大跨刚构—连续梁桥振动控制研究
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摘要
桥梁作为交通枢纽及生命线工程,是交通干线的重要组成部分,是国家和社会发展的重要基础设施。由于刚构—连续组合梁桥放松了多跨连续刚构桥对边主墩高度的要求,因此这种桥型适用于不同的地形、地质条件、通航要求,刚构—连续组合梁是连续梁和连续刚构的组合,它兼顾了两者的优点而扬弃各自的缺点,集连续刚构、连续梁优点于一身,具有整体性好,抗震能力强,结构受力合理,线形优美等特点,在结构受力、使用功能和适应环境等方面均具有一定的优越性,近十几年中在国内也得到了快速发展,并有加快发展的趋势。
地震是一种破坏力巨大而又难以预测的自然灾害,由于其随机性和突发性,地震难以准确预测,往往导致灾难性后果,带来巨大的生命及财产损失,而我国是世界上的多地震国家之一,如何确保结构物在地震中的安全,始终是桥梁发展中的重要问题。传统的抗震方法通过加强结构自身抗力来抵抗地震作用,往往由于地震发生的不确定性,使得结构既不经济也不安全,近年来,基于结构振动控制理论的桥梁抗震技术已经受到各国学者的广泛重视,由于刚构—连续梁桥结构的复杂性,其振动控制方法的研究还处于起步阶段。因此,本文尝试利用主动变阻尼装置对一刚构—连续梁桥的地震震动进行控制,研究其控制效果及工程可行性,为工程应用提供参考。
本文基于结构振动控制的理论,以一实际刚构—连续梁桥为背景,将主动变阻尼装置应用到桥梁的减震控制中,采用限界Hrovat最优半主动控制算法,利用Matlab软件仿真分析了三种地震波(EL-Centro波、Taft波、天津波)无控和半主动控制下的地震反应规律,分别讨论分析了相应的计算结果,对桥梁纵向施加一致地震激励下刚构—连续梁桥地震响应的减震效果进行研究,得出了主动变阻尼装置对刚构—连续梁桥的控制规律。
(1)简介空间梁系有限元分析方法,阐述了利用空间梁单元建立结构有限元模型基本理论,然后利用空间梁单元建立了刚构—连续组合梁桥的空间动力分析模型,为抗震计算和减震研究提供分析对象,说明了结构动力分析地震波的选取和调幅规则和动力微分方程的求解方法;总结了结构振动控制的基本理论和方法。
(2)主动变阻尼装置控制策略分析。基于LQR经典线性二次型最优控制算法,利用主动变阻尼装置对一实例进行振动控制,仿真分析了三种半主动控制策略和被动控制策略的减震效果。研究结果表明:在桥梁结构中附设主动变阻尼装置可有效控制结构在地震作用下的纵向振动;合理的半主动控制算法(限界Hrovat最优控制算法)可以起到较好的控制效果。
(4)刚构—连续组合梁桥纵向无控、主动变阻尼装置半主动控制研究。通过在刚构—连续组合梁桥上安装主动变阻尼装置,采用限界Hrovat最优控制算法,利用Matlab软件研究其沿桥梁纵向输入三种地震波作用下桥梁无控和主动变阻尼装置的半主动控制效果,最后比较分析了控制前后的地震反应,研究结果表明:采用主动变阻尼装置对刚构—连续梁桥进行控制是可行的,有很好的控制效果。
(5)研究了主动变阻尼装置在控制过程中控制算法的实现情况,并比较了半主动控制输出控制力与主动控制力的关系。研究结果表明:主动变阻尼装置很好的实现了本文采用的限界Hrovat最优算法;主动变阻尼装置的半主动控制力与主动控制力有很大差别,采用主动变阻尼装置对桥梁进行控制时只能尽可能接近主动控制力,而不能完全实现主动控制力。
The bridge as the transport hub and the lifeline project and the main lines of communication important component, is national and the social development important basis facility.As Bridge of rigid frame-continuous girders reduced the* side main pillar high requirment with multi-span continuous rigid-framed bridge, therefore this kind of bridge is suitable for the different terrain, the geological condition and the navigation request. Bridge of rigid frame-continuous girders is the combination of continuous beam and continuous rigid frame,it has given consideration to both's merit to develop the good and discarded the respective shortcomings and gathered the advantages of two structures,besides,it has also many characteristics,such as powerful strong seismic capacity, good integrality, reasonable structure stress,beautiful line shape,so it has many superiorities in the acclimatization, mechanical behavior of structure and application functions aspects,and so on. it has also obtained the fast development, and have the tendency. of speeding up the development in near several years.
As a result of its randomness and burst characteristics,the earthquake often causes the disastrous consequence,and brings the huge life and the property damage, is a natural disaster which possesses great destructive power and forecasted with difficulty in advance.How to guarantee that the structure security in earthquake is important question throughout in the bridge development for our country, because the country is one of multi-earthquake countries in world.The traditional earthquake resistance methods by resisting the earthquake function through superstructure own resistance, often can make the structure not only uneconomical but also insecurely due to the uncertainty of earthquake .In recent years, the bridge earthquake resistance technology which is based on the structure vibration control theory already received various countries' scholar widely to take seriously, As a result of the structure complexity for Bridge of rigid frame-continuous girders, its vibration control method's research is also at the start stage.so this paper carried on the control to the bridge earthquake vibration with the active variable damper device,studied its control effect and the project feasibility for the reference of the project application
This paper which was taked an actual Bridge of rigid frame-continuous girders as the background, based on structure vibration control theory, applied the active variable damper in the vibration control for Rigid Frame-Continuous Girders under earthquake action.the control system is simulated during respectively inputting three earthquake waves—EL-Centro wave,Taft wave,Tianjin wave,and studied by the optimal bounding criterion semi-active control algorithms (Hrovat) with MATLAB.the earthquake response of Bridge of rigid frame-continuous girders are given out respectively without control devices and semi-active control.,the corresponding computed result is analyzed and discussed,the research of vibration absorbing effect of earthquake respond of Bridge of rigid frame-continuous girders is conducted,with uniform earthquake excitation which is imposed longitudinally, obtained the vibration control rule of active variable damper device to Bridge of rigid frame-continuous girders.
1、At first,this paper introduces finite element method on spatial beam element and illustrates the base theory for establishing structure finite element model, earthquake wave selection and amplitude modulation rule and solving method of dynamic differential equation,then a model for spatial dynamic analysis of Bridge of rigid frame-continuous girders is presented in order to provide the analysis basis for seismic calculation and vibration reduction analysis.in addition, summarize the structure vibration control elementary theory and the method.
2、Control-strategy analysis of active variable damper device.Based on classical linear optimal control algorithm (LQR), the control policy absorption of shock effect of semi-active control algorithm and passive strategy are analysed.The results calculated indicate that, that active variable damper as a semi-active control device on bridge can effectively control response of longitudinal vibration response; An excellent control effectiveness has been achieved for the control structure. The reasonable control algorithm (Hrovat)may have the good control effect.
3、The research of Longitudinal free vibrations and semi-active control effect for Bridge of rigid frame-continuous girders. applied the active variable damper in the vibration control for Rigid Frame-Continuous Girders under earthquake action.the control system is simulated during respectively inputting three earthquake waves—EL-Centro wave,Taft wave,Tianjin wave,and studied by the optimal bounding criterion semi-active control algorithms (Hrovat) with MATLAB.The results of earthquake responses of pre and post control are comparatively analyzed. The findings indicated that the control for Bridge of rigid frame-continuous girders is feasible, an excellent control effectiveness has been achieved for the control structure.
4、The situation which is realized to the control algorithm is studied about active variable damper in control,and control force between active control and semi-active are compared and analyzed.The results show that the device very good has realized the optimal algorithm(Hrovat); Two kind of control forces exist the very wide difference, the control using active variable damper device for Bridge of rigid frame-continuous girders can only as far as possible the close controlling force, but cannot realize the controlling force completely.
地震是一种破坏力巨大而又难以预测的自然灾害,由于其随机性和突发性,地震难以准确预测,往往导致灾难性后果,带来巨大的生命及财产损失,而我国是世界上的多地震国家之一,如何确保结构物在地震中的安全,始终是桥梁发展中的重要问题。传统的抗震方法通过加强结构自身抗力来抵抗地震作用,往往由于地震发生的不确定性,使得结构既不经济也不安全,近年来,基于结构振动控制理论的桥梁抗震技术已经受到各国学者的广泛重视,由于刚构—连续梁桥结构的复杂性,其振动控制方法的研究还处于起步阶段。因此,本文尝试利用主动变阻尼装置对一刚构—连续梁桥的地震震动进行控制,研究其控制效果及工程可行性,为工程应用提供参考。
本文基于结构振动控制的理论,以一实际刚构—连续梁桥为背景,将主动变阻尼装置应用到桥梁的减震控制中,采用限界Hrovat最优半主动控制算法,利用Matlab软件仿真分析了三种地震波(EL-Centro波、Taft波、天津波)无控和半主动控制下的地震反应规律,分别讨论分析了相应的计算结果,对桥梁纵向施加一致地震激励下刚构—连续梁桥地震响应的减震效果进行研究,得出了主动变阻尼装置对刚构—连续梁桥的控制规律。
(1)简介空间梁系有限元分析方法,阐述了利用空间梁单元建立结构有限元模型基本理论,然后利用空间梁单元建立了刚构—连续组合梁桥的空间动力分析模型,为抗震计算和减震研究提供分析对象,说明了结构动力分析地震波的选取和调幅规则和动力微分方程的求解方法;总结了结构振动控制的基本理论和方法。
(2)主动变阻尼装置控制策略分析。基于LQR经典线性二次型最优控制算法,利用主动变阻尼装置对一实例进行振动控制,仿真分析了三种半主动控制策略和被动控制策略的减震效果。研究结果表明:在桥梁结构中附设主动变阻尼装置可有效控制结构在地震作用下的纵向振动;合理的半主动控制算法(限界Hrovat最优控制算法)可以起到较好的控制效果。
(4)刚构—连续组合梁桥纵向无控、主动变阻尼装置半主动控制研究。通过在刚构—连续组合梁桥上安装主动变阻尼装置,采用限界Hrovat最优控制算法,利用Matlab软件研究其沿桥梁纵向输入三种地震波作用下桥梁无控和主动变阻尼装置的半主动控制效果,最后比较分析了控制前后的地震反应,研究结果表明:采用主动变阻尼装置对刚构—连续梁桥进行控制是可行的,有很好的控制效果。
(5)研究了主动变阻尼装置在控制过程中控制算法的实现情况,并比较了半主动控制输出控制力与主动控制力的关系。研究结果表明:主动变阻尼装置很好的实现了本文采用的限界Hrovat最优算法;主动变阻尼装置的半主动控制力与主动控制力有很大差别,采用主动变阻尼装置对桥梁进行控制时只能尽可能接近主动控制力,而不能完全实现主动控制力。
The bridge as the transport hub and the lifeline project and the main lines of communication important component, is national and the social development important basis facility.As Bridge of rigid frame-continuous girders reduced the* side main pillar high requirment with multi-span continuous rigid-framed bridge, therefore this kind of bridge is suitable for the different terrain, the geological condition and the navigation request. Bridge of rigid frame-continuous girders is the combination of continuous beam and continuous rigid frame,it has given consideration to both's merit to develop the good and discarded the respective shortcomings and gathered the advantages of two structures,besides,it has also many characteristics,such as powerful strong seismic capacity, good integrality, reasonable structure stress,beautiful line shape,so it has many superiorities in the acclimatization, mechanical behavior of structure and application functions aspects,and so on. it has also obtained the fast development, and have the tendency. of speeding up the development in near several years.
As a result of its randomness and burst characteristics,the earthquake often causes the disastrous consequence,and brings the huge life and the property damage, is a natural disaster which possesses great destructive power and forecasted with difficulty in advance.How to guarantee that the structure security in earthquake is important question throughout in the bridge development for our country, because the country is one of multi-earthquake countries in world.The traditional earthquake resistance methods by resisting the earthquake function through superstructure own resistance, often can make the structure not only uneconomical but also insecurely due to the uncertainty of earthquake .In recent years, the bridge earthquake resistance technology which is based on the structure vibration control theory already received various countries' scholar widely to take seriously, As a result of the structure complexity for Bridge of rigid frame-continuous girders, its vibration control method's research is also at the start stage.so this paper carried on the control to the bridge earthquake vibration with the active variable damper device,studied its control effect and the project feasibility for the reference of the project application
This paper which was taked an actual Bridge of rigid frame-continuous girders as the background, based on structure vibration control theory, applied the active variable damper in the vibration control for Rigid Frame-Continuous Girders under earthquake action.the control system is simulated during respectively inputting three earthquake waves—EL-Centro wave,Taft wave,Tianjin wave,and studied by the optimal bounding criterion semi-active control algorithms (Hrovat) with MATLAB.the earthquake response of Bridge of rigid frame-continuous girders are given out respectively without control devices and semi-active control.,the corresponding computed result is analyzed and discussed,the research of vibration absorbing effect of earthquake respond of Bridge of rigid frame-continuous girders is conducted,with uniform earthquake excitation which is imposed longitudinally, obtained the vibration control rule of active variable damper device to Bridge of rigid frame-continuous girders.
1、At first,this paper introduces finite element method on spatial beam element and illustrates the base theory for establishing structure finite element model, earthquake wave selection and amplitude modulation rule and solving method of dynamic differential equation,then a model for spatial dynamic analysis of Bridge of rigid frame-continuous girders is presented in order to provide the analysis basis for seismic calculation and vibration reduction analysis.in addition, summarize the structure vibration control elementary theory and the method.
2、Control-strategy analysis of active variable damper device.Based on classical linear optimal control algorithm (LQR), the control policy absorption of shock effect of semi-active control algorithm and passive strategy are analysed.The results calculated indicate that, that active variable damper as a semi-active control device on bridge can effectively control response of longitudinal vibration response; An excellent control effectiveness has been achieved for the control structure. The reasonable control algorithm (Hrovat)may have the good control effect.
3、The research of Longitudinal free vibrations and semi-active control effect for Bridge of rigid frame-continuous girders. applied the active variable damper in the vibration control for Rigid Frame-Continuous Girders under earthquake action.the control system is simulated during respectively inputting three earthquake waves—EL-Centro wave,Taft wave,Tianjin wave,and studied by the optimal bounding criterion semi-active control algorithms (Hrovat) with MATLAB.The results of earthquake responses of pre and post control are comparatively analyzed. The findings indicated that the control for Bridge of rigid frame-continuous girders is feasible, an excellent control effectiveness has been achieved for the control structure.
4、The situation which is realized to the control algorithm is studied about active variable damper in control,and control force between active control and semi-active are compared and analyzed.The results show that the device very good has realized the optimal algorithm(Hrovat); Two kind of control forces exist the very wide difference, the control using active variable damper device for Bridge of rigid frame-continuous girders can only as far as possible the close controlling force, but cannot realize the controlling force completely.
引文
[1]范立础.桥梁抗震-[M].同济大学出版社,1997,1-30
[2]范立础,胡世德,叶爱君著.大跨度桥梁抗震设计.[M].北京:人民交通出版社,2001,42-56
[3]范立础,卓卫东著.桥梁延性抗震设计.[M].北京:人民交通出版社,2001,31-42
[4]交通部公路规划设计院主编.公路工程抗震设计规范(JTJ 004-89),北京:人民交通出版社,1990,10-16
[5]中华人民共和国国家标准.铁路工程抗震设计规范(GBJ 111-87),北京:中国铁路出版社,1989,3-24
[6]叶爱君,胡世德,范立础.大跨度桥梁抗震设计实用方法.[J].土木工程学报,2001,1(34):1-5
[7]范立础,王君杰.桥梁抗震设计规范的现状与发展趋势.[J].地震工程与工程振动,2001,2(21):70-77
[8]谢礼立,张晓志,周雍年.论工程抗震设防标准.[J].四川地震,1996,4:14-29
[9]洪峰,谢礼立.工程结构抗震设防标准的决策分析.[J].地震工程与工程振动,1999,2(19):95-101
[10]李国豪.桥梁结构稳定与振动.[M].北京:中国铁道出版社,1992,16-38
[11]周云,宗兰,张文芳.土木工程抗震设计.[M].北京:科学出版社,2005.6-15
[12]金成棣.混凝土徐变对超静定结构变形和内力的影响.[J].土木工程学报.1981,3(62):56-61
[13]王文涛.刚构一连续组合梁桥.[M].人民交通出版社,1995.1,26-32
[14]钱登朝.高墩大跨刚构-连续组合梁桥关键技术研究[D].长安大学硕士学位论文,2006,5,
[15]李芮.刚构-连续组合梁桥变形分析及控制.[D].长安大学硕士学位论文,2006,5
[16]汪罗英,郑越.钢筋混凝土柱式桥墩的弹塑性抗震分析.[J].城市道桥与防洪,2005,6(2):53-56
[17]日本建筑学会.隔震结构设计.[M].北京:地震出版社,2006,5-10
[18]中华人民共和国交通部标准.公路工程抗震设计规范(JTJ004-89).13-25
[19]赖苍林.基于环境振动的大跨度连续刚构桥地震响应分析.[D].福州大学硕士学位论文,2004,12
[20]夏志华.大跨度连续刚构桥地震反应分析.[D].西南交通大学硕士论文2003,5
[21]周勇军,贺拴海,宋一凡.连续刚构桥单双薄壁墩地震响应的对比分析.[J].中外公路,2007,3(27):114-118
[22]孙立.多点激励下连续刚构桥反应分析.[D].北京工业大学硕士学位论文,2005,5
[23]史志利.大垮桥梁多点激励地震反应分析与MR阻尼器控制.[D].天津大学博士学位论文,2003,11
[24]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动,2003,2(23):68-76
[25]王成博,史志利,李忠献.随机地震动场多点激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动,2003,6(23):
[26]郑史雄,奚绍中.大跨度刚构桥的地震反应分析.[J].西南交通大学学报1997,6(32):586-592
[27]张海荣.津滨轻轨预应力混凝土连续刚构桥抗震分析.[J].铁道标准设计.2003,8(16):33-35
[28]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动.[J].2003,2(23):68-76.
[29]刘振良.连续刚构桥隔振技术研究.[D].长安大学硕士学位论文,2001,12
[30]姜海鹏.空间变异地震动的人工合成及其作用下长大跨连续刚构桥梁的延性响应分析.[D].北方交通大学硕士论文,2001
[31]范立础,王志强.桥梁减隔震设计.[M].人民交通出版社,2000,9-35
[32]J P Yao.Concept of Structural Control,J.Struct.Div.,ASCE,1972,98(7):I567-1574
[33]孙剑平,朱唏.结构控制方法评述.[J].力学进展,2000,4(30):49-55
[34]张俊平,禹奇才,周福霖.结构振动控制的两个理论问题.[J].地震工程与工程振动,2000,1(20):125-129
[35]周福霖.工程结构减振控制.[M].北京:地震出版社,1997,16-31
[36]T Soong.Active Structural Control:Theory and Practice.Longman Scientific &Technical,UK,1990
[37]徐龙河.基于磁流变流体阻尼器(blRFD)的半主动结构控制理论研究.[D].天津大学硕士学位论文,2000
[38]王肇民.高耸结构振动控制.[M].上海:同济大学出版社,1997,32-53
[39]张俊平,李新平,周福霖.桥梁结构振动控制发展及存在问题.[J].世界地震工程,1998,2(14):9-16
[40]胡开荣.桥梁减震器.[J].国外桥梁,1990,2(13):64-66
[41]史志利,周立志.大跨度桥梁抗震设计和振动控制的研究与应用现状.[J].城市道桥与防洪,2002,4:7-12
[42]陈云侠.桥梁结构地震响应半主动控制研究.[D].大连理工大学硕士学位论文,2008,6
[43]元兴军.桥梁减震半主动控制.[D].中国地震局地球物埋研究所博士论文,2006,6
[44]李春祥,余琼,王肇民.大跨桥梁结构扭转振动的MTMD控制研究.[J].特种结构,2002,4(19):12-21
[45]罗小宝.基于振动控制理论的斜拉桥抗震仿真研究.[D].东南大学硕士学位论文,2006
[46]范立础,王志强.桥梁减隔震设计.[M].北京:人民交通出版社,2001,23-40
[47]叶爱君.桥梁抗震.[M].北京:人民交通出版社,2002,10-15
[48]朱伯芳.有限单元法.[M].北京:清华大学出版社,2004,6,1-36
[49]王焕定,焦兆平.有限单元法基础.[M].北京:高等教育出版社.13-48
[50]田冠伟.有限元结构分析方法及在桥梁结构中的应用.[J].机床与液压,2003,1(12):25-29
[51]江见鲸,贺小刚.工程结构计算仿真分析.[M].北京:清华大学出版社,1996.18-29
[52]肖汝诚.桥梁结构分析及程序系统.[M].北京:人民交通出版社,2002,11,83-87
[53]谢旭.桥梁结构地震响应分析与抗震设计.[M].北京:人民交通出版社2006.212-231,1-17
[54]戴公连,李德建.桥梁结构空间分析设计方法与应用.[M].北京:人民交通出版社,2001.32-54
[55]徐次达,华伯浩.固体力学有限元理论、方法及程序.[M].北京:中国水利水电出版社1983,32-54
[56]曾攀.有限元分析及应用.[M].北京:清华大学出版社,2004,6,90-142
[57]朱伯芳.有限单元法原理与应用(第二版).[M].北京:中国水利水电出版社,1998,56-87
[58]王勖成,邵敏.有限单元法基本原理和数值方法.[M].北京.清华大学出版社,1997,20-38
[59]董军,刘旭红,姚顺忠.基于虚功原理的空间梁单元刚度矩阵分析.[J].西南林学院报.2002,4(22):65-72
[60]张方胜.桥梁结构地震反应时程分析.[D].合肥工业大学硕士论文.2007,12
[61]赵超夔.桥梁结构计算力学.[M].上海:同济大学出版社,1998,36-57,157-175
[63]胡聿贤.地震工程学.[M].北京:地震出版社,1988,13-57
[64]R.M.克拉夫(美).结构动力学.[M].北京:科学出版社,99-191
[65]李杰,李国强.地震工程学导论[M].北京:地震出版社,1992,200-203.
[66]中华人民共和国水利部.水工建筑物抗震设计规范[S](SL203-97).北京:中国水利水电出版社,1997,11-15.
[67]王松涛,曹资.现代抗震设计方法.[M].北京:中国建筑工业出版社,1997,5-13
[68]蔡靖.大跨斜拉桥地震反应的主动控制研究.[D].西南交通大学博士学位论文,2001
[69]江宣城.建筑结构基础隔振扭转反应研究.[D].华中科技大学博士学位论文,2001
[70]欧进萍.结构振动控制-主动、半主动和智能控制.[M].北京:科学出版社,2003,58-67,258-290,421-490
[71]Dyke SI,Spencer BF,Ouast P,Sain MK.Role of control-structure interaction in protective system design.[J].Journal of Engineering,Mechanics 1995,121(2):322-38.
[72]Michael D.Symans,Michael C.Constantinou.Semi-active control systems for seismic protection of structures:a tare-of-the-art review[JT,Engineering Structures 21 (1999):469-487
[73]余钱华.桥梁结构被动控制的理论与实验研究.[D].同济大学博士学位论文,2001
[74]T.T.Soong and A.M.Reinhom.An Overview of Active and Hybrid Structural Control Research in the U.S.,The Struct.Dyn.Design of Tall Buildings,1993,vol.2,pp.192-209.
[75]Kawashima K,U njoh S.Seismic responses control of bridges by variable dampers[J.J Struct Engrg,ASCE,1994,120(9):2583-2601.
[76]Kurata N.Kobori T,TakahashiM,et al.Shaking table experiment of active variable damping system[A].1st World Confon StmcturalControl[C.LosAnglesCalif,1994.
[77]孙作玉.变阻尼半主动结构控制.[D].哈尔滨建筑大学硕士学位论文.1998.
[78]李惠,袁雪松,吴波.粘滞流体变阻尼半主动控制器对结构抗震控制的试验研究.[J].振动工程学报,2002,1(15):25-30
[79]周云.粘滞阻尼减震结构设计.[M].武汉:武汉理工大学出版社,2006.11,48-106
[80]杨润林,闫维明,周锡元,刘锡荟.结构离复位控制的可行性研究.[J].振动工程学报,2005,4(18)::512-518.
[81]隋莉莉,欧进萍.MR减震驱动器用于结构振动控制的算法研究.[J].应用力学学报,2002,3(19):144-149.
[82]阎石,张海.高架桥地震反应半主动控制分析.[J].地震工程与工程震动,2003,6(23):169-174.
[83]邹立华,赵人达,杨治国.铁路柔性桥墩横向抗震加固方法的理论探讨.[J].工程力学,2005.5(223:199-205
[84]Feng Q,Shinozuka M.Use of a variable damper for hybrid control of bridge response under earthquake,Proceeding of U.S.National Workshop on Structural Control Research,USC PublicationNo.CE-9013,1990.
[85](美)Macia,N.E(美)Thaler,G.J.(著);李乃文,孙宏江等(译).动态系统建模与控制.[M].北京:清华大学出版社,2006,5,21-59
[86]苏金明,王永利.MATLAB7.0实用指南.[M].北京:电子工业出版社,2005,10-74
[2]范立础,胡世德,叶爱君著.大跨度桥梁抗震设计.[M].北京:人民交通出版社,2001,42-56
[3]范立础,卓卫东著.桥梁延性抗震设计.[M].北京:人民交通出版社,2001,31-42
[4]交通部公路规划设计院主编.公路工程抗震设计规范(JTJ 004-89),北京:人民交通出版社,1990,10-16
[5]中华人民共和国国家标准.铁路工程抗震设计规范(GBJ 111-87),北京:中国铁路出版社,1989,3-24
[6]叶爱君,胡世德,范立础.大跨度桥梁抗震设计实用方法.[J].土木工程学报,2001,1(34):1-5
[7]范立础,王君杰.桥梁抗震设计规范的现状与发展趋势.[J].地震工程与工程振动,2001,2(21):70-77
[8]谢礼立,张晓志,周雍年.论工程抗震设防标准.[J].四川地震,1996,4:14-29
[9]洪峰,谢礼立.工程结构抗震设防标准的决策分析.[J].地震工程与工程振动,1999,2(19):95-101
[10]李国豪.桥梁结构稳定与振动.[M].北京:中国铁道出版社,1992,16-38
[11]周云,宗兰,张文芳.土木工程抗震设计.[M].北京:科学出版社,2005.6-15
[12]金成棣.混凝土徐变对超静定结构变形和内力的影响.[J].土木工程学报.1981,3(62):56-61
[13]王文涛.刚构一连续组合梁桥.[M].人民交通出版社,1995.1,26-32
[14]钱登朝.高墩大跨刚构-连续组合梁桥关键技术研究[D].长安大学硕士学位论文,2006,5,
[15]李芮.刚构-连续组合梁桥变形分析及控制.[D].长安大学硕士学位论文,2006,5
[16]汪罗英,郑越.钢筋混凝土柱式桥墩的弹塑性抗震分析.[J].城市道桥与防洪,2005,6(2):53-56
[17]日本建筑学会.隔震结构设计.[M].北京:地震出版社,2006,5-10
[18]中华人民共和国交通部标准.公路工程抗震设计规范(JTJ004-89).13-25
[19]赖苍林.基于环境振动的大跨度连续刚构桥地震响应分析.[D].福州大学硕士学位论文,2004,12
[20]夏志华.大跨度连续刚构桥地震反应分析.[D].西南交通大学硕士论文2003,5
[21]周勇军,贺拴海,宋一凡.连续刚构桥单双薄壁墩地震响应的对比分析.[J].中外公路,2007,3(27):114-118
[22]孙立.多点激励下连续刚构桥反应分析.[D].北京工业大学硕士学位论文,2005,5
[23]史志利.大垮桥梁多点激励地震反应分析与MR阻尼器控制.[D].天津大学博士学位论文,2003,11
[24]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动,2003,2(23):68-76
[25]王成博,史志利,李忠献.随机地震动场多点激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动,2003,6(23):
[26]郑史雄,奚绍中.大跨度刚构桥的地震反应分析.[J].西南交通大学学报1997,6(32):586-592
[27]张海荣.津滨轻轨预应力混凝土连续刚构桥抗震分析.[J].铁道标准设计.2003,8(16):33-35
[28]李忠献,史志利.行波激励下大跨度连续刚构桥的地震反应分析.[J].地震工程与工程振动.[J].2003,2(23):68-76.
[29]刘振良.连续刚构桥隔振技术研究.[D].长安大学硕士学位论文,2001,12
[30]姜海鹏.空间变异地震动的人工合成及其作用下长大跨连续刚构桥梁的延性响应分析.[D].北方交通大学硕士论文,2001
[31]范立础,王志强.桥梁减隔震设计.[M].人民交通出版社,2000,9-35
[32]J P Yao.Concept of Structural Control,J.Struct.Div.,ASCE,1972,98(7):I567-1574
[33]孙剑平,朱唏.结构控制方法评述.[J].力学进展,2000,4(30):49-55
[34]张俊平,禹奇才,周福霖.结构振动控制的两个理论问题.[J].地震工程与工程振动,2000,1(20):125-129
[35]周福霖.工程结构减振控制.[M].北京:地震出版社,1997,16-31
[36]T Soong.Active Structural Control:Theory and Practice.Longman Scientific &Technical,UK,1990
[37]徐龙河.基于磁流变流体阻尼器(blRFD)的半主动结构控制理论研究.[D].天津大学硕士学位论文,2000
[38]王肇民.高耸结构振动控制.[M].上海:同济大学出版社,1997,32-53
[39]张俊平,李新平,周福霖.桥梁结构振动控制发展及存在问题.[J].世界地震工程,1998,2(14):9-16
[40]胡开荣.桥梁减震器.[J].国外桥梁,1990,2(13):64-66
[41]史志利,周立志.大跨度桥梁抗震设计和振动控制的研究与应用现状.[J].城市道桥与防洪,2002,4:7-12
[42]陈云侠.桥梁结构地震响应半主动控制研究.[D].大连理工大学硕士学位论文,2008,6
[43]元兴军.桥梁减震半主动控制.[D].中国地震局地球物埋研究所博士论文,2006,6
[44]李春祥,余琼,王肇民.大跨桥梁结构扭转振动的MTMD控制研究.[J].特种结构,2002,4(19):12-21
[45]罗小宝.基于振动控制理论的斜拉桥抗震仿真研究.[D].东南大学硕士学位论文,2006
[46]范立础,王志强.桥梁减隔震设计.[M].北京:人民交通出版社,2001,23-40
[47]叶爱君.桥梁抗震.[M].北京:人民交通出版社,2002,10-15
[48]朱伯芳.有限单元法.[M].北京:清华大学出版社,2004,6,1-36
[49]王焕定,焦兆平.有限单元法基础.[M].北京:高等教育出版社.13-48
[50]田冠伟.有限元结构分析方法及在桥梁结构中的应用.[J].机床与液压,2003,1(12):25-29
[51]江见鲸,贺小刚.工程结构计算仿真分析.[M].北京:清华大学出版社,1996.18-29
[52]肖汝诚.桥梁结构分析及程序系统.[M].北京:人民交通出版社,2002,11,83-87
[53]谢旭.桥梁结构地震响应分析与抗震设计.[M].北京:人民交通出版社2006.212-231,1-17
[54]戴公连,李德建.桥梁结构空间分析设计方法与应用.[M].北京:人民交通出版社,2001.32-54
[55]徐次达,华伯浩.固体力学有限元理论、方法及程序.[M].北京:中国水利水电出版社1983,32-54
[56]曾攀.有限元分析及应用.[M].北京:清华大学出版社,2004,6,90-142
[57]朱伯芳.有限单元法原理与应用(第二版).[M].北京:中国水利水电出版社,1998,56-87
[58]王勖成,邵敏.有限单元法基本原理和数值方法.[M].北京.清华大学出版社,1997,20-38
[59]董军,刘旭红,姚顺忠.基于虚功原理的空间梁单元刚度矩阵分析.[J].西南林学院报.2002,4(22):65-72
[60]张方胜.桥梁结构地震反应时程分析.[D].合肥工业大学硕士论文.2007,12
[61]赵超夔.桥梁结构计算力学.[M].上海:同济大学出版社,1998,36-57,157-175
[63]胡聿贤.地震工程学.[M].北京:地震出版社,1988,13-57
[64]R.M.克拉夫(美).结构动力学.[M].北京:科学出版社,99-191
[65]李杰,李国强.地震工程学导论[M].北京:地震出版社,1992,200-203.
[66]中华人民共和国水利部.水工建筑物抗震设计规范[S](SL203-97).北京:中国水利水电出版社,1997,11-15.
[67]王松涛,曹资.现代抗震设计方法.[M].北京:中国建筑工业出版社,1997,5-13
[68]蔡靖.大跨斜拉桥地震反应的主动控制研究.[D].西南交通大学博士学位论文,2001
[69]江宣城.建筑结构基础隔振扭转反应研究.[D].华中科技大学博士学位论文,2001
[70]欧进萍.结构振动控制-主动、半主动和智能控制.[M].北京:科学出版社,2003,58-67,258-290,421-490
[71]Dyke SI,Spencer BF,Ouast P,Sain MK.Role of control-structure interaction in protective system design.[J].Journal of Engineering,Mechanics 1995,121(2):322-38.
[72]Michael D.Symans,Michael C.Constantinou.Semi-active control systems for seismic protection of structures:a tare-of-the-art review[JT,Engineering Structures 21 (1999):469-487
[73]余钱华.桥梁结构被动控制的理论与实验研究.[D].同济大学博士学位论文,2001
[74]T.T.Soong and A.M.Reinhom.An Overview of Active and Hybrid Structural Control Research in the U.S.,The Struct.Dyn.Design of Tall Buildings,1993,vol.2,pp.192-209.
[75]Kawashima K,U njoh S.Seismic responses control of bridges by variable dampers[J.J Struct Engrg,ASCE,1994,120(9):2583-2601.
[76]Kurata N.Kobori T,TakahashiM,et al.Shaking table experiment of active variable damping system[A].1st World Confon StmcturalControl[C.LosAnglesCalif,1994.
[77]孙作玉.变阻尼半主动结构控制.[D].哈尔滨建筑大学硕士学位论文.1998.
[78]李惠,袁雪松,吴波.粘滞流体变阻尼半主动控制器对结构抗震控制的试验研究.[J].振动工程学报,2002,1(15):25-30
[79]周云.粘滞阻尼减震结构设计.[M].武汉:武汉理工大学出版社,2006.11,48-106
[80]杨润林,闫维明,周锡元,刘锡荟.结构离复位控制的可行性研究.[J].振动工程学报,2005,4(18)::512-518.
[81]隋莉莉,欧进萍.MR减震驱动器用于结构振动控制的算法研究.[J].应用力学学报,2002,3(19):144-149.
[82]阎石,张海.高架桥地震反应半主动控制分析.[J].地震工程与工程震动,2003,6(23):169-174.
[83]邹立华,赵人达,杨治国.铁路柔性桥墩横向抗震加固方法的理论探讨.[J].工程力学,2005.5(223:199-205
[84]Feng Q,Shinozuka M.Use of a variable damper for hybrid control of bridge response under earthquake,Proceeding of U.S.National Workshop on Structural Control Research,USC PublicationNo.CE-9013,1990.
[85](美)Macia,N.E(美)Thaler,G.J.(著);李乃文,孙宏江等(译).动态系统建模与控制.[M].北京:清华大学出版社,2006,5,21-59
[86]苏金明,王永利.MATLAB7.0实用指南.[M].北京:电子工业出版社,2005,10-74