主塔刚度对斜拉桥固有特性的影响分析
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摘要
文章以一类单塔斜拉桥为例,研究了主塔刚度对斜拉桥的固有频率和模态的影响,以欧拉-伯努利梁模型描述桥面和塔的运动,并同时考虑斜拉索的横向和纵向运动,建立斜拉桥的动力学方程、边界条件及子结构间的相容条件,推导出斜拉桥的固有频率方程和振型函数。数值结果表明:将塔视为柔性构件时,塔的刚度对斜拉桥的固有频率和模态影响并不显著;若将塔视为刚性构件,则所求解出的固有频率和模态与柔性塔的情况相差很大,并会丢失某些模态;斜拉桥存在密集固有频率、模态跃迁及频率曲线偏转现象。研究结果可为斜拉桥结构设计及振动分析提供理论依据。
In this paper,the effect of the rigidity of tower on the natural frequencies and mode shapes of the cable-stayed bridge that consists of a simply-supported two-cable-stayed deck beam and a single tower is presented.The bridge deck and tower are modeled by using Euler-Bernoulli beam model.Considering the transverse and longitudinal motions of the stay cables,the partial differential equations that govern vibrations of the stay cables,tower,and segments of the deck beam,respectively,are established,as well as their boundary and matching conditions.The natural frequency equation and mode shape function of the cable-stayed bridge are derived.Numerical results show that when the tower is considered as a flexible body,the rigidity of the tower has little influence on the natural frequencies and mode shapes of the cable-stayed bridge.However,natural frequencies and mode shapes are quite different from those when the tower is considered as a rigid body.Moreover,there are mode jumping phenomenon and frequency curve veering in the process of local symmetry breaking.The study results can provide a theoretical basis for the structural design and vibration analysis of the cable-stayed bridge.
In this paper,the effect of the rigidity of tower on the natural frequencies and mode shapes of the cable-stayed bridge that consists of a simply-supported two-cable-stayed deck beam and a single tower is presented.The bridge deck and tower are modeled by using Euler-Bernoulli beam model.Considering the transverse and longitudinal motions of the stay cables,the partial differential equations that govern vibrations of the stay cables,tower,and segments of the deck beam,respectively,are established,as well as their boundary and matching conditions.The natural frequency equation and mode shape function of the cable-stayed bridge are derived.Numerical results show that when the tower is considered as a flexible body,the rigidity of the tower has little influence on the natural frequencies and mode shapes of the cable-stayed bridge.However,natural frequencies and mode shapes are quite different from those when the tower is considered as a rigid body.Moreover,there are mode jumping phenomenon and frequency curve veering in the process of local symmetry breaking.The study results can provide a theoretical basis for the structural design and vibration analysis of the cable-stayed bridge.
引文
[1]王钱钱.斜拉桥结构采用碳纤维斜拉索与传统钢斜拉索的对比分析[D].西安:长安大学,2014.
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[7]蒋友宝,冯健,孟少平.结构损伤识别中模态跃迁的研究[J].工程力学,2006,23(6):35-40,76.
[8]于岩磊,高维成,刘伟,等.密集模态结构模态跃迁分析的简化摄动法[J].工程力学,2012,29(3):33-40.
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[10]EVERALL P R,HUNT G W.Mode jumping in the buckling of struts and plates:a Comparative study[J].International Journal of Non-Linear Mechanics,2000,35(6):1067-1079.
[11]CHEN H,VIRGIN L N.Dynamic analysis of modal shifting and mode jumping in thermally buckled plates[J].Journal of Sound and Vibration,2004,278(1/2):233-256.
[12]张淼,于澜,鞠伟.模态跳跃现象对振动分析的影响研究[J].合肥工业大学学报(自然科学版),2015,38(11):1524-1529,1569.
[13]GATTULLI V,LEPIDI M.Localization and veering in the dynamics of cable-stayed bridges[J].Computers and Structures,2007,85(21/22)1661-1678.
[14]CAO D Q,SONG M T,ZHU W D,et al.Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge[J].Journal of Sound and Vibration,2012,331(26):5685-5714.
[15]李专干,宋敉淘,曹登庆,等.一类单塔斜拉桥固有频率及模态的计算与分析[J].应用力学学报,2016,33(6):1038-1044.
[2]AU F T K,CHENG Y K,ZHENG D Y.On the determination of natural frequencies and mode shapes of cable-stayed bridges[J].Applied Mathematical Modelling,2001,25(12):1099-1115.
[3]幸厚冰.斜拉结构的动力特性及参数影响分析[D].哈尔滨:哈尔滨工业大学,2009.
[4]CHENG J,JIANG J J,XIAO R C,et al.Advanced aerostatic stability analysis of cable-stayed bridges using finite-element method[J].Computers and Structures,2002,80(13):1145-1158.
[5]刘祥君.桥梁建设中有限单元法应用的研究[D].天津:天津大学,2005.
[6]李朝忠,张海文.收缩徐变对矮塔斜拉桥主梁挠度的影响[J].四川建筑,2007,27(5):101-104.
[7]蒋友宝,冯健,孟少平.结构损伤识别中模态跃迁的研究[J].工程力学,2006,23(6):35-40,76.
[8]于岩磊,高维成,刘伟,等.密集模态结构模态跃迁分析的简化摄动法[J].工程力学,2012,29(3):33-40.
[9]BENDIKSEN O O.Localization phenomena in structural dynamics[J].Chaos,Solitons and Fractals,2000,11(10):1621-1660.
[10]EVERALL P R,HUNT G W.Mode jumping in the buckling of struts and plates:a Comparative study[J].International Journal of Non-Linear Mechanics,2000,35(6):1067-1079.
[11]CHEN H,VIRGIN L N.Dynamic analysis of modal shifting and mode jumping in thermally buckled plates[J].Journal of Sound and Vibration,2004,278(1/2):233-256.
[12]张淼,于澜,鞠伟.模态跳跃现象对振动分析的影响研究[J].合肥工业大学学报(自然科学版),2015,38(11):1524-1529,1569.
[13]GATTULLI V,LEPIDI M.Localization and veering in the dynamics of cable-stayed bridges[J].Computers and Structures,2007,85(21/22)1661-1678.
[14]CAO D Q,SONG M T,ZHU W D,et al.Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge[J].Journal of Sound and Vibration,2012,331(26):5685-5714.
[15]李专干,宋敉淘,曹登庆,等.一类单塔斜拉桥固有频率及模态的计算与分析[J].应用力学学报,2016,33(6):1038-1044.