弹性边界条件下斜拉索弯曲振动特性建模与索力分析
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摘要
针对斜拉索索力估算不准问题,提出一种基于伽辽金原理的弹性边界条件下拉索振动特性分析模型和索力估算分析方法.建立弹性约束边界的斜拉索弯曲振动预测模型,采用切比雪夫级数研究振型函数,推导拉索振动特征方程,通过虚位移原理构建有限个自由度系统,求解拉索振动前n阶固有频率和主振型,以精确计算拉索索力;对比分析已有文献解析求解的计算结果,验证在固支-固支、固支-简支两种经典边界条件下应用本文方法的有效性;改变拉索边界约束的拉伸刚度和扭转刚度,研究其对振动特性影响的变化规律;分析估算当拉索固有频率在±3%范围内变化时索力的变化情况.最后,搭建拉索振动试验平台,通过试验结果与计算结果对比验证本文方法的正确性.结果表明:当拉索边界为固支-固支时,估算索力最大误差为-7.83%～8.17%,当边界为固支-简支时,估算索力最大误差为-6.83%～6.69%,误差变化了-1.00%～1.48%.以上分析表明,应根据拉索两端的实际边界约束情况来计算相应的索力.
In order to solve the problem of inaccurate estimation of cable force, an analytical model of cable vibration characteristics based on Galerkin principle under elastic boundary conditions is presented. The vibration characteristic function of the cable is described as Chebyshev series. According to the principle of virtual displacement, the vibration characteristic equation is constructed and the nth order natural frequency and corresponding mode shapes of the cable are obtained with calculation of the cable force. By comparing with the reference results from literature, the validity of the proposed method is verified. The influence of the cable boundary constraints on cable force and vibration characteristics is studied. Cable force is analyzed and estimated when the natural frequency of the cable changes within ±3%. Finally, a cable vibration test platform is built to verify the method by comparing the test results with the calculation results. The results show that when the cable boundary is fixed-fixed, the maximum error of estimated cable force is around-7.83% to 8.17%. When the boundary is fixed-hinged, the maximum error of estimated cable force is around-6.83% to 6.69%. The error is varied around-1.00% to 1.48%. The above analysis shows that the corresponding cable force should be calculated according to the actual boundary constraints at both ends of the cable.
In order to solve the problem of inaccurate estimation of cable force, an analytical model of cable vibration characteristics based on Galerkin principle under elastic boundary conditions is presented. The vibration characteristic function of the cable is described as Chebyshev series. According to the principle of virtual displacement, the vibration characteristic equation is constructed and the nth order natural frequency and corresponding mode shapes of the cable are obtained with calculation of the cable force. By comparing with the reference results from literature, the validity of the proposed method is verified. The influence of the cable boundary constraints on cable force and vibration characteristics is studied. Cable force is analyzed and estimated when the natural frequency of the cable changes within ±3%. Finally, a cable vibration test platform is built to verify the method by comparing the test results with the calculation results. The results show that when the cable boundary is fixed-fixed, the maximum error of estimated cable force is around-7.83% to 8.17%. When the boundary is fixed-hinged, the maximum error of estimated cable force is around-6.83% to 6.69%. The error is varied around-1.00% to 1.48%. The above analysis shows that the corresponding cable force should be calculated according to the actual boundary constraints at both ends of the cable.
引文
[1]李国强,顾明.拉索振动、动力检测与振动控制理论[M].北京:科学出版社,2014:98-99.
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[3]甘泉.复杂边界条件下索结构的内力识别方法研究[D].广州:华南理工大学,2015.
[4]魏金波,李国强,蒋夏子俊.弹性支承拉索动力特性研究[J].结构工程师,2011,27(3):25-30.
[5]刘文峰,应怀樵,柳春图.考虑刚度及边界条件的索力精确求解[J].振动与冲击,2003,22(4):12-25.
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[7]廖敬波,唐光武,孟利波.固结拉索的一种近似频率计算公式[J].振动与冲击,2013,32(6):149-151;172.
[8]秦小平,廖敬波,孟利波.固支-铰支拉索近似频率计算公式及求解条件讨论[C]//中国土木工程学会桥梁及结构工程分会.第二十一届全国桥梁学术会议论文集(下册).北京:人民交通出版社,2014:969-974.
[9]Kim B H,Park T.Estimation of cable tension force using the frequency-based system identification method[J].Journal of Sound and Vibration,2007,304(3/5):660-676.
[10]Ceballos M A,Prato C A.Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests[J].Journal of Sound and Vibration,2008,317(2):127-141.
[11]Ni Y Q,Gao Z M,Zheng G.Dynamic analysis of largediameter sagged cables taking into account flexural rigidity[J].Journal of Sound and Vibration,2002,257(2):301-319.
[12]郑罡,倪一清,高赞明,等.斜拉索张力测试和参数评估的理论和应用[J].土木工程学报,2005,38(3):64-69.
[13]Strang G,Fix G J.An Analysis of the Finite Element Method[M].Englewood Cliffs:Prentice-Hall,1973:216-240.
[14]唐盛华,方志.考虑中间支撑的拉索等效索长计算方法[J].振动与冲击,2013,32(7):82-87.
[15]Robert J L,Bruhat D,Gervais J P,et al.The measurement of cable tension by the vibratory method[J].Bulletin de Liaison des Laboratoires des Ponts et Chaussees,1991,173(7):109-114.
[16]方志,汪建群,颜江平.基于频率法的拉索及吊杆张力测试[J].振动与冲击,2007,26(9):78-82.
[17]赵子龙.振动力学[M].国防工业出版社,2014:174-175.
[18]方志,张智勇.斜拉桥的索力测试[J].中国公路学报,1997,10(1):51-58.
[19]许俊.斜拉索索力简化计算中的精度分析[J].同济大学学报,2001,29(5):611-615.
[20]宋一凡.公路桥梁动力学[M].北京:人民交通出版社,1999.
[21]王万金,玄志武,张志国.切比雪夫多项式在动态载荷识别中的应用[J].强度与环境,2013,40(6):39-44.
[2]Wei J B,Li G Q,Mohammad R R.Theoretical study on cable tension detection considering support vibration[C]//Transportation and Development Innovative Best Practices.Beijing:ASCE,2008:450-455.
[3]甘泉.复杂边界条件下索结构的内力识别方法研究[D].广州:华南理工大学,2015.
[4]魏金波,李国强,蒋夏子俊.弹性支承拉索动力特性研究[J].结构工程师,2011,27(3):25-30.
[5]刘文峰,应怀樵,柳春图.考虑刚度及边界条件的索力精确求解[J].振动与冲击,2003,22(4):12-25.
[6]林立,李胡生,瞿志豪,等.考虑刚度及固支边界条件的实用索力求解方法与试验研究[J].振动与冲击,2010,29(7):221-224;227.
[7]廖敬波,唐光武,孟利波.固结拉索的一种近似频率计算公式[J].振动与冲击,2013,32(6):149-151;172.
[8]秦小平,廖敬波,孟利波.固支-铰支拉索近似频率计算公式及求解条件讨论[C]//中国土木工程学会桥梁及结构工程分会.第二十一届全国桥梁学术会议论文集(下册).北京:人民交通出版社,2014:969-974.
[9]Kim B H,Park T.Estimation of cable tension force using the frequency-based system identification method[J].Journal of Sound and Vibration,2007,304(3/5):660-676.
[10]Ceballos M A,Prato C A.Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests[J].Journal of Sound and Vibration,2008,317(2):127-141.
[11]Ni Y Q,Gao Z M,Zheng G.Dynamic analysis of largediameter sagged cables taking into account flexural rigidity[J].Journal of Sound and Vibration,2002,257(2):301-319.
[12]郑罡,倪一清,高赞明,等.斜拉索张力测试和参数评估的理论和应用[J].土木工程学报,2005,38(3):64-69.
[13]Strang G,Fix G J.An Analysis of the Finite Element Method[M].Englewood Cliffs:Prentice-Hall,1973:216-240.
[14]唐盛华,方志.考虑中间支撑的拉索等效索长计算方法[J].振动与冲击,2013,32(7):82-87.
[15]Robert J L,Bruhat D,Gervais J P,et al.The measurement of cable tension by the vibratory method[J].Bulletin de Liaison des Laboratoires des Ponts et Chaussees,1991,173(7):109-114.
[16]方志,汪建群,颜江平.基于频率法的拉索及吊杆张力测试[J].振动与冲击,2007,26(9):78-82.
[17]赵子龙.振动力学[M].国防工业出版社,2014:174-175.
[18]方志,张智勇.斜拉桥的索力测试[J].中国公路学报,1997,10(1):51-58.
[19]许俊.斜拉索索力简化计算中的精度分析[J].同济大学学报,2001,29(5):611-615.
[20]宋一凡.公路桥梁动力学[M].北京:人民交通出版社,1999.
[21]王万金,玄志武,张志国.切比雪夫多项式在动态载荷识别中的应用[J].强度与环境,2013,40(6):39-44.