大跨斜拉桥拉索面内参数振动简化模型及工程应用
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摘要
斜拉索是斜拉桥的重要受力构件,当索梁耦合振动时,斜拉索易发生大幅的参数振动。本文提出了一个不计拉索垂度并忽略桥梁自重影响的单自由度力学模型,推出了斜拉索参数振动的简化分析方程。为了考察方程的可行性,利用计算机对该方程进行了仿真,并与另一考虑索桥耦合作用运动方程的仿真分析作了对照,得到了非常相近的结果。基于实验室24.2m的模型斜拉索,辨识了该拉索的固有频率和阻尼,通过试验实现了该斜拉索的一阶参数振动,并分析了发生一阶参数振动时激励频率与固有频率比值。另外运用本文提出的简化方程对实验室拉索作了仿真,得到了参数振动现象,与实验结果对比得到:利用简化分析模型对试验拉索的仿真分析与实验室拉索的实验结果比较吻合,表明不考虑桥梁质量的简化模型具有足够的准确性。最后,结合工程实例,对鄂东大桥的某一可能发生参数振动的拉索进行了仿真分析,表明在桥梁自重较重时本文所提出的简化方程具有较好的适用性;并且发现加装阻尼器可以有效抑制拉索的参数振动。
The stayed cable is an important force member of the cable-stayed bridge. When the beam is coupled with vibration, the cable inclines to having a large parametric vibration. This paper proposes a mechanical model with single-degree-of-freedom in which the bridge weight is neglected, a simplified analytical equation of parametric vibration of stayed cables is built up. In order to investigate the feasibility of the equation, the equation is simulated and compared with another simulation analysis considering the coupled equations of motion of the cable-stayed bridge. The results are very similar. Based on the 24.2 m model diagonal cable in laboratory, the natural frequency and damping of the cable are identified. The first-order parametric vibration of the cable is tested and the ratio between excitation frequency and intrinsic frequency is recognized. In addition, the simplified model presented in this paper was used to simulate the cable in the laboratory. The parametric vibration is obtained. Compared with the experimental results obtained, the simulation analysis of the lab cable using the simplified analysis model is in good agreement with the experimental results of the lab cable, indicating that the simplified model without consideration of the bridge mass has sufficient accuracy. Finally, combining with the engineering example, a certain cable vibration of the E Dong Bridge is simulated. Moreover, it is found that adding dampers has better restraining effects on the parametric vibration of cables.
The stayed cable is an important force member of the cable-stayed bridge. When the beam is coupled with vibration, the cable inclines to having a large parametric vibration. This paper proposes a mechanical model with single-degree-of-freedom in which the bridge weight is neglected, a simplified analytical equation of parametric vibration of stayed cables is built up. In order to investigate the feasibility of the equation, the equation is simulated and compared with another simulation analysis considering the coupled equations of motion of the cable-stayed bridge. The results are very similar. Based on the 24.2 m model diagonal cable in laboratory, the natural frequency and damping of the cable are identified. The first-order parametric vibration of the cable is tested and the ratio between excitation frequency and intrinsic frequency is recognized. In addition, the simplified model presented in this paper was used to simulate the cable in the laboratory. The parametric vibration is obtained. Compared with the experimental results obtained, the simulation analysis of the lab cable using the simplified analysis model is in good agreement with the experimental results of the lab cable, indicating that the simplified model without consideration of the bridge mass has sufficient accuracy. Finally, combining with the engineering example, a certain cable vibration of the E Dong Bridge is simulated. Moreover, it is found that adding dampers has better restraining effects on the parametric vibration of cables.
引文
[1]任淑琰.斜拉桥拉索参数振动研究[D].上海:同济大学,2007.(REN Shuyan.Parametric oscillation of cables in cable-stayed bridges[D].Shanghai:Tongji University,2007(in Chinese)).
[2]KOVACS I.Zur frage der seilschwingungen und der seild?mfung[J].Bautechnik,1981,59(10):325-332.
[3]PACHECO B M,FUJINO Y,SULEKH A.Estimation curve for modal damping in stay cables with viscous damper[J].Journal of structural engineering,1993,119(6):1961-1979.
[4]FUJINO Y,WARNITCHAI P,PACHECO B M.An experimental and analytical study of auto parametric resonance on a 3 DOF model of cable-stayed-beam[J].Nonlinear dynamics,1993,4(2):111-138.
[5]COSTA P D,MARTINS J A C.Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J].Journal of engineering mechanics,1996,12(7):613-622.
[6]黄迪山,张月月.参数振动自由响应的指数三角级数逼近[J].应用力学学报,2016,33(6):936-941.(HUANG Dishan,ZHANGYueyue.Exponential trigonometric series approach to free response of parametric vibration[J].Chinese journal of applied mechanics,2016,33(6):936-941(in Chinese)).
[7]黄迪山,邵何锡.多自由度参数振动受迫响应的三角级数逼近[J].应用力学学报,2014,31(5):703-709.(HUANG Dishan,SHAOHexi.Vector trigonometric series approach to forced response of a multiple freedom parametric vibration[J].Chinese journal of applied mechanics,2014,31(5):703-709(in Chinese)).
[8]汪峰,文晓旭,刘章军.斜拉桥塔-索-桥面连续耦合参数振动特性分析[J].应用力学学报,2015,32(2):340-346.(WANG Feng,WEN Xiaoxu,LIU Zhangjun.Coupled vibration analysis of tower-cable-deck of long-span cable-stayed bridge[J].Chinese journal of applied mechanics,2015,32(2):340-346(in Chinese)).
[9]KANG Zhan,XU Kesheng,LUO Zhen.A numerical study on nonlinear vibration of an inclined cable coupled with the deck in cable-stayed bridges[J].Journal of vibration and control,2011,18(3):404-416.
[10]亢战,钟万勰.斜拉桥参数共振问题的数值研究[J].土木工程学报,1998,31(4):14-22.(KANG Zhan,ZHONG Wanxie.Numerical study on parametric resonance of cable in cable stayed bridge[J].China civil engineering journal,1998,31(4):14-22(in Chinese)).
[11]汪志刚,孙炳楠.斜拉索的参数振动[J].土木工程学报,2002,5(5):28-33.(WANG Zhigang,SUN Bingnan.Parametric vibration of the cable in cable-stayed bridge[J].China civil engineering journal,2002,5(5):28-33(in Chinese)).
[12]赵跃宇,吕建根.索-拱组合结构中斜拉索的非线性参数振动[J].土木工程学报,2006,39(12):67-72.(ZHAO Yueyu,LüJian’gen.Non-linear parametric vibration of cables in cable-arch composite structures[J].China civil engineering journal,2006,39(12):67-72(in Chinese)).
[13]陈丕华,王修勇,陈政清,等.斜拉索面内参数振动的理论和试验研究[J].振动与冲击,2010,29(2):50-53.(CHEN Pihua,WANGXiuyong,CHEN Zhengqing,et al.Theoretical and experimental study on planar parametric oscillations in a stayed-cable[J].Journal of vibration and shock,2010,29(2):50-53(in Chinese)).
[2]KOVACS I.Zur frage der seilschwingungen und der seild?mfung[J].Bautechnik,1981,59(10):325-332.
[3]PACHECO B M,FUJINO Y,SULEKH A.Estimation curve for modal damping in stay cables with viscous damper[J].Journal of structural engineering,1993,119(6):1961-1979.
[4]FUJINO Y,WARNITCHAI P,PACHECO B M.An experimental and analytical study of auto parametric resonance on a 3 DOF model of cable-stayed-beam[J].Nonlinear dynamics,1993,4(2):111-138.
[5]COSTA P D,MARTINS J A C.Oscillations of bridge stay cables induced by periodic motions of deck and/or towers[J].Journal of engineering mechanics,1996,12(7):613-622.
[6]黄迪山,张月月.参数振动自由响应的指数三角级数逼近[J].应用力学学报,2016,33(6):936-941.(HUANG Dishan,ZHANGYueyue.Exponential trigonometric series approach to free response of parametric vibration[J].Chinese journal of applied mechanics,2016,33(6):936-941(in Chinese)).
[7]黄迪山,邵何锡.多自由度参数振动受迫响应的三角级数逼近[J].应用力学学报,2014,31(5):703-709.(HUANG Dishan,SHAOHexi.Vector trigonometric series approach to forced response of a multiple freedom parametric vibration[J].Chinese journal of applied mechanics,2014,31(5):703-709(in Chinese)).
[8]汪峰,文晓旭,刘章军.斜拉桥塔-索-桥面连续耦合参数振动特性分析[J].应用力学学报,2015,32(2):340-346.(WANG Feng,WEN Xiaoxu,LIU Zhangjun.Coupled vibration analysis of tower-cable-deck of long-span cable-stayed bridge[J].Chinese journal of applied mechanics,2015,32(2):340-346(in Chinese)).
[9]KANG Zhan,XU Kesheng,LUO Zhen.A numerical study on nonlinear vibration of an inclined cable coupled with the deck in cable-stayed bridges[J].Journal of vibration and control,2011,18(3):404-416.
[10]亢战,钟万勰.斜拉桥参数共振问题的数值研究[J].土木工程学报,1998,31(4):14-22.(KANG Zhan,ZHONG Wanxie.Numerical study on parametric resonance of cable in cable stayed bridge[J].China civil engineering journal,1998,31(4):14-22(in Chinese)).
[11]汪志刚,孙炳楠.斜拉索的参数振动[J].土木工程学报,2002,5(5):28-33.(WANG Zhigang,SUN Bingnan.Parametric vibration of the cable in cable-stayed bridge[J].China civil engineering journal,2002,5(5):28-33(in Chinese)).
[12]赵跃宇,吕建根.索-拱组合结构中斜拉索的非线性参数振动[J].土木工程学报,2006,39(12):67-72.(ZHAO Yueyu,LüJian’gen.Non-linear parametric vibration of cables in cable-arch composite structures[J].China civil engineering journal,2006,39(12):67-72(in Chinese)).
[13]陈丕华,王修勇,陈政清,等.斜拉索面内参数振动的理论和试验研究[J].振动与冲击,2010,29(2):50-53.(CHEN Pihua,WANGXiuyong,CHEN Zhengqing,et al.Theoretical and experimental study on planar parametric oscillations in a stayed-cable[J].Journal of vibration and shock,2010,29(2):50-53(in Chinese)).