大跨度拱桥地震反应特性及减震控制研究
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摘要
近年来,国内大跨度拱桥的已建和在建项目日益增多。大跨度拱桥作为生命线工程,它们在地震作用下的安全性格外重要,一旦地震使交通线遭到破坏,可能导致的生命财产以及间接经济损失将会非常巨大。然而拱桥被认为是抗震性能相对较差的桥型,拱桥的轴压比较高,延性较低,难于设计成延性抗震结构。因此,对于重要的大跨度拱桥有必要在弄清其地震反应特性的基础上,采取适当的减震措施,以提高和改善其抗震能力。目前对这种桥型结构的减震控制尚缺乏系统地综合性研究,故探索合理可行、有效经济的拱桥耐震、减震新途径,为我国拱桥抗震、减震设计提供理论依据和参考成为主要的研究目标。本文围绕大跨度拱桥地震反应特性及减震控制技术,主要开展了以下几个方面的研究工作。
①基于空间非平稳地震动功率谱模型,考虑地震动的部分相关效应以及时滞效应等因素,应用谐波合成法模拟了空间变化的地震动加速度时程,作为大跨度拱桥多点激励地震反应分析的空间地震动输入。
②构建大跨度拱桥结构的理论分析模型,确定拱桥结构多点激励下的动力学方程以及相应的求解方法,编制三维动力有限元分析程序,实现了大跨度拱桥多点激励地震反应时程分析。
③对大跨度拱桥结构进行模型降阶,提出按最大模态位移方法确定控制模态。采用基于模态分析和平衡降阶的方法来对拱桥模型降阶,解决了大跨度拱桥减震控制中由于模型离散自由度较多,难以进行仿真控制分析的困难。对按振型贡献率选择控制模态的方法进行了改进,按最大模态位移方法确定控制模态,分析表明,该方法考虑了外部激励的影响,克服了振型贡献率只考虑结构动力特性选取控制模态的缺点,这对于必须考虑多点地震激励影响的大跨度拱桥更为合理。
④探索合理可行的拱桥减震措施。考虑拱桥的结构特点,给出了在拱桥上设置阻尼器的减震方案。对于上承式拱桥,由于拱脚为嵌固,可考虑采用阻尼器斜撑的减震方案。对中承式拱桥除了在桥墩与桥面主梁间设置阻尼器外,还可在拱桥吊杆端部布置阻尼器。实例分析表明,上述减震措施对于减小拱桥地震反应是有效的。
⑤将粘滞阻尼器用于拱桥的被动减震控制。对阻尼器表现非线性阻尼性能的拱桥被动减震系统非线性时程分析,将非线性阻尼力等效为外部控制作用,对处于弹性状态的主体结构进行模型降阶,采用基于现代控制理论的状态空间分析方法或状态方程精细时程积分法进行求解,可提高计算效率,而且实现了拱桥被动减震分析与半主动减震控制仿真分析程序的统一。并对粘滞阻尼器阻尼力计算模型中的阻尼系数、速度指数等参数的取值进行了模拟计算与分析。
⑥综合研究了磁流变阻尼器用于大跨度拱桥的半主动减震控制。结合磁流变阻尼器半主动控制特性,选定磁流变阻尼器的力学模型,基于H∞控制器-Sign函数的半主动控制策略建立了半主动减震控制系统。对控制系统中的半主动控制算法、阻尼器的布置和参数等进行了优化分析。为解决大跨度拱桥模型降阶控制中由于含有未建模频域不确定性所导致的溢出问题,提出采用基于混合灵敏度的鲁棒控制策略来消除溢出不稳定。分析表明,该方法能有效地抑制溢出,保证系统具有更好的鲁棒性能。
⑦选取大跨度拱桥中具有代表意义的桥型,一座上承式拱桥-西藏尼木大桥和一座中承式系杆拱桥-重庆菜园坝长江大桥为例,分别进行了一致激励、行波输入及多点激励输入下的地震反应分析和粘滞阻尼器被动减震以及磁流变阻尼器半主动减震控制分析。深入探讨了行波效应对大跨度拱桥被动、半主动减震效果的影响,得出了有益的结论,为提高大跨度拱桥的抗震安全性以及将阻尼器用于大跨度拱桥减震控制的工程应用提供了理论参考。
Recently, long-span arch bridges are widely used in our country. And being traffic lifeline, the safety of long-span arch bridge by seismic excitation is very important. Once traffic line damaged, loss on life and property may be serious. However, the seismic behavior of arch bridge is poor, and traditional ductile design is unsuitable because of the high axial compressive ratio of arch rib. Moreover, it is lacking in research on seismic control of arch bridge. So making an investigation on some new, proper, effective, economical approaches of seismic control of arch bridge is the principal objective of this paper .The research is mainly focused on the following aspects.
①The spatial variable seismic acceleration time history is simulated. Based on a power spectral model of spatial nonstationary earthquake ground motion and considering the spatial partial coherence and traveling wave effect , the seismic acceleration time history are simulated by the wave superposition method.
②Establishing finite element model of long-span arch bridge and dynamic equation, and selecting analysis methods, the finite element dynamic analysis program is realized to make analysis on seismic response of arch bridge by multi-support excitation.
③In order to solving the primary difficult in seismic control of long-span arch bridge that designing control system based on original model of long-span arch bridge is almost impossible because of the very large degree of freedom (DOF), methods of model reduction including critical modal analysis and balanced model reduction are proposed. As for the critical modes selection, an approach based on the maximum modal displacement is presented, which consider the effect of seismic excitation and is more reasonable than the method based on modal contribution ratio that only considers dynamic characteristics of bridge.
④The seismic control schemes for arch bridge are presented after considering the structural characteristics of arch bridge. For top-through arch bridge, diagonal bracing with damper can be mounted on bridge. As for half-through arch bridge, dampers can be installed at the connection of deck and bridge pier, and the dampers can also be set at the end of suspenders. Numerical results show that the seismic control schemes mentioned above are effective for seismic control of arch bridge.
⑤For the long-span arch bridge with nonlinear viscous dampers, an efficient method considering nonlinear damping force is presented. In the nonlinear time-history analysis of long-span arch bridge, this paper regards the nonlinear damping force as external control force which act upon bridge, and arch bridge is in the state of elasticity where the initial critical modes of the bridge are used in the model reduction. Then the state space method based on modern control theory or the precise integration method is used to command the state equations. The solving process for the nonlinear dynamic equation has high computation efficiency and realize a program which can perform passive control as well as semi-active control analysis .Taking Nimu arch bridge as an example, analysis are carried out to determine the optimal values of damping coefficient and velocity exponent for viscous damper for which the Maxwell model is used as computation model .
⑥For semi-active control, Magnetorheological Fluid damper (MRFD) is used for seismic control of arch bridge. Modified phenomenological model is selected as the mechanical model of MRFD, and H∞-based Sign function control algorithm is proposed to command MRFD. Optimum analysis for semi-active control system consisting of installation position and number of MRFD and comparison between different semi-active control algorithms are performed. About the problem of overflow in the model reduction control, equivalent normal H∞control system of mixed sensitivity optimization is established to eliminate destabilization due to overflow. The analysis results demonstrate that this method can suppress overflow efficiently and has better robust performance.
⑦At last, taking a top-though arch bridge, Nimu arch bridge in Tibet, and a half-though arch bridge,CaiYuanBa arch bridge in Chongqing , as examples, the seismic responses of the two bridges under uniform excitation and traveling wave excitation and multi-support excitation, and seismic absorption with viscous dampers and semi-active control with MR dampers, are numerically simulated. The traveling wave effect on the seismic control is investigated, and some valuable suggestions have been got. These works provide an important theoretical reference for improving seismic safety of the long-span arch bridge.
①基于空间非平稳地震动功率谱模型,考虑地震动的部分相关效应以及时滞效应等因素,应用谐波合成法模拟了空间变化的地震动加速度时程,作为大跨度拱桥多点激励地震反应分析的空间地震动输入。
②构建大跨度拱桥结构的理论分析模型,确定拱桥结构多点激励下的动力学方程以及相应的求解方法,编制三维动力有限元分析程序,实现了大跨度拱桥多点激励地震反应时程分析。
③对大跨度拱桥结构进行模型降阶,提出按最大模态位移方法确定控制模态。采用基于模态分析和平衡降阶的方法来对拱桥模型降阶,解决了大跨度拱桥减震控制中由于模型离散自由度较多,难以进行仿真控制分析的困难。对按振型贡献率选择控制模态的方法进行了改进,按最大模态位移方法确定控制模态,分析表明,该方法考虑了外部激励的影响,克服了振型贡献率只考虑结构动力特性选取控制模态的缺点,这对于必须考虑多点地震激励影响的大跨度拱桥更为合理。
④探索合理可行的拱桥减震措施。考虑拱桥的结构特点,给出了在拱桥上设置阻尼器的减震方案。对于上承式拱桥,由于拱脚为嵌固,可考虑采用阻尼器斜撑的减震方案。对中承式拱桥除了在桥墩与桥面主梁间设置阻尼器外,还可在拱桥吊杆端部布置阻尼器。实例分析表明,上述减震措施对于减小拱桥地震反应是有效的。
⑤将粘滞阻尼器用于拱桥的被动减震控制。对阻尼器表现非线性阻尼性能的拱桥被动减震系统非线性时程分析,将非线性阻尼力等效为外部控制作用,对处于弹性状态的主体结构进行模型降阶,采用基于现代控制理论的状态空间分析方法或状态方程精细时程积分法进行求解,可提高计算效率,而且实现了拱桥被动减震分析与半主动减震控制仿真分析程序的统一。并对粘滞阻尼器阻尼力计算模型中的阻尼系数、速度指数等参数的取值进行了模拟计算与分析。
⑥综合研究了磁流变阻尼器用于大跨度拱桥的半主动减震控制。结合磁流变阻尼器半主动控制特性,选定磁流变阻尼器的力学模型,基于H∞控制器-Sign函数的半主动控制策略建立了半主动减震控制系统。对控制系统中的半主动控制算法、阻尼器的布置和参数等进行了优化分析。为解决大跨度拱桥模型降阶控制中由于含有未建模频域不确定性所导致的溢出问题,提出采用基于混合灵敏度的鲁棒控制策略来消除溢出不稳定。分析表明,该方法能有效地抑制溢出,保证系统具有更好的鲁棒性能。
⑦选取大跨度拱桥中具有代表意义的桥型,一座上承式拱桥-西藏尼木大桥和一座中承式系杆拱桥-重庆菜园坝长江大桥为例,分别进行了一致激励、行波输入及多点激励输入下的地震反应分析和粘滞阻尼器被动减震以及磁流变阻尼器半主动减震控制分析。深入探讨了行波效应对大跨度拱桥被动、半主动减震效果的影响,得出了有益的结论,为提高大跨度拱桥的抗震安全性以及将阻尼器用于大跨度拱桥减震控制的工程应用提供了理论参考。
Recently, long-span arch bridges are widely used in our country. And being traffic lifeline, the safety of long-span arch bridge by seismic excitation is very important. Once traffic line damaged, loss on life and property may be serious. However, the seismic behavior of arch bridge is poor, and traditional ductile design is unsuitable because of the high axial compressive ratio of arch rib. Moreover, it is lacking in research on seismic control of arch bridge. So making an investigation on some new, proper, effective, economical approaches of seismic control of arch bridge is the principal objective of this paper .The research is mainly focused on the following aspects.
①The spatial variable seismic acceleration time history is simulated. Based on a power spectral model of spatial nonstationary earthquake ground motion and considering the spatial partial coherence and traveling wave effect , the seismic acceleration time history are simulated by the wave superposition method.
②Establishing finite element model of long-span arch bridge and dynamic equation, and selecting analysis methods, the finite element dynamic analysis program is realized to make analysis on seismic response of arch bridge by multi-support excitation.
③In order to solving the primary difficult in seismic control of long-span arch bridge that designing control system based on original model of long-span arch bridge is almost impossible because of the very large degree of freedom (DOF), methods of model reduction including critical modal analysis and balanced model reduction are proposed. As for the critical modes selection, an approach based on the maximum modal displacement is presented, which consider the effect of seismic excitation and is more reasonable than the method based on modal contribution ratio that only considers dynamic characteristics of bridge.
④The seismic control schemes for arch bridge are presented after considering the structural characteristics of arch bridge. For top-through arch bridge, diagonal bracing with damper can be mounted on bridge. As for half-through arch bridge, dampers can be installed at the connection of deck and bridge pier, and the dampers can also be set at the end of suspenders. Numerical results show that the seismic control schemes mentioned above are effective for seismic control of arch bridge.
⑤For the long-span arch bridge with nonlinear viscous dampers, an efficient method considering nonlinear damping force is presented. In the nonlinear time-history analysis of long-span arch bridge, this paper regards the nonlinear damping force as external control force which act upon bridge, and arch bridge is in the state of elasticity where the initial critical modes of the bridge are used in the model reduction. Then the state space method based on modern control theory or the precise integration method is used to command the state equations. The solving process for the nonlinear dynamic equation has high computation efficiency and realize a program which can perform passive control as well as semi-active control analysis .Taking Nimu arch bridge as an example, analysis are carried out to determine the optimal values of damping coefficient and velocity exponent for viscous damper for which the Maxwell model is used as computation model .
⑥For semi-active control, Magnetorheological Fluid damper (MRFD) is used for seismic control of arch bridge. Modified phenomenological model is selected as the mechanical model of MRFD, and H∞-based Sign function control algorithm is proposed to command MRFD. Optimum analysis for semi-active control system consisting of installation position and number of MRFD and comparison between different semi-active control algorithms are performed. About the problem of overflow in the model reduction control, equivalent normal H∞control system of mixed sensitivity optimization is established to eliminate destabilization due to overflow. The analysis results demonstrate that this method can suppress overflow efficiently and has better robust performance.
⑦At last, taking a top-though arch bridge, Nimu arch bridge in Tibet, and a half-though arch bridge,CaiYuanBa arch bridge in Chongqing , as examples, the seismic responses of the two bridges under uniform excitation and traveling wave excitation and multi-support excitation, and seismic absorption with viscous dampers and semi-active control with MR dampers, are numerically simulated. The traveling wave effect on the seismic control is investigated, and some valuable suggestions have been got. These works provide an important theoretical reference for improving seismic safety of the long-span arch bridge.
引文
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