雨滴冲击荷载对斜拉桥拉索风雨激振影响的初步分析
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摘要
为探讨雨滴冲击荷载对斜拉桥斜拉索风雨激振的影响,进行了研讨分析。由于拉索本身的振动会影响雨滴冲击力,对雨滴运动与拉索振动之间的相互作用进行了分析,结果表明雨滴冲击力的大小与拉索的振动无关,可以单独考虑雨滴冲击荷载;原运动方程包含水线项及拉索振动项,许多学者都对其进行过简化,该研究对这些简化方法进行了比较,从风速振幅曲线来看较好,但简化使得原本简洁的运动方程复杂化,不利于运用,而该研究对原始方程进行数值求解很好地解决了这一问题。针对影响冲击荷载的一些因素进行讨论的结果表明:在低风速情况下,雨滴冲击荷载的影响很小可忽略不计;而在强风环境下,随着风速增大,雨滴冲击荷载也增大,且此时拉索振动幅值远大于无冲击荷载时拉索振幅,故此时冲击荷载不可忽略。
In order to investigate the effect of raindrop impact loads on the rain-wind-induced vibration of stay cables of cable-stayed bridges, three aspects were discussed, namely the interaction, modification and influential factors. As the vibration of the cable itself affects the impact force of the raindrops, the interaction between the raindrop impact and cable was analyzed in detail. The results show that the impact force of the raindrops is independent of the vibration of the cable, and the raindrop loads can be considered separately. Secondly, the brief original motion equations implicitly contain the vibration of rivulets and cable, and is difficult to solve, so many scholars have modified them. In the paper, some modified methods were compared through their results, and the solved curves of the wind speed amplitude display rather perfect characters. But the modification makes the original compact motion equation become very complicated and not conducive to be used. This paper presents the numerical solution for the original equation without any modification. Finally, some influenctial factors for the impact loads were studied. It is found that the impact loads of the raindrops are very small and almost could be negligible under the condition of low wind speed. However, in the strong wind environment, the impact load of the raindrops increases with the increase of the wind speed, and the amplitude of the cable vibration is far greater than that without impact loads, so in this case the impact load can not be ignored.
In order to investigate the effect of raindrop impact loads on the rain-wind-induced vibration of stay cables of cable-stayed bridges, three aspects were discussed, namely the interaction, modification and influential factors. As the vibration of the cable itself affects the impact force of the raindrops, the interaction between the raindrop impact and cable was analyzed in detail. The results show that the impact force of the raindrops is independent of the vibration of the cable, and the raindrop loads can be considered separately. Secondly, the brief original motion equations implicitly contain the vibration of rivulets and cable, and is difficult to solve, so many scholars have modified them. In the paper, some modified methods were compared through their results, and the solved curves of the wind speed amplitude display rather perfect characters. But the modification makes the original compact motion equation become very complicated and not conducive to be used. This paper presents the numerical solution for the original equation without any modification. Finally, some influenctial factors for the impact loads were studied. It is found that the impact loads of the raindrops are very small and almost could be negligible under the condition of low wind speed. However, in the strong wind environment, the impact load of the raindrops increases with the increase of the wind speed, and the amplitude of the cable vibration is far greater than that without impact loads, so in this case the impact load can not be ignored.
引文
[ 1 ] HIKAMI Y,SHIRAISHI N.Rain-wind-induced vibrations of cables in cable stayed bridges [J].Journal of Wind Engineering and Industrial Aerodynamics,1988,29:409-418.
[ 2 ] 陈政清.斜拉索风雨振现场观测与振动控制[J].建筑科学与工程学报,2005,22(4):5-10.CHEN Zhengqing.On site observation of wind rain induced vibration of stay cables and its control [J].Journal of Architecture and Civil Engineering,2005,22(4):5-10.
[ 3 ] JING Haiquan,XIA Yong,LI Hui,et al.Excitation mechanism of rain-wind induced cable vibration in a wind tunnel [J].Journal of Fluids and Structures,2017,68:32-47.
[ 4 ] 刘小兵,陈帅,郑云飞,等.斜拉索风雨激振试验新装置的设计与应用[J].振动与冲击,2017,36(15):230-234.LIU Xiaobing,CHEN Shuai,ZHENG Yunfei,et al.Design and application of a new test rig for stay cables’ rain-wind induced vibration [J].Journal of Vibration and Shock,2017,36(15):230-234.
[ 5 ] GU M,DU X Q,LI S Y.Experimental and theoretical simulations on wind-rain-induced vibration of 3 D rigid stay cables [J].Journal of Sound and Vibration,2009,320:184-200.
[ 6 ] 张琪昌,李伟义,王炜.斜拉索风雨振的动力学行为研究[J].振动与冲击,2010,29(4):173-176.ZHANG Qichang,LI Weiyi,WANG Wei.Nonlinear dynamic behavior of rain-wind-induced vibration of a stay cable [J].Journal of Vibration and Shock,2010,29(4):173-176.
[ 7 ] 李暾,陈政清,李寿英.拉索风雨激振的多模态耦合及面内-面外振动[J].振动与冲击,2012,31(4):115-122.LI Tun,CHEN Zhengqing,LI Shouying.Modes coupling and in-plane/out-of-plane vibration in rain-wind induced vibration of cable [J].Journal of Vibration and Shock,2012,31(4):115-122.
[ 8 ] WANG J,LU P,BI J H,et al.Three-phase coupled modeling research on rain-wind induced vibration of stay cable based on lubrication theory [J].Journal of Fluids and Structures,2016,63:16-39.
[ 9 ] 毕继红,武冀,关健,等.斜拉索风雨激振数值模拟及其机理探究[J].振动与冲击,2017,36(11):111-117.BI Jihong,WU Ji,GUAN Jian,et al.Numerical simulation of rain-wind induced vibration of stay cables and its mechanism study [J].Journal of Vibration and Shock,2017,36(11):111-117.
[10] 徐刚,王靖夫,任文敏.斜拉桥拉索雨风振机理探讨[J].工程力学,2004,21(3):44-49.XU Gang,WANG Jingfu,REN Wenmin.Mechanism of rain-wind-induced vibrations of cables in cable-stayed bridges [J].Engineering Mechanics,2004,21(3):44-49.
[11] 黄麟,郭志明,王国砚,等.斜拉桥拉索风雨激振的理论分析[J].同济大学学报,2002,30(5):569-572.HUANG Lin,GUO Zhiming,WANG Guoyan,et al.Theoretical analysis of rain-wind-induced vibration of cable of cable-stayed bridges [J].Journal of Tongji University,2002,30(5):569-572.
[12] 李寿英,顾明,陈政清.准运动水线三维连续弹性拉索风雨激振理论模型[J].工程力学,2007,24(6):7-15.LI Shouying,GU Ming,CHEN Zhengqing.Analytical model for rain-wind-induced vibration of three-dimensional continuous stay cable with quasi-moving rivulet [J].Engineering Mechanics,2007,24(6):7-15.
[13] 李寿英,顾明,陈政清.运动水线三维连续弹性拉索风雨激振理论模型[J].湖南大学学报(自然科学版),2009,36(2):1-7.LI Shouying,GU Ming,CHEN Zhengqing.An analytical model of rain-wind-induced vibration of three-dimensional continuous stay cable with actual moving rivulet [J].Journal of Hunan University (Natural Sciences),2009,36(2):1-7.
[14] WANG Lingyun,XU Y L.Wind-rain-induced vibration of cable:an analytical model (1) [J].International Journal of Solids and Structures,2003,40:1265-1280.
[15] XU Y L,WANG L Y.Analytical study of wind-rain-induced cable vibration:SDOF model [J].Journal of Wind Engineering and Industrial Aerodynamics,2003,91:27-40.
[16] WILDE K,WIKOWSKI W.Simple model of rain-wind-induced vibrations of stayed cables [J].Journal of Wind Engineering and Industrial Aerodynamics,2003,91:873-891.
[17] 何向东,廖海黎.斜拉索风雨振动分析及机理初探[J].空气动力学学报,2005,23(4):480-483.HE Xiangdong,LIAO Haili.Analysis and initial mechanism research of rain-wind-induced vibration of stay-cable [J].Acta Aerodynamica Sinica,2005,23(4):480-483.
[18] 李宏男,任月明,白海峰.输电塔体系风雨激励的动力分析模型[J].中国电机工程学报,2007,27(30):43-48.LI Hongnan,REN Yueming,BAI Haifeng.Rain-wind-induced dynamic model for transmission tower system [J].Proceeding of the CSEE,2007,27(30):43-48.
[ 2 ] 陈政清.斜拉索风雨振现场观测与振动控制[J].建筑科学与工程学报,2005,22(4):5-10.CHEN Zhengqing.On site observation of wind rain induced vibration of stay cables and its control [J].Journal of Architecture and Civil Engineering,2005,22(4):5-10.
[ 3 ] JING Haiquan,XIA Yong,LI Hui,et al.Excitation mechanism of rain-wind induced cable vibration in a wind tunnel [J].Journal of Fluids and Structures,2017,68:32-47.
[ 4 ] 刘小兵,陈帅,郑云飞,等.斜拉索风雨激振试验新装置的设计与应用[J].振动与冲击,2017,36(15):230-234.LIU Xiaobing,CHEN Shuai,ZHENG Yunfei,et al.Design and application of a new test rig for stay cables’ rain-wind induced vibration [J].Journal of Vibration and Shock,2017,36(15):230-234.
[ 5 ] GU M,DU X Q,LI S Y.Experimental and theoretical simulations on wind-rain-induced vibration of 3 D rigid stay cables [J].Journal of Sound and Vibration,2009,320:184-200.
[ 6 ] 张琪昌,李伟义,王炜.斜拉索风雨振的动力学行为研究[J].振动与冲击,2010,29(4):173-176.ZHANG Qichang,LI Weiyi,WANG Wei.Nonlinear dynamic behavior of rain-wind-induced vibration of a stay cable [J].Journal of Vibration and Shock,2010,29(4):173-176.
[ 7 ] 李暾,陈政清,李寿英.拉索风雨激振的多模态耦合及面内-面外振动[J].振动与冲击,2012,31(4):115-122.LI Tun,CHEN Zhengqing,LI Shouying.Modes coupling and in-plane/out-of-plane vibration in rain-wind induced vibration of cable [J].Journal of Vibration and Shock,2012,31(4):115-122.
[ 8 ] WANG J,LU P,BI J H,et al.Three-phase coupled modeling research on rain-wind induced vibration of stay cable based on lubrication theory [J].Journal of Fluids and Structures,2016,63:16-39.
[ 9 ] 毕继红,武冀,关健,等.斜拉索风雨激振数值模拟及其机理探究[J].振动与冲击,2017,36(11):111-117.BI Jihong,WU Ji,GUAN Jian,et al.Numerical simulation of rain-wind induced vibration of stay cables and its mechanism study [J].Journal of Vibration and Shock,2017,36(11):111-117.
[10] 徐刚,王靖夫,任文敏.斜拉桥拉索雨风振机理探讨[J].工程力学,2004,21(3):44-49.XU Gang,WANG Jingfu,REN Wenmin.Mechanism of rain-wind-induced vibrations of cables in cable-stayed bridges [J].Engineering Mechanics,2004,21(3):44-49.
[11] 黄麟,郭志明,王国砚,等.斜拉桥拉索风雨激振的理论分析[J].同济大学学报,2002,30(5):569-572.HUANG Lin,GUO Zhiming,WANG Guoyan,et al.Theoretical analysis of rain-wind-induced vibration of cable of cable-stayed bridges [J].Journal of Tongji University,2002,30(5):569-572.
[12] 李寿英,顾明,陈政清.准运动水线三维连续弹性拉索风雨激振理论模型[J].工程力学,2007,24(6):7-15.LI Shouying,GU Ming,CHEN Zhengqing.Analytical model for rain-wind-induced vibration of three-dimensional continuous stay cable with quasi-moving rivulet [J].Engineering Mechanics,2007,24(6):7-15.
[13] 李寿英,顾明,陈政清.运动水线三维连续弹性拉索风雨激振理论模型[J].湖南大学学报(自然科学版),2009,36(2):1-7.LI Shouying,GU Ming,CHEN Zhengqing.An analytical model of rain-wind-induced vibration of three-dimensional continuous stay cable with actual moving rivulet [J].Journal of Hunan University (Natural Sciences),2009,36(2):1-7.
[14] WANG Lingyun,XU Y L.Wind-rain-induced vibration of cable:an analytical model (1) [J].International Journal of Solids and Structures,2003,40:1265-1280.
[15] XU Y L,WANG L Y.Analytical study of wind-rain-induced cable vibration:SDOF model [J].Journal of Wind Engineering and Industrial Aerodynamics,2003,91:27-40.
[16] WILDE K,WIKOWSKI W.Simple model of rain-wind-induced vibrations of stayed cables [J].Journal of Wind Engineering and Industrial Aerodynamics,2003,91:873-891.
[17] 何向东,廖海黎.斜拉索风雨振动分析及机理初探[J].空气动力学学报,2005,23(4):480-483.HE Xiangdong,LIAO Haili.Analysis and initial mechanism research of rain-wind-induced vibration of stay-cable [J].Acta Aerodynamica Sinica,2005,23(4):480-483.
[18] 李宏男,任月明,白海峰.输电塔体系风雨激励的动力分析模型[J].中国电机工程学报,2007,27(30):43-48.LI Hongnan,REN Yueming,BAI Haifeng.Rain-wind-induced dynamic model for transmission tower system [J].Proceeding of the CSEE,2007,27(30):43-48.
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