基础激励下桥梁斜拉索振动分析与控制
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摘要
斜拉索是斜拉桥中的主要承重结构,它具有阻尼小、柔度大、质量轻的特点,极易在地震激励、风致激励和动载激励等作用下产生大幅振动,影响桥梁结构的安全、使用性能与寿命,因而有必要对拉索的振动采取一定的控制措施。当荷载作用于桥梁结构时,桥面和桥塔会按一定频率振动,而拉索的两端分别与桥面和桥塔相连,因而桥面和桥塔的振动为拉索施加了运动的边界条件,带来一定的基础激励。通过分析基础激励作用下拉索的振动机理可以在实践中避免并减小拉索的大幅振动,防止桥梁结构的破坏。在拉索近锚固端安装阻尼器可以提高拉索系统的等效阻尼比,消耗外界的输入的能量,有效控制拉索的振动。其中,磁流变阻尼器是由智能材料组成的可调参数阻尼器,通过调节外加的直流电压来选取不同的阻尼系数,从而很好地控制桥梁斜拉索的大幅振动,在土木工程中具有广泛的应用前景。
本文运用有限元软件ANSYS建立了斜拉桥(深圳湾公路大桥)的力学模型,通过对其进行仿真模拟,得出了斜拉桥在地震、车辆、风等荷载作用下桥面及桥塔上最长拉索锚固点的振动响应,将比较得出的最不利荷载施加于单根斜拉索上,从而更加真实地模拟了斜拉索在基础激励下的振动反应特性,并在此基础上研究了斜拉索的谐波共振和参数共振这两种大幅振动,讨论了各种内部和外部因素对以上两种拉索共振的影响。其中的影响参数包括:位移激励幅值、初始索力、模态阻尼比及拉索倾角。最后,本文通过模拟斜拉索与磁流变阻尼器共同组成的振动控制系统,介绍了磁流变阻尼器的工作原理及力学模型,研究了其对拉索的振动控制机理及特性,进一步探讨了阻尼力大小、阻尼器位置、激振力幅值及初始索力等相关参数对振动控制系统减振效果的影响,通过优化相关参数,可以使磁流变阻尼器达到最优的减振效果。
Cable-Stayed is the main load-bearing components in cable-stayed structure. It is vulnerable to generate significant vibration under the incentives such as the seismic, wind, and vehicle loading because of the characteristics of low damping, great flexibility and light weight. So it will affect the safety, performance and life expectancy of bridge structures. And it is necessary to take vibration control measurement for the cables. When the load acting on the bridge structure, the bridge deck and the bridge towers will have a certain frequency of vibration, and the two ends of cable are connected to the bridge deck and the bridge towers respectively, so the vibration of bridge deck and towers impose the boundary conditions for cable movement, which is certain foundation incentive. By analyzing the vibration mechanism under foundation excitation for cable, we will avoid and reduce the significantly vibration of the cable in practice. and prevent the destruction of the bridge structure. To install damper near the end of anchor will improve equivalent damping ratio of the cable-stayed system, consumption of external energy, and then effectively control the vibration of cables. Magneto-Rheological damper has a wide range of applications in civil engineering, since the MR damper can select different damping coefficient by adjusting the DC voltage applied. Thus it will control the great vibration in cable-stayed bridge perfectly.
This thesis establishes a mechanical model of a cable-stayed bridge (Shenzhen Bay Bridge) with the finite element software ANSYS. Then simulate the seismic, wind, vehicle loading and other loads. Obtaining the maximum response of vibration at the deck and tower anchorage points with the longest cable in the bridge, as the displacement load imposed on the cable-stayed and thus more truly simulate the vibration characteristics of the cable under the foundation excitation. And on this basis to study two substantial vibration of harmonic resonance and parametric vibration, then analyze different influencing factors of these two kinds of vibration. The impact of parameters which include: excitation amplitude of displacement, the initial cable force, modal damping ratio, and the cable angle.
Finally, by simulating cable-damper control system, this thesis analyze the control mechanism and features of MR damper in vibration control system, and to further study the relevant parameters which effect the cable-MR damper control system. These parameters include: the damping force, damper position, excitation amplitude and the initial cable force. By optimizing the relevant parameters, the MR damper will attend the Optimal damping effect.
本文运用有限元软件ANSYS建立了斜拉桥(深圳湾公路大桥)的力学模型,通过对其进行仿真模拟,得出了斜拉桥在地震、车辆、风等荷载作用下桥面及桥塔上最长拉索锚固点的振动响应,将比较得出的最不利荷载施加于单根斜拉索上,从而更加真实地模拟了斜拉索在基础激励下的振动反应特性,并在此基础上研究了斜拉索的谐波共振和参数共振这两种大幅振动,讨论了各种内部和外部因素对以上两种拉索共振的影响。其中的影响参数包括:位移激励幅值、初始索力、模态阻尼比及拉索倾角。最后,本文通过模拟斜拉索与磁流变阻尼器共同组成的振动控制系统,介绍了磁流变阻尼器的工作原理及力学模型,研究了其对拉索的振动控制机理及特性,进一步探讨了阻尼力大小、阻尼器位置、激振力幅值及初始索力等相关参数对振动控制系统减振效果的影响,通过优化相关参数,可以使磁流变阻尼器达到最优的减振效果。
Cable-Stayed is the main load-bearing components in cable-stayed structure. It is vulnerable to generate significant vibration under the incentives such as the seismic, wind, and vehicle loading because of the characteristics of low damping, great flexibility and light weight. So it will affect the safety, performance and life expectancy of bridge structures. And it is necessary to take vibration control measurement for the cables. When the load acting on the bridge structure, the bridge deck and the bridge towers will have a certain frequency of vibration, and the two ends of cable are connected to the bridge deck and the bridge towers respectively, so the vibration of bridge deck and towers impose the boundary conditions for cable movement, which is certain foundation incentive. By analyzing the vibration mechanism under foundation excitation for cable, we will avoid and reduce the significantly vibration of the cable in practice. and prevent the destruction of the bridge structure. To install damper near the end of anchor will improve equivalent damping ratio of the cable-stayed system, consumption of external energy, and then effectively control the vibration of cables. Magneto-Rheological damper has a wide range of applications in civil engineering, since the MR damper can select different damping coefficient by adjusting the DC voltage applied. Thus it will control the great vibration in cable-stayed bridge perfectly.
This thesis establishes a mechanical model of a cable-stayed bridge (Shenzhen Bay Bridge) with the finite element software ANSYS. Then simulate the seismic, wind, vehicle loading and other loads. Obtaining the maximum response of vibration at the deck and tower anchorage points with the longest cable in the bridge, as the displacement load imposed on the cable-stayed and thus more truly simulate the vibration characteristics of the cable under the foundation excitation. And on this basis to study two substantial vibration of harmonic resonance and parametric vibration, then analyze different influencing factors of these two kinds of vibration. The impact of parameters which include: excitation amplitude of displacement, the initial cable force, modal damping ratio, and the cable angle.
Finally, by simulating cable-damper control system, this thesis analyze the control mechanism and features of MR damper in vibration control system, and to further study the relevant parameters which effect the cable-MR damper control system. These parameters include: the damping force, damper position, excitation amplitude and the initial cable force. By optimizing the relevant parameters, the MR damper will attend the Optimal damping effect.
引文
1汪至刚,孙炳楠.斜拉索的参数振动.土木工程学报. 2002, 35 (5): 29~33
2徐克生.斜拉桥拉索非线性振动的数值研究.大连理工大学硕士学位论文. 2007: 4~6
3 Richard E, Christenson B S. Semiactive Control of Civil Structures for Natural Hazard Mitigation, Analytical and Experimental Studies[D]. the University of Notre Dame. 2001
4 Lilien JL, Costa A Pinto Da. Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structures. Journal of Sound and Vibration. 1994, 174(2): 9~90
5 Ni Y Q, Chen Y, Ko JM. Neuro-Control of Vibration using Semi-active Magneto-Rheological Dampers. Engineering Structures. 2002, 24: 295~312
6赵跃宇,蒋丽忠.索—梁组合结构的动力学建模理论及其内共振分析.土木工程学报. 2004, 37(3): 70~72
7康厚军,赵跃宇,王连华.斜拉桥中拉索对桥面动力特性的影响.动力学与控制学报. 2007, 5(1): 44
8 Takahashi K. Dynamic Stability of Cables Subjected to an Axial Periodic Load. Journal of Sound and Vibration. 1991, 144(2): 323~330
9 Costa A Pinto Da, Martins J A C, Branco F, Lilien J L. Oscillations of Bridge Stay Cables Induced by Periodic Motions of Deck and Towers. Journal of Engineering Mechanics. 1996, (7): 613~621
10杨素哲,陈艾荣.超长斜拉索的参数振动.同济大学学报. 2005, 33(10): 1303~1308
11 Ko J M, Chen Y, Zheng G. Experimental Study on Vibration Mitigation of a Stay Cable Using Nonlinear Hysteretic Damper. Advances in Structural Dynamics. Elsevier Science Ltd,Oxford,UK. 2000, 2: 1325~1332
12 Sun BN, Wang ZG, Ko JM, Ni YQ. Parametrically Eexcited Oscillation of Stay-Cable and Iits Control in Cable-Stayed Bridges. Journal of Zhejiang University Science. 2003, 4(I): 13~20.
13陈明宪.斜拉桥建造技术.人民交通出版社, 2004: 170~171
14邬喆华,陈勇.磁流变阻尼器对斜拉索的振动控制.科学出版社, 2007: 15~17
15曾德子,赵章力,卿迟.深圳湾公路大桥(深圳侧通航孔桥)索塔施工.广东交通职业技术学院学报. 2007, 6(3): 23
16吴存全,曾德子,冯飞敏.深圳湾公路大桥通航孔桥斜拉索安装.技术园地. 2007, 8: 51
17康国政. Ansys高级工程应用实例分析与二次开发.电子工业出版社, 2006: 69~81
18袁万城.大跨桥梁空间非线性地震反应分析.同济大学博士学位论文. 1990: 20~24
19席张群.桥梁抗震分析方法对比研究.中国水运. 2007, 7(5): 95~96
20周强,郭少进.支座轴向运动控制拉索风致振动的研究.武汉理工大学学报. 2007, 29(1): 128~131
21梅葵花,吕志涛,孙胜江. CFRP拉索的非线性参数振动特性.中国公路学报. 2007, 20(1): 52~56
22 Chri Genrts, Ton Vrouwenvelder, Piet van. Numerical Modeling of Rain-Wind-Induced Vibration. Structural Engineering International,Erasmus Bridge, Rotterdam. 1998: 129.
23王波,郭翠翠,张海龙,徐丰.端部激励下斜拉索非线性振动及振动松弛.武汉理工大学学报. 2008, 30(2): 75~78
24 Warnitchai P, Fujino Y. A Non-linear Dynamic Modal for Cables and its Application to a Cable-Structure System. Journal of Sound and Vibration. 1995, 187(4): 695~699
25陈水生,孙炳楠.斜拉桥索—桥耦合非线性参数振动数值研究.土木工程学报. 2003, 36(4): 70~71
26 Olivier F. Rain-Wind Induced Vibrations of Cables. Journal of Engineering and Industrial Aerodynamics. 1995(57): 353~362
27刘习军,王霞,张素侠,贾启芬,李强.斜拉桥中索—桥耦合非线性振动的理论研究.工程力学. 2007, 24(7): 125~126
28郑阿奇. MATLAB实用教程.电子工业出版社, 2005
29亢战,钟万勰.斜拉索参数共振问题的数值研究.土木工程学报. 1998, 31(4): 14 -22
30 SIAI-Noury, Ali S A. Large-Amplitude Vibration of Parabolic Cable. Journal of Sound and Vibration. 1985, 101(4): 451~462
31汪至刚,孙炳楠.斜拉索参数振动引起的拉索大幅振动.工程力学. 2000, 17(6): 103~106
32 Visweswara Rao G.. Internal Resonance and Non-Linear Response of a Cable under Periodic Excitation. Journal of Sound and Vibration. 1991, 149(1): 25~40
33陈水生,孙炳楠.斜拉索受轴向激励引起的面内参数振动分析.振动工程学报. 2002, 15(2): 144~150
34 Wang P H, Fung R F, Lee M J. Finite Element Analysis of a Three-Dimensional Underwater Cable with Time-Dependent Length. Journal of Sound and Vibtation. 1998, 209(2): 240~249
35 Y. Cai, S. S. Chen. Dynamics Response of a Stack/Cable System Subjected to Vortex Induced Vibration. J. Sound Vib. 1996, 196(3): 337~340
36 J. L. Lilien, A. P. Da Costa. Vibration Amplitudes Caused by Parametric Excitation Of Cable Stayed Structures. J. Sound Vib. 1994, 174(1): 69~87
37邬喆华,楼文娟. MR磁流变阻尼器对斜拉索被动控制的研究.土木工程学报. 2005, 38(4): 78-~83
38 Johnson E A, Christenson R E, Spencer Jr B F. Semiactive Damping of cables with Sag. Computer Aided Civil and Infrastructure Engineering. 2003,18(2): 132~140
39 Pasca M, Vestron F, Gattulli V. Active Longitudinal Control of Wind-Induced Oscillations of Suspension Cable. Mecanica. 1998, 33(3): 255~259
40邬喆华,陈勇,楼文娟.磁流变阻尼器对斜拉索减振效果的试验研究.振动工程学报. 2004, 17(2):102~107
41关新春,欧进萍.磁流变耗能器的阻尼力模型及其参数确定.振动与冲击. 2001, 20(1): 5~8
42 Xu Y L, Yu Z. Mitigation of Three-Dimensional Vibtation of INclinrd Sag Cable UsingDiscrete Oil Damper. Iournal of Sound and Vibration. 1998, 214(4): 659
43邬喆华,楼文娟,陈勇,朱瑶宏.斜拉索基于最优控制力的振动控制.宁波大学学报. 2007, 20(4): 532~534
44丁美林,李镇,张群.斜拉桥斜拉索减振应用技术.江苏技术. 2006(6): 17
45 Susumpow T, Fujino Y. Active Control of Multin mode Cable Vibrations by Axial Support Motion. Journal of Engineering Mechanics ASCE. 1995, 121(9): 964~970
46习燕.拉索——磁流变阻尼器系统数值分析.重庆交通大学硕士学位论文. 2007: 38
47 Pacheco Benito M, Fujino Yozo, Sulekh Ajai. Estimation Curve for Modal Damping in Stay Cables with Viscous Damper. Journal of Structural Engineering. 1993, 119(6): 220~225
48金林,应祖光,罗银淼.斜拉索的不稳定振动及控制.噪声与振动控制. 2004(5): 5~7
49 Spencer B F, Dyke D J, Sain M K. Phenomenological Model of a Magnetorheological Damper. Journal Engineering. Mechanics, 1997, 123: 230~234
2徐克生.斜拉桥拉索非线性振动的数值研究.大连理工大学硕士学位论文. 2007: 4~6
3 Richard E, Christenson B S. Semiactive Control of Civil Structures for Natural Hazard Mitigation, Analytical and Experimental Studies[D]. the University of Notre Dame. 2001
4 Lilien JL, Costa A Pinto Da. Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structures. Journal of Sound and Vibration. 1994, 174(2): 9~90
5 Ni Y Q, Chen Y, Ko JM. Neuro-Control of Vibration using Semi-active Magneto-Rheological Dampers. Engineering Structures. 2002, 24: 295~312
6赵跃宇,蒋丽忠.索—梁组合结构的动力学建模理论及其内共振分析.土木工程学报. 2004, 37(3): 70~72
7康厚军,赵跃宇,王连华.斜拉桥中拉索对桥面动力特性的影响.动力学与控制学报. 2007, 5(1): 44
8 Takahashi K. Dynamic Stability of Cables Subjected to an Axial Periodic Load. Journal of Sound and Vibration. 1991, 144(2): 323~330
9 Costa A Pinto Da, Martins J A C, Branco F, Lilien J L. Oscillations of Bridge Stay Cables Induced by Periodic Motions of Deck and Towers. Journal of Engineering Mechanics. 1996, (7): 613~621
10杨素哲,陈艾荣.超长斜拉索的参数振动.同济大学学报. 2005, 33(10): 1303~1308
11 Ko J M, Chen Y, Zheng G. Experimental Study on Vibration Mitigation of a Stay Cable Using Nonlinear Hysteretic Damper. Advances in Structural Dynamics. Elsevier Science Ltd,Oxford,UK. 2000, 2: 1325~1332
12 Sun BN, Wang ZG, Ko JM, Ni YQ. Parametrically Eexcited Oscillation of Stay-Cable and Iits Control in Cable-Stayed Bridges. Journal of Zhejiang University Science. 2003, 4(I): 13~20.
13陈明宪.斜拉桥建造技术.人民交通出版社, 2004: 170~171
14邬喆华,陈勇.磁流变阻尼器对斜拉索的振动控制.科学出版社, 2007: 15~17
15曾德子,赵章力,卿迟.深圳湾公路大桥(深圳侧通航孔桥)索塔施工.广东交通职业技术学院学报. 2007, 6(3): 23
16吴存全,曾德子,冯飞敏.深圳湾公路大桥通航孔桥斜拉索安装.技术园地. 2007, 8: 51
17康国政. Ansys高级工程应用实例分析与二次开发.电子工业出版社, 2006: 69~81
18袁万城.大跨桥梁空间非线性地震反应分析.同济大学博士学位论文. 1990: 20~24
19席张群.桥梁抗震分析方法对比研究.中国水运. 2007, 7(5): 95~96
20周强,郭少进.支座轴向运动控制拉索风致振动的研究.武汉理工大学学报. 2007, 29(1): 128~131
21梅葵花,吕志涛,孙胜江. CFRP拉索的非线性参数振动特性.中国公路学报. 2007, 20(1): 52~56
22 Chri Genrts, Ton Vrouwenvelder, Piet van. Numerical Modeling of Rain-Wind-Induced Vibration. Structural Engineering International,Erasmus Bridge, Rotterdam. 1998: 129.
23王波,郭翠翠,张海龙,徐丰.端部激励下斜拉索非线性振动及振动松弛.武汉理工大学学报. 2008, 30(2): 75~78
24 Warnitchai P, Fujino Y. A Non-linear Dynamic Modal for Cables and its Application to a Cable-Structure System. Journal of Sound and Vibration. 1995, 187(4): 695~699
25陈水生,孙炳楠.斜拉桥索—桥耦合非线性参数振动数值研究.土木工程学报. 2003, 36(4): 70~71
26 Olivier F. Rain-Wind Induced Vibrations of Cables. Journal of Engineering and Industrial Aerodynamics. 1995(57): 353~362
27刘习军,王霞,张素侠,贾启芬,李强.斜拉桥中索—桥耦合非线性振动的理论研究.工程力学. 2007, 24(7): 125~126
28郑阿奇. MATLAB实用教程.电子工业出版社, 2005
29亢战,钟万勰.斜拉索参数共振问题的数值研究.土木工程学报. 1998, 31(4): 14 -22
30 SIAI-Noury, Ali S A. Large-Amplitude Vibration of Parabolic Cable. Journal of Sound and Vibration. 1985, 101(4): 451~462
31汪至刚,孙炳楠.斜拉索参数振动引起的拉索大幅振动.工程力学. 2000, 17(6): 103~106
32 Visweswara Rao G.. Internal Resonance and Non-Linear Response of a Cable under Periodic Excitation. Journal of Sound and Vibration. 1991, 149(1): 25~40
33陈水生,孙炳楠.斜拉索受轴向激励引起的面内参数振动分析.振动工程学报. 2002, 15(2): 144~150
34 Wang P H, Fung R F, Lee M J. Finite Element Analysis of a Three-Dimensional Underwater Cable with Time-Dependent Length. Journal of Sound and Vibtation. 1998, 209(2): 240~249
35 Y. Cai, S. S. Chen. Dynamics Response of a Stack/Cable System Subjected to Vortex Induced Vibration. J. Sound Vib. 1996, 196(3): 337~340
36 J. L. Lilien, A. P. Da Costa. Vibration Amplitudes Caused by Parametric Excitation Of Cable Stayed Structures. J. Sound Vib. 1994, 174(1): 69~87
37邬喆华,楼文娟. MR磁流变阻尼器对斜拉索被动控制的研究.土木工程学报. 2005, 38(4): 78-~83
38 Johnson E A, Christenson R E, Spencer Jr B F. Semiactive Damping of cables with Sag. Computer Aided Civil and Infrastructure Engineering. 2003,18(2): 132~140
39 Pasca M, Vestron F, Gattulli V. Active Longitudinal Control of Wind-Induced Oscillations of Suspension Cable. Mecanica. 1998, 33(3): 255~259
40邬喆华,陈勇,楼文娟.磁流变阻尼器对斜拉索减振效果的试验研究.振动工程学报. 2004, 17(2):102~107
41关新春,欧进萍.磁流变耗能器的阻尼力模型及其参数确定.振动与冲击. 2001, 20(1): 5~8
42 Xu Y L, Yu Z. Mitigation of Three-Dimensional Vibtation of INclinrd Sag Cable UsingDiscrete Oil Damper. Iournal of Sound and Vibration. 1998, 214(4): 659
43邬喆华,楼文娟,陈勇,朱瑶宏.斜拉索基于最优控制力的振动控制.宁波大学学报. 2007, 20(4): 532~534
44丁美林,李镇,张群.斜拉桥斜拉索减振应用技术.江苏技术. 2006(6): 17
45 Susumpow T, Fujino Y. Active Control of Multin mode Cable Vibrations by Axial Support Motion. Journal of Engineering Mechanics ASCE. 1995, 121(9): 964~970
46习燕.拉索——磁流变阻尼器系统数值分析.重庆交通大学硕士学位论文. 2007: 38
47 Pacheco Benito M, Fujino Yozo, Sulekh Ajai. Estimation Curve for Modal Damping in Stay Cables with Viscous Damper. Journal of Structural Engineering. 1993, 119(6): 220~225
48金林,应祖光,罗银淼.斜拉索的不稳定振动及控制.噪声与振动控制. 2004(5): 5~7
49 Spencer B F, Dyke D J, Sain M K. Phenomenological Model of a Magnetorheological Damper. Journal Engineering. Mechanics, 1997, 123: 230~234