风及列车荷载作用下大跨度桥梁振动响应研究
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摘要
大跨度桥梁由于柔度很大,对风荷载非常敏感,在风的动力作用下会产生较大的变形和振动。在沿江、沿海这些风速较大的地区修建跨江、跨海铁路大桥时,必须综合考虑风和列车荷载对桥梁的动力作用,以确保桥梁结构及列车运行安全。随着桥梁跨度的增大,非线性因素也愈加明显,这就给本已经非常复杂的风-车-桥系统研究增加了难度。本文在综合国内外关于车桥耦合振动及桥梁抗风研究的基础上,考虑大跨度桥梁的几何非线性因素,建立了风-列车-桥梁体系非线性动力分析模型,以综合考虑风荷载和列车荷载对桥梁的动力作用。全文内容主要包括以下五部分内容：
1.结合国内外大跨度桥梁的修建情况,对不同结构型式的大跨度桥梁发展史及现状进行综述,回顾了车桥系统动力相互作用、桥梁风致振动以及各种型式大跨度桥梁的非线性研究情况。总结了当前研究的特点,在此基础上阐述了将风、列车和桥梁统一为一个交互作用、协调工作的耦合振动系统进行研究的必要性。
2.研究了列车变速行驶情况下的车桥耦合振动问题,通过共振曲线解释了车辆变速运行时桥梁位移极值的变化规律。计算结果表明,车辆变速行驶与匀速行驶时相比较,桥梁的位移时程曲线振动趋势没有变化,桥梁的最大位移相差也很小,因此为简化计算,不必考虑车辆的变速作用。
3.通过分析脉动风的特性,采用谐波叠加法对大跨度桥梁的风场进行模拟,考虑作用在桥梁上的静风力、抖振风力和自激风力,作用在车辆上的静风力和抖振风力,采用具有27个自由度的四轴列车车辆模型,分别建立了桥梁广义坐标及考虑非线性因素的动力分析模型,形成了风-列车-桥梁系统相互作用分析模型,编制了相应计算程序,并简单介绍了编程过程中能够提高计算效率的一些技巧。
4.将所建立的风-车-桥模型应用于九江长江大桥三拱连续钢桁梁部分的动力响应研究。对桥梁进行模态分析,得到了其各阶自振频率及主梁节点振型。通过逐步施加不同的风荷载,计算了静风荷载和脉动风荷载对桥梁的作用效应；分析了风速变化对桥梁振动时程曲线及振动响应极值的影响；综合考虑了风速变化和列车速度对桥梁振动的影响。通过计算得出以下结论：
(1)静风荷载使桥梁位移偏向一侧,而脉动风荷载使其在静风位移的基础上呈现波动趋势；
(2)桥梁的竖向位移极值随着风速的增加而减小,横向及扭转位移极值均随着风速的增加而增大,桥梁的振动加速度均随着风荷载的增加而加剧；
(3)车速及风速变化对桥梁的振动响应极值均有较大影响。
5.以移动车轮-簧上质量的车辆模型为基础,考虑桥梁结构的位移与应变的非线性关系,推导了简支梁桥广义坐标下的动力平衡微分方程,采用Newmark积分与直接迭代法进行求解,并以某公路简支梁桥为例进行计算验证。在此基础上探讨了非简支梁桥在列车移动荷载作用下的非线性振动响应研究方法,作为后面采用复杂车辆模型作用下大跨度桥梁非线性振动计算的基础研究。计算了九江长江大桥吊杆初始内力及结构大位移非线性的影响。然后考虑悬索桥结构的几何非线性因素,以主跨1120m的五峰山悬索桥设计方案为例,进行了风车桥非线性振动响应计算。研究了非线性因素、风速与车速变化对悬索桥振动的影响,并与九江长江大桥大跨度钢桁拱桥振动响应进行比较。通过计算得到以下结论：
(1)悬索桥缆索结构在自重和恒载下的初始内力会明显增大结构刚度,使其各阶自振频率提高,但不影响其振型。
(2)悬索桥结构的几何非线性因素没有改变桥梁节点位移及加速度时程曲线变化趋势,但由于几何刚度的存在,使各项振动响应极值有所减小；
(3)静风荷载使桥梁结构向一侧偏移,脉动风荷载使其在静风位移的基础上产生波动,风荷载产生的作用效应对九江长江大桥和五峰山悬索桥的一致；
(4)风速增加后,悬索桥的振动呈加剧趋势,风速变化对其横向及扭转位移、加速度产生很大影响。当风速增大到一定程度时,会使悬索桥的竖向振动加剧,对其竖向振动响应也产生较大影响,这点与九江长江大桥的计算结果不同；
(5)车速变化对桥梁的各项振动响应均有所影响,特别是对桥梁竖向位移的影响比较明显。而横向、扭转位移及加速度则对风速变化比较敏感。
(6)大位移非线性的影响会随着位移的急剧增大更加明显,但非线性误差与位移值并不成线性关系。
Long-span bridges are so susceptible to wind actions due to their high flexibility characteristic that large displacement and vibration will be induced with the action of strong wind loads. If a railway bridge is built to span river or sea, its dynamic response to the action of wind and train should be studied to ensure the safety of bridge structure and the running train. Furthermore, the nonlinear characteristics will be more and more obvious with the increase of bridge span, which further adds the difficulty of analysis for the coupled wind-train-bridge system. Based on the research background review of the dynamic interaction of bridge with running train and the wind induced vibrations of long-span bridges, a nonlinear wind-train-bridge model is established considering the geometric nonlinearities of the long-span bridge, and a corresponding computer code is written. In this way, the dynamic actions of both wind and running train to the long-span bride are studied synthetically. The main contents of this paper are as following:
1. The current construction state and the current study of long-span bridges in the world are summarized, including a review of the rapid development of long span bridges with different style, the research background of the dynamic interaction of bridge with running trains, the wind-induced vibrations of bridges, and the nonlinear analysis of long-span bridges. The significance and necessary of studying this problem by regarding the wind, running train and long-span bridge to a coupled system are set out.
2. The effect of train speed varying is studied based on the coupling vibration of train and bridge system. The distribution curve of the bridge maximum deflection versus vehicle speed is given, with which the varying tendency of maximum displacement with speed varying is explained. The calculated results show that the tendency of the bridge displacement time history does not change when the train runs with varying speed, and the values of the maximum displacements have little difference. Therefore, for simplification of study, the speed varying of train can be ignored.
3. The dynamic characteristics of fluctuating winds are analyzed. Wind forces, including steady-state, buffeting and self-excited forces acting on the bridge, and steady-state, buffeting ones acting on the train, are simulated in time domain by harmonic superposition technique. A dynamic model of wind-train-bridge system is established, by considering27degrees-of-freedom for the4-axle train, and adopting the modal superposition technique for the bridge model, while the geometric nonlinearity is considering further. The framework for solving the coupled dynamic train-bridge system subjected to wind action is proposed. A computer code is written, and some skills in writing the code are introduced.
4. The proposed framework is then applied to a real long-span steel truss arch bridge across the Jiujiang River. The natural frequencies and node modes of the bridge are gained via modal analysis. The effect of static wind loads and fluctuating wind loads are calculated through applying different wind loads. The dynamic responses of the bridge are calculated with different wind velocity, and the influences of wind velocity and train speed are synthetically analyzed. The conclusions obtained are given below:
(1) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement.
(2) The vertical displacements reduce with increase of wind velocity, while the lateral and torsional displacements increase, and the accelerations of the bridge in both directions increase with wind velocity.
(3) Both train speed and wind velocity have great influence on the dynamic responses of the bridge.
5. Considering the nonlinear relation between displacement and strain, a dynamic model of simply-supported bridge with moving wheel-sprung mass is established, and the dynamic differential equations of bridge with generalized coordinates are derived, which is solved by the Newmark numerical integration and the direct interactive method. The proposed analysis model is validated with a real highway bridge. On this basis, the analysis method is investigated for nonlinear dynamic responses of non-simply-supported bridges subjected to running train, which is the basic study for the nonlinear analysis of complex train model and long-span bridge. The influence of initial force in the hangers and large displacement effect of the Jiujiang Yangtze River Bridge are calculated. By taking the Wufengshan suspension bridge with the main span1120m as an example, and considering the geometric nonlinear characteristics of the long-span suspension bridge, the nonlinear dynamic responses of wind-train-bridge system are analyzed. The influences of structure geometric nonlinearity, wind velocity and train speed are analyzed, and are compared with those of the Jiujiang steel arch bridge. The corresponding conclusions are as following:
(1) The initial forces of gravity and dead load in the main cable and·suspenders may increase the structural stiffness and the frequencies of the bridge, but not influence its vibration, modes.
(2) The geometric nonlinearity of the structure does not influence the shape of bridge displacement and acceleration histories, but reduces the maximum values of the responses.
(3) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement. The wind load effect to the Wufengshan suspension bridge is the same to the Jiujiang steel arch bridge.
(4) The bridge vibration will be exacerbated under higher wind velocity. The lateral and torsional displacements and accelerations are affected significantly by wind velocity. The vertical responses will be exacerbated when the wind velocity is high enough, which is different to the results of the Jiujiang steel arch bridge.
(5) Train speed has certain influences on the dynamic response of the bridge, and especially the influence to the vertical displacement is obvious. While the lateral and torsional displacements and accelerations are more sensitive to the wind velocity.
(6) Influence of the large displacement increases with the bridge displacement, but it is not a linear relation between the nonlinear error and displacement.
1.结合国内外大跨度桥梁的修建情况,对不同结构型式的大跨度桥梁发展史及现状进行综述,回顾了车桥系统动力相互作用、桥梁风致振动以及各种型式大跨度桥梁的非线性研究情况。总结了当前研究的特点,在此基础上阐述了将风、列车和桥梁统一为一个交互作用、协调工作的耦合振动系统进行研究的必要性。
2.研究了列车变速行驶情况下的车桥耦合振动问题,通过共振曲线解释了车辆变速运行时桥梁位移极值的变化规律。计算结果表明,车辆变速行驶与匀速行驶时相比较,桥梁的位移时程曲线振动趋势没有变化,桥梁的最大位移相差也很小,因此为简化计算,不必考虑车辆的变速作用。
3.通过分析脉动风的特性,采用谐波叠加法对大跨度桥梁的风场进行模拟,考虑作用在桥梁上的静风力、抖振风力和自激风力,作用在车辆上的静风力和抖振风力,采用具有27个自由度的四轴列车车辆模型,分别建立了桥梁广义坐标及考虑非线性因素的动力分析模型,形成了风-列车-桥梁系统相互作用分析模型,编制了相应计算程序,并简单介绍了编程过程中能够提高计算效率的一些技巧。
4.将所建立的风-车-桥模型应用于九江长江大桥三拱连续钢桁梁部分的动力响应研究。对桥梁进行模态分析,得到了其各阶自振频率及主梁节点振型。通过逐步施加不同的风荷载,计算了静风荷载和脉动风荷载对桥梁的作用效应；分析了风速变化对桥梁振动时程曲线及振动响应极值的影响；综合考虑了风速变化和列车速度对桥梁振动的影响。通过计算得出以下结论：
(1)静风荷载使桥梁位移偏向一侧,而脉动风荷载使其在静风位移的基础上呈现波动趋势；
(2)桥梁的竖向位移极值随着风速的增加而减小,横向及扭转位移极值均随着风速的增加而增大,桥梁的振动加速度均随着风荷载的增加而加剧；
(3)车速及风速变化对桥梁的振动响应极值均有较大影响。
5.以移动车轮-簧上质量的车辆模型为基础,考虑桥梁结构的位移与应变的非线性关系,推导了简支梁桥广义坐标下的动力平衡微分方程,采用Newmark积分与直接迭代法进行求解,并以某公路简支梁桥为例进行计算验证。在此基础上探讨了非简支梁桥在列车移动荷载作用下的非线性振动响应研究方法,作为后面采用复杂车辆模型作用下大跨度桥梁非线性振动计算的基础研究。计算了九江长江大桥吊杆初始内力及结构大位移非线性的影响。然后考虑悬索桥结构的几何非线性因素,以主跨1120m的五峰山悬索桥设计方案为例,进行了风车桥非线性振动响应计算。研究了非线性因素、风速与车速变化对悬索桥振动的影响,并与九江长江大桥大跨度钢桁拱桥振动响应进行比较。通过计算得到以下结论：
(1)悬索桥缆索结构在自重和恒载下的初始内力会明显增大结构刚度,使其各阶自振频率提高,但不影响其振型。
(2)悬索桥结构的几何非线性因素没有改变桥梁节点位移及加速度时程曲线变化趋势,但由于几何刚度的存在,使各项振动响应极值有所减小；
(3)静风荷载使桥梁结构向一侧偏移,脉动风荷载使其在静风位移的基础上产生波动,风荷载产生的作用效应对九江长江大桥和五峰山悬索桥的一致；
(4)风速增加后,悬索桥的振动呈加剧趋势,风速变化对其横向及扭转位移、加速度产生很大影响。当风速增大到一定程度时,会使悬索桥的竖向振动加剧,对其竖向振动响应也产生较大影响,这点与九江长江大桥的计算结果不同；
(5)车速变化对桥梁的各项振动响应均有所影响,特别是对桥梁竖向位移的影响比较明显。而横向、扭转位移及加速度则对风速变化比较敏感。
(6)大位移非线性的影响会随着位移的急剧增大更加明显,但非线性误差与位移值并不成线性关系。
Long-span bridges are so susceptible to wind actions due to their high flexibility characteristic that large displacement and vibration will be induced with the action of strong wind loads. If a railway bridge is built to span river or sea, its dynamic response to the action of wind and train should be studied to ensure the safety of bridge structure and the running train. Furthermore, the nonlinear characteristics will be more and more obvious with the increase of bridge span, which further adds the difficulty of analysis for the coupled wind-train-bridge system. Based on the research background review of the dynamic interaction of bridge with running train and the wind induced vibrations of long-span bridges, a nonlinear wind-train-bridge model is established considering the geometric nonlinearities of the long-span bridge, and a corresponding computer code is written. In this way, the dynamic actions of both wind and running train to the long-span bride are studied synthetically. The main contents of this paper are as following:
1. The current construction state and the current study of long-span bridges in the world are summarized, including a review of the rapid development of long span bridges with different style, the research background of the dynamic interaction of bridge with running trains, the wind-induced vibrations of bridges, and the nonlinear analysis of long-span bridges. The significance and necessary of studying this problem by regarding the wind, running train and long-span bridge to a coupled system are set out.
2. The effect of train speed varying is studied based on the coupling vibration of train and bridge system. The distribution curve of the bridge maximum deflection versus vehicle speed is given, with which the varying tendency of maximum displacement with speed varying is explained. The calculated results show that the tendency of the bridge displacement time history does not change when the train runs with varying speed, and the values of the maximum displacements have little difference. Therefore, for simplification of study, the speed varying of train can be ignored.
3. The dynamic characteristics of fluctuating winds are analyzed. Wind forces, including steady-state, buffeting and self-excited forces acting on the bridge, and steady-state, buffeting ones acting on the train, are simulated in time domain by harmonic superposition technique. A dynamic model of wind-train-bridge system is established, by considering27degrees-of-freedom for the4-axle train, and adopting the modal superposition technique for the bridge model, while the geometric nonlinearity is considering further. The framework for solving the coupled dynamic train-bridge system subjected to wind action is proposed. A computer code is written, and some skills in writing the code are introduced.
4. The proposed framework is then applied to a real long-span steel truss arch bridge across the Jiujiang River. The natural frequencies and node modes of the bridge are gained via modal analysis. The effect of static wind loads and fluctuating wind loads are calculated through applying different wind loads. The dynamic responses of the bridge are calculated with different wind velocity, and the influences of wind velocity and train speed are synthetically analyzed. The conclusions obtained are given below:
(1) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement.
(2) The vertical displacements reduce with increase of wind velocity, while the lateral and torsional displacements increase, and the accelerations of the bridge in both directions increase with wind velocity.
(3) Both train speed and wind velocity have great influence on the dynamic responses of the bridge.
5. Considering the nonlinear relation between displacement and strain, a dynamic model of simply-supported bridge with moving wheel-sprung mass is established, and the dynamic differential equations of bridge with generalized coordinates are derived, which is solved by the Newmark numerical integration and the direct interactive method. The proposed analysis model is validated with a real highway bridge. On this basis, the analysis method is investigated for nonlinear dynamic responses of non-simply-supported bridges subjected to running train, which is the basic study for the nonlinear analysis of complex train model and long-span bridge. The influence of initial force in the hangers and large displacement effect of the Jiujiang Yangtze River Bridge are calculated. By taking the Wufengshan suspension bridge with the main span1120m as an example, and considering the geometric nonlinear characteristics of the long-span suspension bridge, the nonlinear dynamic responses of wind-train-bridge system are analyzed. The influences of structure geometric nonlinearity, wind velocity and train speed are analyzed, and are compared with those of the Jiujiang steel arch bridge. The corresponding conclusions are as following:
(1) The initial forces of gravity and dead load in the main cable and·suspenders may increase the structural stiffness and the frequencies of the bridge, but not influence its vibration, modes.
(2) The geometric nonlinearity of the structure does not influence the shape of bridge displacement and acceleration histories, but reduces the maximum values of the responses.
(3) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement. The wind load effect to the Wufengshan suspension bridge is the same to the Jiujiang steel arch bridge.
(4) The bridge vibration will be exacerbated under higher wind velocity. The lateral and torsional displacements and accelerations are affected significantly by wind velocity. The vertical responses will be exacerbated when the wind velocity is high enough, which is different to the results of the Jiujiang steel arch bridge.
(5) Train speed has certain influences on the dynamic response of the bridge, and especially the influence to the vertical displacement is obvious. While the lateral and torsional displacements and accelerations are more sensitive to the wind velocity.
(6) Influence of the large displacement increases with the bridge displacement, but it is not a linear relation between the nonlinear error and displacement.
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