协作体系斜拉桥竖向自由振动理论研究
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摘要
基于大位移非线性弹性理论的广义变分原理,考虑加劲梁轴向压缩应变能和剪切应变能的影响,建立了协作体系斜拉桥空间耦合自由振动的大位移不完全广义势能泛函,通过约束变分导出了协作体系斜拉桥的加劲主梁竖向挠曲振动微分方程.同时以金马大桥为例,构造了T构与斜拉桥协作体系的边界条件.求解出的竖向振动方程的解析解,与有限元数值结果对比吻合良好,证明了方法的正确性.这一方法可为同类型结构的固有振动特性分析提供参考.
Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection,the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder.By constraint variation,the differential equations of vertical vibration of the stiffening girder of collaborated system cable-stayed bridge were derived.The Golden Horse Bridge with T-shape rigid structure and single-tower cable-stayed bridge is taken as an example for the solution of vertical vibration differential equation through the presented boundary condition.By comparing with finite element numerical results the correctness of the method is testified,and the method can provide more attention to the analysis of free vibration of this kind of structure.
Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection,the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder.By constraint variation,the differential equations of vertical vibration of the stiffening girder of collaborated system cable-stayed bridge were derived.The Golden Horse Bridge with T-shape rigid structure and single-tower cable-stayed bridge is taken as an example for the solution of vertical vibration differential equation through the presented boundary condition.By comparing with finite element numerical results the correctness of the method is testified,and the method can provide more attention to the analysis of free vibration of this kind of structure.
引文
[1]李国豪.桥梁结构稳定与振动[M].北京:中国铁道出版社,1992
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[9]楼梦麟,任志刚.Timoshenko简支梁的振动模态特性精确解[J].同济大学学报(自然科学版),2002,8(2):911-915
[10]孙焕纯,曲乃泗,林家浩.计算结构动力学[M].北京:高等教育出版社,1989
[11]张哲.金马大桥设计实践与理论探索[J].大连理工大学学报,1999,39(3):285-293(ZHANG Zhe.Design practice and theoreticalexploration of Jinma Bridge[J].J Dalian UnivTechnol,1999,39(3):285-293)
[2]武秀丽.结构工程中的振动理论及其应用[M].北京:中国铁道出版社,1980
[3]陈淮.大跨度斜拉桥动力特性分析[J].计算力学学报,1997,14(1):57-63
[4]陈幼平.斜拉桥地震反应特性的研究[D].武汉:铁道部科学研究院,1994
[5]伏魁先,张惠群.几何非线性因素对密索型斜拉桥自振特性的影响[J].西南交通大学学报,1990,76(2):10-13
[6]颜娟.金马大桥工程的结构分析与研究[M].北京:中国铁道出版社,1980
[7]ALLAM S M,DATTA T K.Analysis ofcable-stayed bridges under multi-component randomground motion by response spectrum method[J].Eng Struct,2000,22:1365-1367
[8]钱伟长.变分法及有限元[M].北京:科学出版社,1980
[9]楼梦麟,任志刚.Timoshenko简支梁的振动模态特性精确解[J].同济大学学报(自然科学版),2002,8(2):911-915
[10]孙焕纯,曲乃泗,林家浩.计算结构动力学[M].北京:高等教育出版社,1989
[11]张哲.金马大桥设计实践与理论探索[J].大连理工大学学报,1999,39(3):285-293(ZHANG Zhe.Design practice and theoreticalexploration of Jinma Bridge[J].J Dalian UnivTechnol,1999,39(3):285-293)
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