华中科技大学博士学位论文斜拉桥车桥耦合振动及其MTMD振动控制姓名：万信华申请学位级别：博士专业：结构工程指导教师：朱宏平20060419华 中 科 技 大 学 博 士 学 位 论 文华 中 科 技 大 学 博 士 学 位 论 文I摘摘 要要随着交通事业和现代物流业的发展，桥梁结构处于繁忙的运输状态。交通密度的日益增加、荷载的逐渐加重以及车速的不断提高，使得车辆与结构的动力相互作用问题越来越受到人们的重视。一方面，移动车辆的动力作用对桥梁结构物的工作状态和使用寿命产生直接影响；另一方面，桥梁结构上运行车辆的平稳性和安全性又是评价结构动力设计参数合理与否的重要考虑因素。因此，对车桥动力耦合系统进行综合研究，以便对桥梁结构的动力性能和结构上车辆的走行性作出动力分析和评估，进而采取对策减小结构的动力响应，是合理进行桥梁结构物设计的工程实际需要，对结构工程学科的发展具有十分重要的理论和实际意义。在教育部新世纪优秀人才计划(2004 年)科研项目资助下，本文以一座实际斜拉桥沪蓉西国道铁罗坪大桥为研究对象，研究车桥系统动力相互作用及 MTMD 控制下桥梁结构的动力响应，为铁罗坪大桥合理设计提供力学理论参考。铁罗坪大桥主桥为一高墩大跨双塔双索面混凝土斜拉结构，论文采用有限元非线性分析理论和方法对该结构进行静力分析，通过调整斜拉索张拉力建立结构合理的初始成桥状态，在此基础上，研究结构动力特性；同时将桥梁上运行车辆模拟成 2轴 6 自由度且具有 3 个质量的振动系统并分析其动力特性。通过基于桥面随机不平顺的车桥耦合单元建立包含车辆振动和结构振动的耦合系统，用数值积分法求解动力学方程。分别从汽车通过桥梁时的速度、车辆的个数、车辆的偏载等几个方面研究了斜拉桥结构的动力响应以及乘客的舒适度与车速的关系。在分析铁罗坪大桥固有振动的基础上，确定结构跨中动挠度的控制振型，将汽车荷载作为对主桥结构的随机激励，建立结构振动控制振型坐标和 MTMD 构成的新系统动力平衡方程，由此推导了结构控制振型坐标的幅频响应表达式。分析了 MTMD 的平均阻尼比、频率间距、广义质量比、数量、布置间距与控制振型坐标幅值的关系，给出了确定 MTMD各参数的具体步骤， 由主桥跨中动挠度为控制目标设计了 MTMD， 进而研究了 MTMD控制下车桥系统的动力响应。计算结果表明，在随机不平顺桥面条件下，MTMD 能够有效减小结构对汽车荷载激励的动力响应。车桥耦合动力相互作用及其控制研究领域虽然还有许多问题需要探讨，但它的研究和应用有着光明的未来，其巨大的经济效益和社会效益已初见成效。可以预见，经过广大科研工作者的不懈努力，车桥动力相互作用的研究成果更好地应用于工程设计，而结构控制技术会以它独有的魅力在结构的防振减灾中发挥日益重要的作用。关键词：关键词：车桥耦合单元； 不平顺桥面； 动力响应； 随机激励； 振动控制；多重调质阻尼器（MTMD）华 中 科 技 大 学 博 士 学 位 论 文华 中 科 技 大 学 博 士 学 位 论 文IIABSTRACTNowadays the bridge structures are always under a busy transportation condition forthe development of traffic and logistics. The traffic density, the load and moving speedincrease day by day, which attract much attention on the interaction of the vehicles andbridges. On one hand, the dynamic characteristics of the moving vehicle influence theworking condition and the age of structure directly. On the other hand, the comfortable andsafe requirement is a critical factor for evaluating whether or not the structural dynamicparameters are chosen suitably in the design. Therefore, discussion on the dynamiccoupling system of vehicles and bridge, analysis on the dynamic performances of thestructure and the balanced moving performance of the vehicles, and the research on thecountermeasure to minimize the dynamic response are an available demand for the rationaldesign of the large-span bridges, which will contribute deeply to the theoretical andpractical improvement of structural engineering field. Supported by the Program for NewCentury Excellent Talents in University (2004), an actual cable-stayed bridge named Tie-luo-ping bridge in the west part of Shanghai-Chengdu national highway is chosen as a casestudy in this thesis. The study focuses on the dynamic interaction of vehicle-bridge systemand the dynamic responses of the bridge under MTMD control, which will providemechanical reference to the rational design.The bridge is a long span concrete cable-stayed structure of high-pier with doubletowers and double cable planes. Firstly, the static analysis is carried out using the finiteelement method, and reasonable original stress condition of the bridge is established byregulating original cable stress, afterwards, the dynamic characteristics are discussed.Secondly, the vehicle on the bridge is simulated as a vibration system with two axes, sixfreedom and three masses, and the vehicles dynamic characteristics are studied. Thecoupling system including the vibration of vehicles and bridge structure is set up based onthe vehicle-bridge coupling element due to pavements stochastic irregulation, the motionequation is solved by numerical integration method. Attention has been paid on therelationship among the bridges dynamic response, passengers comfort degree with themoving vehicle under different speeds, vehicle number and eccentric loading. Thirdly,华 中 科 技 大 学 博 士 学 位 论 文华 中 科 技 大 学 博 士 学 位 论 文IIIbased on the analysis of Tie-luo-ping bridges natural vibration, the structures controlmodal of dynamic deflection in mid-span is acquired. The vehicle load is considered as thestochastic excitation. The dynamic equation of the new system which is constituted withcontrol modal coordinate of structural vibration and MTMD is founded, from which theamplitude frequency response equation is deduced. The relationship between the averagedamp ratio, frequency space, generalized mass, quantity, layout space with coordinateamplitude of control modal is analyzed, and the process of how to determine the variousMTMD parameters is offered in details. The MTMD is designed to aim at controlling thedynamic deflection of mid-span, and the dynamic response of vehicle-bridge system isstudied under the control of MTMD. The numerical results show that, for the stochasticirregular pavement, MTMD can effectively minimize the structures dynamic responseunder vehicle load excitation.Finally, the future research on the vehicle-bridge coupling interaction and its control isdiscussed. It will be prosperous in the economic and societal efficiency. Consequentially,with the endeavor of researchers, the application of vehicle-bridge dynamic interactiontheoretical achievements will be more effective in prac