地震及汽车作用下长大混凝土桥梁振动研究
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摘要
随着经济和社会的发展，鉴于线路平顺性和稳定性要求、环境保护等诸多因素的考量，可能建造连续几公里甚至是几十公里的长大桥梁。桥梁结构，尤其是预应力混凝土结构桥梁，在公路交通线路总长的比重日益增加。在地震多发区域，一方面，长大桥梁的不同支撑可能经受差异较大地震作用，而对地震动的空间变异性研究相对滞后；另外一方面，汽车行驶在桥梁上遭遇突发地震作用的可能性大大提高，地震及汽车联合作用下桥梁耦合振动响应需要深入研究，然而国内外的相关研究几乎是一片空白。在总结和吸取前人研究成果的基础上，本论文以长大混凝土桥梁为背景，重点对地震动空间变异性、地震及汽车联合作用下桥梁耦合振动这两个方面的关键问题进行了研究。
本文主要的研究内容和结论如下：
1.深入研究了地震波空间变异性机理，提出了一套切实可行的地震动模拟方案：在已知场地特征、空间相关模型条件下使用无条件模拟技术产生多点地震加速度时程样本；在给定参考点地震波、空间相干模型条件下使用有条件模拟技术产生多点地震加速度时程样本。针对地震波中存在的误差问题，系统的研究了剔除方法，给出了各种方法的适用性。
2.采用解析方法研究简支梁遭遇两点地震激励的振动问题，并结合数值方法给出了梁体的动力响应。研究结果表明地震波中相位成分的变化对结构的动力响应有显著的影响。
3.针对桥梁抗震计算方法中存在的误区，研究了精确求解法、大质量法、大刚度法的适用性。研究结果表明：不同的时程输入方式对数值求解方法的收敛速度、计算精度有较大影响；精确求解法中输入地震加速度时程只能用于线性分析，输入地震位移时程的求解方法可以用于非线性分析；相对于大刚度法而言，大质量法求解精度较高。
4.选取某连续刚构桥梁作为研究对象，选定一条实际地震加速度时程记录作为参考，采用有条件模拟技术生成满足空间变异特征的多点地震加速度时程，借助于零残余位移法对其进行修正，消除误差影响，并施加到桥梁纵向上；采用大质量法求解结构动力响应。数值分析结果表明：在实际桥梁抗震分析过程中，地震波失相干性的影响不可忽略，只有充分考虑完全变异特性才能得到偏于安全的分析结果。
5.提出了地震激励及汽车联合作用下桥梁耦合振动问题，并建立了相关分析模型。将耦合系统划分为桥梁、车辆两个子系统；引入刚体部件，基于有限元方法推导并建立车辆运动方程；采用有限元方法建立桥梁子系统模型，并使用振型叠加法缩减动力自由度；桥面平整度作为耦合系统的自激励源，而地震荷载直接施加到桥梁结构上；使用耦合关系将两个子系统联结在一起。提出了数值求解流程以及其中关键问题的解决方案，并编制DIARVB计算软件。
6.应用地震及汽车联合作用下桥梁耦合振动分析模型及DIARVB计算软件，分析一辆两轴货车以不同行驶速度通过三跨预应力混凝土连续刚构桥梁遭遇突发地震作用时耦合系统的动力响应。研究结果表明：桥梁子系统的动力响应完全由地震激励决定；地震激励通过桥梁结构传递给汽车子系统，会导致其振动放大的现象，从而危及汽车的行走安全；车速对汽车系统动力响应影响较大；地震波的频谱特性改变了汽车-桥梁耦合振动系统的动力响应规律以及峰值。
With the development of economy and society, the long-extension bridges of which totallengths are beyond several or tens of kilometers have been built in order to meet therequirements including the smoothness and the stability of the road and the environmentalprotection pressure. And the ratio of the concrete bridges to the road traffic line increasesgreatly. On one hand, different supports of the long-extension bridge may suffer fromvariational seismic ground motions. Yet the spatial variability of ground motion study islagging behind. On the other hand, the possiblity that a road vehicle is driven on a bridgewhen earthquakes occur is higher and higher, which shows that road vehicle-bridge coupledsystem subjected to seismic excitation should be in-depth study. However, no valuableinformation on this subject is available. On the basis of the summary and general study of thepredecessor’s research experiences in China and abroad, the paper deals with the vibration oflong-extension concrete bridge under the actions of earthquake and road vehicle, in which thespatial variation of seismic ground motion and the bridge vibration under the simultaneousaction of earthquake and road vehicle are considered.
The main contents and research results are as follows:
1. The mechanism of spatial variability of seismic ground motion is discussed. Anoperable scheme for the seismic wave simulation is presented. According to the spectraltheory, the unconditional simulation method is used to generate seismic acceleration timehistories of bridge supports where site characteristics and coherent model are known. Theconditional simulation method based on multivariate linear prediction theory is used wherethe seismic acceleration time history of one support and coherent model are provided. Themethods to eliminate error of earthquake wave and their applicabilities are discussed.
2. Dynamic response of a simply-supported beam subjected to two-point seismicexcitation is studied using the analytic method and the numerical solution, which results showthat the phase component of seismic wave plays an important role.
3. Some mistakes are popular in the computation methods of the bridge seismic analysis.The applicabilities of accurate solution method, large mass method and large stiffness methodin bridge aseisimatic analysis are discussed. The numberical results show that different input pattern of seismic has great impact to convergence speed and solving precision. Input patternof seismic acceleration in accurate solution method is only suitable for linear analysis, andinput pattern of seismic displacement applies to nonlinear analysis. Compare with largestiffness method, the solving precision of large mass method is higher.
4. A continuous rigid frame bridge is taken as a case study. The time history of realearthquake record is taken as a reference. The conditional simulation method is used togenerate seismic acceleration time histories of bridge supports. The errors in time historiesare eliminated using residual value method of zero final displacement. Large mass method isused to solve the equilibrium equations of motion bridge structure. The numberical resultsshow that the influence of loss of earthquake wave coherence on bridge dynamic responsecan not be neglected and only full consideration of spatial variability can obtain safer results.
5. The dynamic interaction model of road vehicle-bridge coupled system subjected toseismic ground motion is established, which consists of road vehicle subsystem and bridgesubsystem. Both of them are established with finite element method. The rigid componentassumption is introduced to the road vehicle subsystem, the mode superposition method isapplied to the bridge subsystem to reduce the degrees-of-freedom, and the dynamicinteraction between two subsystems is expressed with wheel road relation. The numbericalsolution flow is introduced, in which some key schemes are presented. And a calculationsoftware named DIARVB is prepared.
6. A freight car running over a3-span continuous rigid frame bridge subject toearthquakes is taken as a case study to verify the applicability. The results show that dynamicof bridge subsystem is completely controlled by seismic excitation. The seismic excitationtransferred by bridge subsystem may amplify the vibration of road vehicle, which mayendanger the running safety of vehicle. The vehicle speed plays an important role in dynamicresponse of vehicle subsystem. And the spectral characteristic of earthquake wave influencesdynamic response of coupled system.
本文主要的研究内容和结论如下：
1.深入研究了地震波空间变异性机理，提出了一套切实可行的地震动模拟方案：在已知场地特征、空间相关模型条件下使用无条件模拟技术产生多点地震加速度时程样本；在给定参考点地震波、空间相干模型条件下使用有条件模拟技术产生多点地震加速度时程样本。针对地震波中存在的误差问题，系统的研究了剔除方法，给出了各种方法的适用性。
2.采用解析方法研究简支梁遭遇两点地震激励的振动问题，并结合数值方法给出了梁体的动力响应。研究结果表明地震波中相位成分的变化对结构的动力响应有显著的影响。
3.针对桥梁抗震计算方法中存在的误区，研究了精确求解法、大质量法、大刚度法的适用性。研究结果表明：不同的时程输入方式对数值求解方法的收敛速度、计算精度有较大影响；精确求解法中输入地震加速度时程只能用于线性分析，输入地震位移时程的求解方法可以用于非线性分析；相对于大刚度法而言，大质量法求解精度较高。
4.选取某连续刚构桥梁作为研究对象，选定一条实际地震加速度时程记录作为参考，采用有条件模拟技术生成满足空间变异特征的多点地震加速度时程，借助于零残余位移法对其进行修正，消除误差影响，并施加到桥梁纵向上；采用大质量法求解结构动力响应。数值分析结果表明：在实际桥梁抗震分析过程中，地震波失相干性的影响不可忽略，只有充分考虑完全变异特性才能得到偏于安全的分析结果。
5.提出了地震激励及汽车联合作用下桥梁耦合振动问题，并建立了相关分析模型。将耦合系统划分为桥梁、车辆两个子系统；引入刚体部件，基于有限元方法推导并建立车辆运动方程；采用有限元方法建立桥梁子系统模型，并使用振型叠加法缩减动力自由度；桥面平整度作为耦合系统的自激励源，而地震荷载直接施加到桥梁结构上；使用耦合关系将两个子系统联结在一起。提出了数值求解流程以及其中关键问题的解决方案，并编制DIARVB计算软件。
6.应用地震及汽车联合作用下桥梁耦合振动分析模型及DIARVB计算软件，分析一辆两轴货车以不同行驶速度通过三跨预应力混凝土连续刚构桥梁遭遇突发地震作用时耦合系统的动力响应。研究结果表明：桥梁子系统的动力响应完全由地震激励决定；地震激励通过桥梁结构传递给汽车子系统，会导致其振动放大的现象，从而危及汽车的行走安全；车速对汽车系统动力响应影响较大；地震波的频谱特性改变了汽车-桥梁耦合振动系统的动力响应规律以及峰值。
With the development of economy and society, the long-extension bridges of which totallengths are beyond several or tens of kilometers have been built in order to meet therequirements including the smoothness and the stability of the road and the environmentalprotection pressure. And the ratio of the concrete bridges to the road traffic line increasesgreatly. On one hand, different supports of the long-extension bridge may suffer fromvariational seismic ground motions. Yet the spatial variability of ground motion study islagging behind. On the other hand, the possiblity that a road vehicle is driven on a bridgewhen earthquakes occur is higher and higher, which shows that road vehicle-bridge coupledsystem subjected to seismic excitation should be in-depth study. However, no valuableinformation on this subject is available. On the basis of the summary and general study of thepredecessor’s research experiences in China and abroad, the paper deals with the vibration oflong-extension concrete bridge under the actions of earthquake and road vehicle, in which thespatial variation of seismic ground motion and the bridge vibration under the simultaneousaction of earthquake and road vehicle are considered.
The main contents and research results are as follows:
1. The mechanism of spatial variability of seismic ground motion is discussed. Anoperable scheme for the seismic wave simulation is presented. According to the spectraltheory, the unconditional simulation method is used to generate seismic acceleration timehistories of bridge supports where site characteristics and coherent model are known. Theconditional simulation method based on multivariate linear prediction theory is used wherethe seismic acceleration time history of one support and coherent model are provided. Themethods to eliminate error of earthquake wave and their applicabilities are discussed.
2. Dynamic response of a simply-supported beam subjected to two-point seismicexcitation is studied using the analytic method and the numerical solution, which results showthat the phase component of seismic wave plays an important role.
3. Some mistakes are popular in the computation methods of the bridge seismic analysis.The applicabilities of accurate solution method, large mass method and large stiffness methodin bridge aseisimatic analysis are discussed. The numberical results show that different input pattern of seismic has great impact to convergence speed and solving precision. Input patternof seismic acceleration in accurate solution method is only suitable for linear analysis, andinput pattern of seismic displacement applies to nonlinear analysis. Compare with largestiffness method, the solving precision of large mass method is higher.
4. A continuous rigid frame bridge is taken as a case study. The time history of realearthquake record is taken as a reference. The conditional simulation method is used togenerate seismic acceleration time histories of bridge supports. The errors in time historiesare eliminated using residual value method of zero final displacement. Large mass method isused to solve the equilibrium equations of motion bridge structure. The numberical resultsshow that the influence of loss of earthquake wave coherence on bridge dynamic responsecan not be neglected and only full consideration of spatial variability can obtain safer results.
5. The dynamic interaction model of road vehicle-bridge coupled system subjected toseismic ground motion is established, which consists of road vehicle subsystem and bridgesubsystem. Both of them are established with finite element method. The rigid componentassumption is introduced to the road vehicle subsystem, the mode superposition method isapplied to the bridge subsystem to reduce the degrees-of-freedom, and the dynamicinteraction between two subsystems is expressed with wheel road relation. The numbericalsolution flow is introduced, in which some key schemes are presented. And a calculationsoftware named DIARVB is prepared.
6. A freight car running over a3-span continuous rigid frame bridge subject toearthquakes is taken as a case study to verify the applicability. The results show that dynamicof bridge subsystem is completely controlled by seismic excitation. The seismic excitationtransferred by bridge subsystem may amplify the vibration of road vehicle, which mayendanger the running safety of vehicle. The vehicle speed plays an important role in dynamicresponse of vehicle subsystem. And the spectral characteristic of earthquake wave influencesdynamic response of coupled system.
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