跨座式单轨交通曲线梁桥车桥耦合振动分析
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摘要
跨座式单轨交通是一种新型的城市轨道交通型式,具有爬坡能力强、适应城市复杂地形的优点,特别适用于地面起伏较大的山区城市。该交通系统以高架线路和曲线线形为主,其轨道梁既是承重结构,又是车辆运行的轨道；车辆采用橡胶轮转向架,其运行、导向机理和轮轨接触关系均不同于传统的钢轮一钢轨制式轨道交通系统,因而其车桥动力相互作用具有独特之处。目前,国内外对跨座式单轨交通动力性能的研究仅局限于分析直线梁桥的车桥动力作用,车桥耦合振动理论还不完善,影响了这项新技术的进一步推广应用。本文以重庆市跨座式单轨交通较新线Ⅰ期工程为依托,推导并建立了跨座式单轨交通曲线梁桥的车桥耦合振动方程,引入了轨道不平顺及地震激励的影响,开发了相应的车桥耦合分析程序,并进行了试验检测验证；进一步讨论了桥梁跨度、行车速度、轨道不平顺、曲线半径、地震激励等对跨座式单轨交通曲线梁桥车桥耦合振动性能的影响。主要研究工作和成果如下：
(1)曲线梁桥动力分析模型的建立
基于单纯扭转理论,采用结构力学的方法精确推导了曲梁单元的刚度矩阵,研究了曲梁单元节间集中荷载及节间均布荷载作用下的等效节点荷载矩阵。推导并建立了曲梁单元的一致质量矩阵。按照“对号入座”法则形成了曲线桥梁的整体刚度矩阵、质量矩阵和节点荷载矩阵。基于瑞利比例阻尼的形式建立了曲梁的阻尼矩阵。
(2)跨座式单轨交通车辆动力分析模型的建立
根据跨座式单轨交通车辆结构及走行部特点,建立了15个自由度的车辆空间振动分析模型。基于充气橡胶轮胎点接触模型,对轮胎进行了简化,并推导了跨座式单轨车辆各轮对的径向力、阻尼力、侧偏力和回正力矩以及走行轮的摇头力矩。基于达朗贝尔原理,并考虑曲线半径和超高的影响建立了跨座式单轨交通曲线梁桥的车桥耦合动力方程。曲线梁桥车桥耦合振动模型中曲线半径趋于无穷大时吻合于直线梁桥的车桥耦合振动分析模型。
(3)轨道不平顺模拟及车桥耦合振动方程求解算法的编制
借鉴美国六级轨道谱密度函数、公路不平度功率谱及日本文献实测钢轨道梁表面不平顺功率谱密度函数,对跨座式单轨交通PC轨道梁轨道不平顺进行了研究,基于三角级数法模拟生成了轨道不平顺时间序列。车桥耦合振动方程求解采用逐步积分的Newmark-β迭代法,每一时间步采用了“预测—校正”的方法。
(4)跨座式单轨交通曲线梁桥车桥耦合振动分析程序编制和试验验证
基于推导的车桥耦合振动理论方程和设计的车桥耦合振动分析求解思路,编制了车桥耦合振动分析程序。通过重庆市跨座式单轨交通较新线Ⅰ期工程直线段、曲线段试验检测结果的验证,证实了车桥耦合理论分析的正确性和程序的有效性。
(5)桥梁结构设计参数及车辆运行参数对车桥振动响应的影响
基于验证的车桥耦合分析程序,分析了桥梁跨度、曲线半径、行车速度、轨道不平顺等对车桥耦合振动性能的影响。研究表明：①桥梁跨度、行车速度对车桥动力性能的影响比较复杂,呈现出复杂的影响形态；②当曲线半径大于600m时,可以近似忽略曲线半径的影响；③轨道不平顺对车桥耦合动力性能影响显著,轨道不平顺模拟准确性直接关系着车桥耦合分析结果的准确性。
(6)地震作用下的车桥耦合振动分析理论与参数敏感性分析
研究了地震作用下车桥耦合振动分析合理的地震波输入方式,推导了地震作用下的车桥耦合振动方程,编制了地震作用下的车桥耦合振动分析程序,分析了车辆行驶速度、初始条件、曲线半径等对地震激励下车桥振动响应的影响。研究表明：①地震激励影响轨道梁和车辆的耦合振动；②地震激励可以按照地震加速度波的形式输入；③地震荷载作用下,单轨车辆在桥上相当于增加了阻尼器,桥梁的振动响应稍有削弱,但车辆的振动响应显著增加；④地震发生时车辆的初始位置对车桥耦合振动响应结果有很大的影响；⑤当曲线半径小于600m,曲线半径减小,车桥振动响应明显增加,曲线半径大于600m时,可以近似忽略曲线半径的影响；⑥地震作用下车辆行驶速度对车桥振动响应有一定的影响,但影响并不明显。
Straddle-type monorail transit is a new type of urban rail transit. It has better ability of grade climbing and better adaptability to pass complex terrain, and it is particularly well suited to be used for the primary transportation in the mountain cities that are more ups and downs on the ground. The construction of the new traffic system is mainly elevated bridge and the most of route is curve, its track beam is bridge structures that bear loads as well as the guide of the vehicles. The body's structure of monorail vehicles is unique, and bogies with rubber tires wheel are adopted, so the running and guiding mechanism and the wheel-rail contact relationship are obviously different from the tradition steel wheel and steel rail transit system, and all of the feature lead to the bridge-vehicle interaction to straddle monorail system is peculiarity. At present, research on straddle monorail transit is still little, only a few research papers are limited to the analysis of the dynamic interaction of the straddle-type monorail built by straight beam. The theory of bridge-vehicle coupling vibration interaction is imperfect and immature, and that has effect on the further promotion and application of the new technology. On the base of the straddle-type monorail system numbered two in Chongqing, equations of bridge-vehicle coupling vibration are derived and established, the track irregularity and seismic load are introduced to the analysis, the corresponding analysis software of vehicle-bridge coupling vibration is developed and also verified by test, based on the verification software, the author discuss the influence to the result of vehicle-bridge coupling vibration for the difference such as bridge span, vehicle speed, track irregularity, curve radius, earthquake, etc. The main contents and research results are as follows:
1) Dynamic analysis model of curved track beam
Based on the simple torsion theory, using the methods of structural mechanics, the stiffness matrix of the curved beam element is derived in the flow curve coordinate system, the concentrated load and uniform load on the curved element are equivalent to the node load, and all of the node load is assembled to the node matrix. Further more, the consistent mass matrix of a curved beam is derived and established. Final, the global stiffness matrix, mass matrix and node load matrix are established by "set-in-right-position" rule. The curved beam damping matrix is also created that is based on the Rayleigh proportional damping.
2) Dynamic analysis model of monorail vehicle
According to the structure and running gear features of straddle-type monorail vehicle, the dynamic model of monorail vehicle with15DOFS is established. Based on point contact model of the inflatable rubber tires, the tire has been simplified. That are deduced included the radial force of the wheel, damping force, side force, self aligning torque(SAT) and moment produced by yaw. According to D'Alembert principle, dynamic equations of straddle-type monorail bridge-train interaction are deduced. When the radius of curve beam tends to infinity, dynamic mode of straddle monorail transit with curve beam is approached to that with straight beam.
3) The simulation of track irregularity and preparation for solution algorithm on bridge-vehicle coupling analysis program
Referring to the sixth track irregularity power-spectral-density function of U.S.A railways, and power spectrum of road roughness and power spectral density function of surface roughness of rail beam measured in Japanese literatures, based on triangle series method, track irregularity series on time are simulated to be generated. Step by step integration algorithm of Nemark's β method is adopted to solve the vibration equations, and the "prediction-correction" method is used at each time step.
4) Development program and test verification on analysis of bridge-vehicle coupling vibration to the curve bridge of straddle monorail transit
Based on the theoretical equations on bridge-vehicle coupling vibration and design ideas to solve bridge-vehicle vibration analysis, the program on bridge-vehicle coupling vibration analysis is developed. By verification of test in straight and curve bridge of straddle monorail transit in Chongqing, theory on bridge-vehicle coupling vibration in this paper is proved to be accurate and the program is effective.
5) The influence of bridge structure design parameters and operating parameters to dynamic response of bridge-vehicle system
It is based on the bridge-vehicle coupling vibration program of verification for the dynamic behaviors analysis of straddle monorail bridge and vehicle, the influence is discussed of the bridge span, the radius of curve, train speed, track irregularity, etc. The results are as follows:①The influence of bridge-vehicle coupling vibration performance on the bridge span and train speed is complex and is showed the impact of complex shape.②When the curve radius is greater than600m, the influence of the curve radius can be approximation ignored;③Track irregularity on the surface of bridge significantly affect the bridge-vehicle coupling vibration performance, the accuracy of track irregularity simulated is directly related to the reliability of the analysis result.
6) Theory of bridge-vehicle coupling vibration analysis with earthquake and parameter sensitivity analysis
The input pattern of earthquake wave is study, bridge-vehicle coupling vibration equations with earthquake is derived, the program is developed, the bridge-vehicle coupling vibration performance under earthquake is discussed on the influence of the initial conditions, train speed, the curve radius, etc. The research results are as follows:①Seismic influence the coupled vibration of the track beam and vehicle;②The input pattern of seismic excitation can be seismic acceleration wave;③Monorail vehicle is equivalent to the role of the bridge damper, the vibration response of the bridge is slightly weakened, but the vehicle has a significantly increase in the vibration response;④The initial position of the train at the time of earthquake coming has a great impact on the results of bridge-vehicle coupling vibration.⑤When the curve radius is less than600m, the bridge-train vibration significantly increased with the reduction of the radius, and when the curve radius is greater than600m, the influence of the radius can be ignored.⑥The effect of train speed to vibration response under earthquake is not obvious.
(1)曲线梁桥动力分析模型的建立
基于单纯扭转理论,采用结构力学的方法精确推导了曲梁单元的刚度矩阵,研究了曲梁单元节间集中荷载及节间均布荷载作用下的等效节点荷载矩阵。推导并建立了曲梁单元的一致质量矩阵。按照“对号入座”法则形成了曲线桥梁的整体刚度矩阵、质量矩阵和节点荷载矩阵。基于瑞利比例阻尼的形式建立了曲梁的阻尼矩阵。
(2)跨座式单轨交通车辆动力分析模型的建立
根据跨座式单轨交通车辆结构及走行部特点,建立了15个自由度的车辆空间振动分析模型。基于充气橡胶轮胎点接触模型,对轮胎进行了简化,并推导了跨座式单轨车辆各轮对的径向力、阻尼力、侧偏力和回正力矩以及走行轮的摇头力矩。基于达朗贝尔原理,并考虑曲线半径和超高的影响建立了跨座式单轨交通曲线梁桥的车桥耦合动力方程。曲线梁桥车桥耦合振动模型中曲线半径趋于无穷大时吻合于直线梁桥的车桥耦合振动分析模型。
(3)轨道不平顺模拟及车桥耦合振动方程求解算法的编制
借鉴美国六级轨道谱密度函数、公路不平度功率谱及日本文献实测钢轨道梁表面不平顺功率谱密度函数,对跨座式单轨交通PC轨道梁轨道不平顺进行了研究,基于三角级数法模拟生成了轨道不平顺时间序列。车桥耦合振动方程求解采用逐步积分的Newmark-β迭代法,每一时间步采用了“预测—校正”的方法。
(4)跨座式单轨交通曲线梁桥车桥耦合振动分析程序编制和试验验证
基于推导的车桥耦合振动理论方程和设计的车桥耦合振动分析求解思路,编制了车桥耦合振动分析程序。通过重庆市跨座式单轨交通较新线Ⅰ期工程直线段、曲线段试验检测结果的验证,证实了车桥耦合理论分析的正确性和程序的有效性。
(5)桥梁结构设计参数及车辆运行参数对车桥振动响应的影响
基于验证的车桥耦合分析程序,分析了桥梁跨度、曲线半径、行车速度、轨道不平顺等对车桥耦合振动性能的影响。研究表明：①桥梁跨度、行车速度对车桥动力性能的影响比较复杂,呈现出复杂的影响形态；②当曲线半径大于600m时,可以近似忽略曲线半径的影响；③轨道不平顺对车桥耦合动力性能影响显著,轨道不平顺模拟准确性直接关系着车桥耦合分析结果的准确性。
(6)地震作用下的车桥耦合振动分析理论与参数敏感性分析
研究了地震作用下车桥耦合振动分析合理的地震波输入方式,推导了地震作用下的车桥耦合振动方程,编制了地震作用下的车桥耦合振动分析程序,分析了车辆行驶速度、初始条件、曲线半径等对地震激励下车桥振动响应的影响。研究表明：①地震激励影响轨道梁和车辆的耦合振动；②地震激励可以按照地震加速度波的形式输入；③地震荷载作用下,单轨车辆在桥上相当于增加了阻尼器,桥梁的振动响应稍有削弱,但车辆的振动响应显著增加；④地震发生时车辆的初始位置对车桥耦合振动响应结果有很大的影响；⑤当曲线半径小于600m,曲线半径减小,车桥振动响应明显增加,曲线半径大于600m时,可以近似忽略曲线半径的影响；⑥地震作用下车辆行驶速度对车桥振动响应有一定的影响,但影响并不明显。
Straddle-type monorail transit is a new type of urban rail transit. It has better ability of grade climbing and better adaptability to pass complex terrain, and it is particularly well suited to be used for the primary transportation in the mountain cities that are more ups and downs on the ground. The construction of the new traffic system is mainly elevated bridge and the most of route is curve, its track beam is bridge structures that bear loads as well as the guide of the vehicles. The body's structure of monorail vehicles is unique, and bogies with rubber tires wheel are adopted, so the running and guiding mechanism and the wheel-rail contact relationship are obviously different from the tradition steel wheel and steel rail transit system, and all of the feature lead to the bridge-vehicle interaction to straddle monorail system is peculiarity. At present, research on straddle monorail transit is still little, only a few research papers are limited to the analysis of the dynamic interaction of the straddle-type monorail built by straight beam. The theory of bridge-vehicle coupling vibration interaction is imperfect and immature, and that has effect on the further promotion and application of the new technology. On the base of the straddle-type monorail system numbered two in Chongqing, equations of bridge-vehicle coupling vibration are derived and established, the track irregularity and seismic load are introduced to the analysis, the corresponding analysis software of vehicle-bridge coupling vibration is developed and also verified by test, based on the verification software, the author discuss the influence to the result of vehicle-bridge coupling vibration for the difference such as bridge span, vehicle speed, track irregularity, curve radius, earthquake, etc. The main contents and research results are as follows:
1) Dynamic analysis model of curved track beam
Based on the simple torsion theory, using the methods of structural mechanics, the stiffness matrix of the curved beam element is derived in the flow curve coordinate system, the concentrated load and uniform load on the curved element are equivalent to the node load, and all of the node load is assembled to the node matrix. Further more, the consistent mass matrix of a curved beam is derived and established. Final, the global stiffness matrix, mass matrix and node load matrix are established by "set-in-right-position" rule. The curved beam damping matrix is also created that is based on the Rayleigh proportional damping.
2) Dynamic analysis model of monorail vehicle
According to the structure and running gear features of straddle-type monorail vehicle, the dynamic model of monorail vehicle with15DOFS is established. Based on point contact model of the inflatable rubber tires, the tire has been simplified. That are deduced included the radial force of the wheel, damping force, side force, self aligning torque(SAT) and moment produced by yaw. According to D'Alembert principle, dynamic equations of straddle-type monorail bridge-train interaction are deduced. When the radius of curve beam tends to infinity, dynamic mode of straddle monorail transit with curve beam is approached to that with straight beam.
3) The simulation of track irregularity and preparation for solution algorithm on bridge-vehicle coupling analysis program
Referring to the sixth track irregularity power-spectral-density function of U.S.A railways, and power spectrum of road roughness and power spectral density function of surface roughness of rail beam measured in Japanese literatures, based on triangle series method, track irregularity series on time are simulated to be generated. Step by step integration algorithm of Nemark's β method is adopted to solve the vibration equations, and the "prediction-correction" method is used at each time step.
4) Development program and test verification on analysis of bridge-vehicle coupling vibration to the curve bridge of straddle monorail transit
Based on the theoretical equations on bridge-vehicle coupling vibration and design ideas to solve bridge-vehicle vibration analysis, the program on bridge-vehicle coupling vibration analysis is developed. By verification of test in straight and curve bridge of straddle monorail transit in Chongqing, theory on bridge-vehicle coupling vibration in this paper is proved to be accurate and the program is effective.
5) The influence of bridge structure design parameters and operating parameters to dynamic response of bridge-vehicle system
It is based on the bridge-vehicle coupling vibration program of verification for the dynamic behaviors analysis of straddle monorail bridge and vehicle, the influence is discussed of the bridge span, the radius of curve, train speed, track irregularity, etc. The results are as follows:①The influence of bridge-vehicle coupling vibration performance on the bridge span and train speed is complex and is showed the impact of complex shape.②When the curve radius is greater than600m, the influence of the curve radius can be approximation ignored;③Track irregularity on the surface of bridge significantly affect the bridge-vehicle coupling vibration performance, the accuracy of track irregularity simulated is directly related to the reliability of the analysis result.
6) Theory of bridge-vehicle coupling vibration analysis with earthquake and parameter sensitivity analysis
The input pattern of earthquake wave is study, bridge-vehicle coupling vibration equations with earthquake is derived, the program is developed, the bridge-vehicle coupling vibration performance under earthquake is discussed on the influence of the initial conditions, train speed, the curve radius, etc. The research results are as follows:①Seismic influence the coupled vibration of the track beam and vehicle;②The input pattern of seismic excitation can be seismic acceleration wave;③Monorail vehicle is equivalent to the role of the bridge damper, the vibration response of the bridge is slightly weakened, but the vehicle has a significantly increase in the vibration response;④The initial position of the train at the time of earthquake coming has a great impact on the results of bridge-vehicle coupling vibration.⑤When the curve radius is less than600m, the bridge-train vibration significantly increased with the reduction of the radius, and when the curve radius is greater than600m, the influence of the radius can be ignored.⑥The effect of train speed to vibration response under earthquake is not obvious.
引文
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