斜拉索非线性参数振动与振动控制
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摘要
斜拉索具有质量小、刚度小、阻尼小的特点,极易在各种激励下发生横向振动,影响桥梁结构安全、使用性能与寿命。作为主要振动形式之一的参数振动,由于现代斜拉桥均采用密索体系,拉索固有频率分布广,且主梁振动的基频均较低,很容易满足其发生的条件,从而激起拉索大幅振动。这对桥梁的安全性及稳定性是个很大的冲击。因此,准确分析其振动特性并制定合理控制措施对于斜拉桥的建设和维护意义重大。
本文首先介绍了斜拉索的非线性特征及拉索振动的基本概况,回顾了国内外学者在斜拉索参数振动方面所做过的主要工作,并对参数振动的机理进行了简要阐述。在综合考虑拉索的垂度效应、大变形效应、拉索与桥梁的倾角效应的基础上,建立了斜拉索轴向激励下非线性参数振动模型,具体推导出斜拉索单自由度方程。并进一步建立拉索-桥面-桥塔耦合振动模型,推导出三自由度非线性参数振动微分方程组。以武汉天兴洲长江大桥为工程背景,利用ANSYS结构分析程序建立了有限元模型,通过模态分析得到了该桥的动力特性。将前三十阶频率与全桥拉索自振频率相匹配,找出可能发生参数振动的拉索。采用龙格-库塔数值分析方法,针对拉索进行参数振动分析,研究其振动特性。详细分析了激励频率、初始索力、倾角、初始扰动、桥面及桥塔质量与刚度、阻尼对参数振动特性的影响。
本文还介绍了各种拉索振动控制方法,重点针对粘弹性阻尼器,对本文所建立的耦合参数振动模型进行了振动控制分析,并提出实际工程中的应用方法。
Due to the small rigidity, small mass and low damping, cables in cable-stayed bridge are prone to exhibit transverse oscillations of large amplitude which may affect the safety of the whole bridge, reduce the service performance and life. Usually, the multi-cable systems are extensively used in modern cable-stayed bridges, the natural frequencies of cables have a wide distribution and the basic frequencies of girders are lower. As a result, the parametric vibration, one of the kinds of cable vibrations, may provoke large amplitude and impact on the safety and stability of bridges as the occurrence conditions are met easily. Therefore, accurate investigation of vibration characteristics and rational countermeasures are very important for construction and maintenance of cable-stayed bridges.
At the first chapter of the paper, the nonlinear characteristics and general situation of cable vibration are introduced, the major works that the domestic and the foreign scholars have done in the field of parametric vibration are reviewed, and the mechanism related are briefly analyzed. Based on the comprehensive effect of sag, large deformation and inclination, the nonlinear model of parametric vibration in axial motivation is built and the single-degree-of-freedom equation is deduced. Furthermore, the cable-girder-tower coupling vibration model is built and the three-degree-of-freedom nonlinear parametric vibration differential equations are gained. The paper sets Tianxinzhou Bridge as the project background and the ANSYS structural analysis procedures are used to develop the dynamic calculation model. Then the dynamic properties are obtained through modal analysis. Comparing the first thirty frequencies of the model with the natural frequencies of cables, the cables that may exhibit parametric vibration were found. The characteristics of vibration are analyzed by Runge-kutta numerical analysis method. The influence of the various parameters, such as excitation frequency, the initial force of cables, the inclination, the initial disturbances, the mass and the stiffness of girder and tower and so on, are investigated.
In addition, the vibration controlling measures are introduced. The coupling vibration model proposed in this paper was used to analyze the effectiveness of the viscoelastic damper employed in vibration controlling measures. At last, the practical controlling methods are presented.
本文首先介绍了斜拉索的非线性特征及拉索振动的基本概况,回顾了国内外学者在斜拉索参数振动方面所做过的主要工作,并对参数振动的机理进行了简要阐述。在综合考虑拉索的垂度效应、大变形效应、拉索与桥梁的倾角效应的基础上,建立了斜拉索轴向激励下非线性参数振动模型,具体推导出斜拉索单自由度方程。并进一步建立拉索-桥面-桥塔耦合振动模型,推导出三自由度非线性参数振动微分方程组。以武汉天兴洲长江大桥为工程背景,利用ANSYS结构分析程序建立了有限元模型,通过模态分析得到了该桥的动力特性。将前三十阶频率与全桥拉索自振频率相匹配,找出可能发生参数振动的拉索。采用龙格-库塔数值分析方法,针对拉索进行参数振动分析,研究其振动特性。详细分析了激励频率、初始索力、倾角、初始扰动、桥面及桥塔质量与刚度、阻尼对参数振动特性的影响。
本文还介绍了各种拉索振动控制方法,重点针对粘弹性阻尼器,对本文所建立的耦合参数振动模型进行了振动控制分析,并提出实际工程中的应用方法。
Due to the small rigidity, small mass and low damping, cables in cable-stayed bridge are prone to exhibit transverse oscillations of large amplitude which may affect the safety of the whole bridge, reduce the service performance and life. Usually, the multi-cable systems are extensively used in modern cable-stayed bridges, the natural frequencies of cables have a wide distribution and the basic frequencies of girders are lower. As a result, the parametric vibration, one of the kinds of cable vibrations, may provoke large amplitude and impact on the safety and stability of bridges as the occurrence conditions are met easily. Therefore, accurate investigation of vibration characteristics and rational countermeasures are very important for construction and maintenance of cable-stayed bridges.
At the first chapter of the paper, the nonlinear characteristics and general situation of cable vibration are introduced, the major works that the domestic and the foreign scholars have done in the field of parametric vibration are reviewed, and the mechanism related are briefly analyzed. Based on the comprehensive effect of sag, large deformation and inclination, the nonlinear model of parametric vibration in axial motivation is built and the single-degree-of-freedom equation is deduced. Furthermore, the cable-girder-tower coupling vibration model is built and the three-degree-of-freedom nonlinear parametric vibration differential equations are gained. The paper sets Tianxinzhou Bridge as the project background and the ANSYS structural analysis procedures are used to develop the dynamic calculation model. Then the dynamic properties are obtained through modal analysis. Comparing the first thirty frequencies of the model with the natural frequencies of cables, the cables that may exhibit parametric vibration were found. The characteristics of vibration are analyzed by Runge-kutta numerical analysis method. The influence of the various parameters, such as excitation frequency, the initial force of cables, the inclination, the initial disturbances, the mass and the stiffness of girder and tower and so on, are investigated.
In addition, the vibration controlling measures are introduced. The coupling vibration model proposed in this paper was used to analyze the effectiveness of the viscoelastic damper employed in vibration controlling measures. At last, the practical controlling methods are presented.
引文
[1]林元培.斜拉桥.北京:人民交通出版社, 2004
[2] Linlien J L, Pinto da Costa A P. Vibration amplitude caused by parametric excitation of cable stayed structures[J]. Journal of Sound and Vibration, 1994, 171(1): 69-90
[3] Randall W Poston, Cable-stay conundrum. Civil Engineering, ASCE, 1998, 68(8): 58-61
[4] Benito, M. Pacheo, Yozo Fujino. Keeping cables clam. Civil Engineering, ASCE, 1993: 56-58
[5] H. Yamaguchi, Y Fujino. Stayed cable dynamics and its vibration control. Bridge Aerodynamics, 1998, Balkema, Rotterdam: 235-253
[6]任淑琰.斜拉桥拉索参数振动研究: [博士学位论文].上海:同济大学, 2007
[7] H. Max Irvine. Cable structure. The Massachusetts Institute of Technology, 1981
[8] I. Kovacs. Zur frage der seilschwingungen and der Seildampfung. Die Bautechnik, 1982
[9] G. Tagata. Harmonically forced, finite amplitude vibration of a string. Journal of Sound and Vibration, 1977, 51(4): 483-492
[10] A. pinto Da Costa, J.A. C. Martins , F. Branco, et al. Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J], Journal of Engineering Mechanics, 1996, 122(7): 613-622
[11] Michel Virlogeux. Cable vibration in cable-stayed bridges[J]. Bridge dynamic, 1998: 212-233
[12] Q. Wu, K. Takahashi, S. Nakamura. Non-linear vibrations of cables considering loosening [J]. Journal of Sound and Vibration, 2003, 261(3): 385-402
[13] Q. Wu, K. Takahashi, S. Nakamura. Non-linear response of cables subjected to periodic support excitation considering cable loosening [J]. Journal of Sound and Vibration, 2004, 271(2): 453-463
[14] B. N. Sun, Z. G. Wang, J. M. Kao, et al. Cable oscillation induced by parametricexcitation of cable-stayed bridge[J]. Advances in Structural Dynamics, J. M. Ko and Y. L. Xu(eds), Elsevier Science Ltd, Oxford, UK, 2000, 1: 553-560
[15]亢战,钟万勰.斜拉桥参数共振问题的数值研究.土木工程学报, 1998, 31(4): 14-22
[16]魏建东,杨佑发,车惠民.斜拉桥拉索的参数振动有限元分析.工程力学, 2000, 17(6): 130-134
[17]汪至刚,孙炳楠.斜拉桥参数振动引起的拉索大幅振动.工程力学, 2001, 18(1): 103-109
[18]赵跃宇,王连华,陈得良等.斜拉索三维非线性动力学性态.湖南大学学报(自然科学版), 2001, 28(3): 90-96
[19]汪至刚,孙炳楠.斜拉索的参数振动.土木工程学报, 2002, 35(5): 28-33
[20]赵跃宇,王连华,陈得良等.斜拉索面内振动和面外摆振的耦合分析.土木工程学报, 2003, 33(4): 65-69
[21]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): 70-75
[22]李忠献,陈海泉,李延涛.斜拉桥参数振动有限元分析与半主动控制.工程力学, 2004, 21(1): 131-135
[23]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
[24]赵跃宇,杨相展,刘伟长等.索梁组合结构中拉索的非线性响应.工程力学, 2006, 23(11): 153-158
[25]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): 52-57
[26]周岱,柳杰,郭军慧等.轴向激励下斜拉索大幅度振动分析.工程力学, 2007, 24(3): 34-41
[27]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社, 2002
[28]王波.斜拉桥索塔参数共振的数值研究: [硕士学位论文].广州:暨南大学, 2006
[29]谭长建.斜拉索参数振动及斜拉桥有限元分析: [硕士学位论文].成都:西南交通大学, 2006
[30]华孝良,徐光辉.桥梁结构非线性分析.北京:高等教育出版社, 1997
[31]宋一凡.公路桥梁动力学.北京:人民交通出版社, 2000
[32] Duane Hanselman, Bruce Littlefield.精通MATLAB综合辅导与指南.李人厚,张平安等译校.西安:西安交通大学出版社, 1998
[33] Nayfeh A. H, Mook D.T,非线性振动.北京:高等教育出版社, 1990
[34]褚亦清,李翠英.非线性振动分析.北京:北京理工大学出版社, 1996
[35]闻邦椿,李以农,韩清凯.非线性振动理论中的解析方法及工程应用.沈阳:东北大学出版社, 2001
[36]陈水生.大跨度斜拉桥拉索的振动及被动、半主动控制: [博士学位论文].杭州:浙江大学, 2002
[37]王修勇.斜拉桥拉索振动控制新技术研究: [博士学位论文].长沙:中南大学, 2002
[38]张伟,岳澄,石九州.桥梁减振技术的发展与应用.青岛理工大学学报, 2007, 28(1): 30-34
[39]钱雪松,艾永明.斜拉桥拉索的减振措施.工业技术经济, 2004, 23(6): 106-108
[40]王金峰,刘斌.斜拉索的振动与抑振措施探讨.中国港湾建设, 2006, (1): 34-37
[41]杨光,王丽荣,王国峰.斜拉桥拉索振动控制新技术研究.黑龙江工程学院学报, 2006, 20(4): 26-28
[42]汪正兴.阻尼减振技术及其在桥梁与塔式结构中的应用.桥梁建设, 1999, 4(26): 22-25
[43] Z.Yu, Y. L. Xu. Mitigation of three-dimensional vibration of induced sag cable using discrete oil dampers. Journal of Sound and Vibration, 1998, 214(4): 659-673
[44] Wu Qingxiong, Takahashi Kazuo, Chen baochun. Influence of cable loosening on nonlinear parametric vibrations of inclined cables. Structural Engineering and Mechanic, 2007, 25(2): 219-237
[2] Linlien J L, Pinto da Costa A P. Vibration amplitude caused by parametric excitation of cable stayed structures[J]. Journal of Sound and Vibration, 1994, 171(1): 69-90
[3] Randall W Poston, Cable-stay conundrum. Civil Engineering, ASCE, 1998, 68(8): 58-61
[4] Benito, M. Pacheo, Yozo Fujino. Keeping cables clam. Civil Engineering, ASCE, 1993: 56-58
[5] H. Yamaguchi, Y Fujino. Stayed cable dynamics and its vibration control. Bridge Aerodynamics, 1998, Balkema, Rotterdam: 235-253
[6]任淑琰.斜拉桥拉索参数振动研究: [博士学位论文].上海:同济大学, 2007
[7] H. Max Irvine. Cable structure. The Massachusetts Institute of Technology, 1981
[8] I. Kovacs. Zur frage der seilschwingungen and der Seildampfung. Die Bautechnik, 1982
[9] G. Tagata. Harmonically forced, finite amplitude vibration of a string. Journal of Sound and Vibration, 1977, 51(4): 483-492
[10] A. pinto Da Costa, J.A. C. Martins , F. Branco, et al. Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J], Journal of Engineering Mechanics, 1996, 122(7): 613-622
[11] Michel Virlogeux. Cable vibration in cable-stayed bridges[J]. Bridge dynamic, 1998: 212-233
[12] Q. Wu, K. Takahashi, S. Nakamura. Non-linear vibrations of cables considering loosening [J]. Journal of Sound and Vibration, 2003, 261(3): 385-402
[13] Q. Wu, K. Takahashi, S. Nakamura. Non-linear response of cables subjected to periodic support excitation considering cable loosening [J]. Journal of Sound and Vibration, 2004, 271(2): 453-463
[14] B. N. Sun, Z. G. Wang, J. M. Kao, et al. Cable oscillation induced by parametricexcitation of cable-stayed bridge[J]. Advances in Structural Dynamics, J. M. Ko and Y. L. Xu(eds), Elsevier Science Ltd, Oxford, UK, 2000, 1: 553-560
[15]亢战,钟万勰.斜拉桥参数共振问题的数值研究.土木工程学报, 1998, 31(4): 14-22
[16]魏建东,杨佑发,车惠民.斜拉桥拉索的参数振动有限元分析.工程力学, 2000, 17(6): 130-134
[17]汪至刚,孙炳楠.斜拉桥参数振动引起的拉索大幅振动.工程力学, 2001, 18(1): 103-109
[18]赵跃宇,王连华,陈得良等.斜拉索三维非线性动力学性态.湖南大学学报(自然科学版), 2001, 28(3): 90-96
[19]汪至刚,孙炳楠.斜拉索的参数振动.土木工程学报, 2002, 35(5): 28-33
[20]赵跃宇,王连华,陈得良等.斜拉索面内振动和面外摆振的耦合分析.土木工程学报, 2003, 33(4): 65-69
[21]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): 70-75
[22]李忠献,陈海泉,李延涛.斜拉桥参数振动有限元分析与半主动控制.工程力学, 2004, 21(1): 131-135
[23]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
[24]赵跃宇,杨相展,刘伟长等.索梁组合结构中拉索的非线性响应.工程力学, 2006, 23(11): 153-158
[25]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): 52-57
[26]周岱,柳杰,郭军慧等.轴向激励下斜拉索大幅度振动分析.工程力学, 2007, 24(3): 34-41
[27]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社, 2002
[28]王波.斜拉桥索塔参数共振的数值研究: [硕士学位论文].广州:暨南大学, 2006
[29]谭长建.斜拉索参数振动及斜拉桥有限元分析: [硕士学位论文].成都:西南交通大学, 2006
[30]华孝良,徐光辉.桥梁结构非线性分析.北京:高等教育出版社, 1997
[31]宋一凡.公路桥梁动力学.北京:人民交通出版社, 2000
[32] Duane Hanselman, Bruce Littlefield.精通MATLAB综合辅导与指南.李人厚,张平安等译校.西安:西安交通大学出版社, 1998
[33] Nayfeh A. H, Mook D.T,非线性振动.北京:高等教育出版社, 1990
[34]褚亦清,李翠英.非线性振动分析.北京:北京理工大学出版社, 1996
[35]闻邦椿,李以农,韩清凯.非线性振动理论中的解析方法及工程应用.沈阳:东北大学出版社, 2001
[36]陈水生.大跨度斜拉桥拉索的振动及被动、半主动控制: [博士学位论文].杭州:浙江大学, 2002
[37]王修勇.斜拉桥拉索振动控制新技术研究: [博士学位论文].长沙:中南大学, 2002
[38]张伟,岳澄,石九州.桥梁减振技术的发展与应用.青岛理工大学学报, 2007, 28(1): 30-34
[39]钱雪松,艾永明.斜拉桥拉索的减振措施.工业技术经济, 2004, 23(6): 106-108
[40]王金峰,刘斌.斜拉索的振动与抑振措施探讨.中国港湾建设, 2006, (1): 34-37
[41]杨光,王丽荣,王国峰.斜拉桥拉索振动控制新技术研究.黑龙江工程学院学报, 2006, 20(4): 26-28
[42]汪正兴.阻尼减振技术及其在桥梁与塔式结构中的应用.桥梁建设, 1999, 4(26): 22-25
[43] Z.Yu, Y. L. Xu. Mitigation of three-dimensional vibration of induced sag cable using discrete oil dampers. Journal of Sound and Vibration, 1998, 214(4): 659-673
[44] Wu Qingxiong, Takahashi Kazuo, Chen baochun. Influence of cable loosening on nonlinear parametric vibrations of inclined cables. Structural Engineering and Mechanic, 2007, 25(2): 219-237