舒适性则急剧降低。
2.随着车速的提高,桥梁跨中动力响应和冲击系数增大,车速对车辆动力响应的影响还与路面状况有关。
3.随着车重的增大,桥梁跨中动力响应先减小后增大；车体竖向振动响应减小。
4.随着车悬架刚度和悬架阻尼的增大,桥梁跨中动力响应、冲击系数增大。
5.随着轮胎刚度的增大,桥梁跨中节点最大动位移、加速度、弯矩的变化趋势为先增大后减小,而跨中最大剪力的变化趋势为增大；除跨中剪力外,桥梁其它跨中动力响应都随轮胎阻尼增大而增加；轮胎刚度和阻尼对冲击系数的影响较小。随着车轮刚度的增大,车体所有动力响应都先减小后增大；随车轮阻尼的增加,汽车所有动力响应都减缓,乘客舒适性有所提高。
6.随桥梁抗弯刚度的增大,桥梁跨中节点动位移和加速度减小,剪力和弯矩增大,汽车对桥梁的冲击系数增加。随着桥梁阻尼比增大,桥梁动力响应均降低,阻尼对汽车冲击系数的影响较小。桥梁抗弯刚度和阻尼对车体动力响应的影响较小,整体趋势是随桥梁抗弯刚度和阻尼的增大,车体动力响应增加,乘客舒适性降低。
本文方法具有很强的通用性,易于考虑复杂车辆和桥梁模型,可以方便进行车桥耦合振动研究。
本文得到了河南省杰出人才计划项目“桥梁健康监测与损伤诊断的整体方法研究”(项目编号：084200510003)的资助。
It is of great theoretical and practical significance to study the highway vehicle-bridge coupling vibration.On the basis of dynamical theory, the vibration differential equations of vehicle model with five degrees of freedom are derived. Road roughness, which is main motivation to vehicle-bridge system, of grade A、B、C and D divided by national standard is simulated by the use of Triangular Series Method. In this thesis, bridge and vehicle are taken as two separate systems, which are connected by the conditions of geometric compatibility and force equilibrium. The forces acting on the vehicle are formed according to roughness and initial condition. Newmark-B method is used to solve the differential equations and to obtain the time-response sequence of vehicle system, and then the forces acting on the bridge are formed according to the results calculated. The large-scale software Ansys for structural analysis is used to calculate the dynamic responses of bridge, and then the forces acting on the vehicle are formed again according to the dynamic responses of bridge and roughness. The command stream, which is compiled by APDL language for secondary development in Ansys, is used to calculate the dynamic responses of vehicle-bridge system. The complicated models of bridge and vehicle can be taken into account by this method, so the method is highly versatile and can make up the deficiencies in previous methods to study the problems of highway vehicle-bridge coupling vibration.
On the basis of the method, the influences of different kinds of factors such as road roughness, vehicle weight, velocity, suspension stiffness and damping, tire stiffness and damping, bridge stiffness and damping on the dynamic responses of bridge and vehicle, vehicle impact factor and the passenger's comfort are analyzed. In the end, some significant conclusions are obtained:
1. With the decrement of road grade, the dynamic responses of the bridge and vehicle and the vehicle impact factor increase doubly, whereas the passenger's comfort decreases significantly.
2. With the increment of vehicle velocity, vehicle impact factor and the dynamic responses in midpoint of the bridge span increase. The effect of the vehicle velocity on vehicle dynamic responses is related to the grade of road irregularity.
3. While the increment of vehicle weight, the dynamic responses in the midpoint of the bridge span decrease first and then increase; the vertica dynamic responses of the vehicle decrease.
4. With the increment of the bridge suspension stiffness and damping, the dynamic responses in the midpoint of the bridge span, vehicle impact factor increase.
5. With tire stiffness increasing, the maximum dynamic displacement, acceleration and bending moment of midspan tend to increase first and then decrease, while the maximum dynamic shear tend to increase; except dynamic shear of midspan, dynamic responses will increase with the augmentation of tire damping. Tire stiffness and damping have little effect on vehicle impact factors. With the increment of tire stiffness, the dynamic responses of vehicle decrease first, and then increase. With the increment of tire damping, the dynamic responses of vehicle decrease and passenger's comfort improves.
6. With the increment of the bridge stiffness, the dynamic displacement and the acceleration in the midpoint of bridge span decrease, the shear force and the bending moment in the midpoint of bridge span increase, and vehicle impact factor increases. With the increment of the bridge damping ratio, the dynamic responses of bridge decrease. The magnitude of damping has little influence on vehicle impact factor. The effect of bridge stiffness and damping on vehicle dynamic responses is small, the overall tendency is that the vehicle dynamic responses increase and passenger's comfort decreases with the increment of the bridge stiffness and damping.
The method has a wide range of application and is able to analyze the coupled vibration of vehicle-bridge of complex vehicle and bridge expediently.
1.随着路面等级的降低,桥梁动力响应、车辆动力响应、汽车对桥梁的冲击系数都增大,而乘客的舒适性则急剧降低。
2.随着车速的提高,桥梁跨中动力响应和冲击系数增大,车速对车辆动力响应的影响还与路面状况有关。
3.随着车重的增大,桥梁跨中动力响应先减小后增大；车体竖向振动响应减小。
4.随着车悬架刚度和悬架阻尼的增大,桥梁跨中动力响应、冲击系数增大。
5.随着轮胎刚度的增大,桥梁跨中节点最大动位移、加速度、弯矩的变化趋势为先增大后减小,而跨中最大剪力的变化趋势为增大；除跨中剪力外,桥梁其它跨中动力响应都随轮胎阻尼增大而增加；轮胎刚度和阻尼对冲击系数的影响较小。随着车轮刚度的增大,车体所有动力响应都先减小后增大；随车轮阻尼的增加,汽车所有动力响应都减缓,乘客舒适性有所提高。
6.随桥梁抗弯刚度的增大,桥梁跨中节点动位移和加速度减小,剪力和弯矩增大,汽车对桥梁的冲击系数增加。随着桥梁阻尼比增大,桥梁动力响应均降低,阻尼对汽车冲击系数的影响较小。桥梁抗弯刚度和阻尼对车体动力响应的影响较小,整体趋势是随桥梁抗弯刚度和阻尼的增大,车体动力响应增加,乘客舒适性降低。
本文方法具有很强的通用性,易于考虑复杂车辆和桥梁模型,可以方便进行车桥耦合振动研究。
本文得到了河南省杰出人才计划项目“桥梁健康监测与损伤诊断的整体方法研究”(项目编号：084200510003)的资助。
It is of great theoretical and practical significance to study the highway vehicle-bridge coupling vibration.On the basis of dynamical theory, the vibration differential equations of vehicle model with five degrees of freedom are derived. Road roughness, which is main motivation to vehicle-bridge system, of grade A、B、C and D divided by national standard is simulated by the use of Triangular Series Method. In this thesis, bridge and vehicle are taken as two separate systems, which are connected by the conditions of geometric compatibility and force equilibrium. The forces acting on the vehicle are formed according to roughness and initial condition. Newmark-B method is used to solve the differential equations and to obtain the time-response sequence of vehicle system, and then the forces acting on the bridge are formed according to the results calculated. The large-scale software Ansys for structural analysis is used to calculate the dynamic responses of bridge, and then the forces acting on the vehicle are formed again according to the dynamic responses of bridge and roughness. The command stream, which is compiled by APDL language for secondary development in Ansys, is used to calculate the dynamic responses of vehicle-bridge system. The complicated models of bridge and vehicle can be taken into account by this method, so the method is highly versatile and can make up the deficiencies in previous methods to study the problems of highway vehicle-bridge coupling vibration.
On the basis of the method, the influences of different kinds of factors such as road roughness, vehicle weight, velocity, suspension stiffness and damping, tire stiffness and damping, bridge stiffness and damping on the dynamic responses of bridge and vehicle, vehicle impact factor and the passenger's comfort are analyzed. In the end, some significant conclusions are obtained:
1. With the decrement of road grade, the dynamic responses of the bridge and vehicle and the vehicle impact factor increase doubly, whereas the passenger's comfort decreases significantly.
2. With the increment of vehicle velocity, vehicle impact factor and the dynamic responses in midpoint of the bridge span increase. The effect of the vehicle velocity on vehicle dynamic responses is related to the grade of road irregularity.
3. While the increment of vehicle weight, the dynamic responses in the midpoint of the bridge span decrease first and then increase; the vertica dynamic responses of the vehicle decrease.
4. With the increment of the bridge suspension stiffness and damping, the dynamic responses in the midpoint of the bridge span, vehicle impact factor increase.
5. With tire stiffness increasing, the maximum dynamic displacement, acceleration and bending moment of midspan tend to increase first and then decrease, while the maximum dynamic shear tend to increase; except dynamic shear of midspan, dynamic responses will increase with the augmentation of tire damping. Tire stiffness and damping have little effect on vehicle impact factors. With the increment of tire stiffness, the dynamic responses of vehicle decrease first, and then increase. With the increment of tire damping, the dynamic responses of vehicle decrease and passenger's comfort improves.
6. With the increment of the bridge stiffness, the dynamic displacement and the acceleration in the midpoint of bridge span decrease, the shear force and the bending moment in the midpoint of bridge span increase, and vehicle impact factor increases. With the increment of the bridge damping ratio, the dynamic responses of bridge decrease. The magnitude of damping has little influence on vehicle impact factor. The effect of bridge stiffness and damping on vehicle dynamic responses is small, the overall tendency is that the vehicle dynamic responses increase and passenger's comfort decreases with the increment of the bridge stiffness and damping.
The method has a wide range of application and is able to analyze the coupled vibration of vehicle-bridge of complex vehicle and bridge expediently.
引文
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[2]卫星,李小珍,李俊,强士中.铁路大跨连续刚构桥动力性能研究[J].振动与冲击,2009,28(11)：118～121
[3]李国豪.桥梁结构稳定与振动(修订版)[M].北京：中国铁道出版社,2003
[4]宋一凡.公路桥梁动力学[M].北京：人民交通出版社,2006
[5]林梅,肖盛燮.桥梁车辆振动分析理论评述[J].重庆交通学院学报,1998,17(3)：1-8
[6]王少钦,岳祖润,马骚.车辆对桥梁动力作用简化方法的研究[J].石家庄铁道学院学报,2005,18(3)：47～51
[7]Leslaw Kwasniewski, Jerry Wekezer, Roufa Carry, etal. Experimental evaluation of dynamic effects for a selected highway bridge [J]. Journal of Performance of Constructed Facilities, 2006,20 (3):253-260
[8]Mitsuo Kawatani, Seiji Nishiyama, Yasunori Yamada. Dynamic response analysis of highway girder bridges under moving vehicles [R]. Technology Reports of the Osaka University 1993,43(2124-41):109-118
[9]Chatterjee P K, Datta T K. Vibration of continues bridges under moving vehicles [J]. Journal of Sound andVibration,1994,169(5):619-632
[10]Green M.F., Cebon D. Dynamic interaction between heavy vehicles and highway bridges [J]. Computers and Structures,1997,62(2):253～264
[11]Wang Ton-Lo, Huang Dong-zhou, Mohsen Shahawy. Dynamic behavior of slant-legged rigid-frame highway bridge [J]. Journal of structural engineering,1994,120 (3):885～ 902
[12]Kou, Jine-Wen, DeWolf, et al. Vibration behavior of continuous span highway bridge-influ-encing variables [J]. Journal of structural engineering,1997,123(3):333～344
[13]Elkasem N.Z. Abu, Abdel-Mooty M.A., Mourad S.A. Dynamic response of highway bridges to moving vehicles considering higher modes [J]. Journal of Engineering and Applied Science,2009,56(1):21-38
[14]Da Silva J.G.S. Dynamical performance of highway bridge decks with irregular pavement surface [J]. Computers and Structures,2004,82(11-12):871～881
[15]Nishiyama, Shuji. Research on vibration characteristics of vehicle-passenger dynamic interaction on highway bridge induced by large-sized vehicle [J]. Nippon Kikai Gakkai Ronbunshu C Hen,1994,60(569):16～23
[16]Green M.F., Cebon D. Dynamic response of highway bridges to heavy vehicle loads: Theory and experimental validation [J]. Journal of Sound and Vibration,1994,170(1): 51-78
[17]王晓臣.移动荷载作用下梁桥动力响应的数值分析[D].杭州：浙江工业大学,2008
[18]孙韦.车辆荷载作用下连续梁桥的动力响应研究[D].西安：长安大学,2009
[19]陈炎,黄小清,马友发.车桥系统的耦合振动[J].应用数学和力学,2004,25(4)：354～358
[20]袁明.高墩大垮连续刚构桥的车桥系统耦合振动分析[D].长沙：长沙理工大学,2005
[21]刘钰.特殊行车状态下的车桥耦合振动研究[D].成都：西南交通大学,2008
[22]陈姣.移动荷载作用下桥梁的车桥耦合振动分析[D].合肥：合肥工业大学,2009
[23]刘福寿.基于车桥耦合振动的混凝土简支梁桥动力特性研究[D].长春：吉林大学,2009
[24]谭国辉.桥梁与车辆相互作用的系统模拟[J].土木工程学报,1996,29(3)：34-42
[25]张洁.公路车辆与桥梁耦合振动分析研究[D].成都：西南交通大学,2007
[26]吴启宏.公路钢筋混凝土简支梁桥在移动荷载下的竖向振动[J].公路交通科技,1989,(1)：25～32
[27]吴启宏.动力系数的影响因素试验研究[J].中国公路学报,1991,4(2)：57-64
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