Axial force identification for uncertain stiffness and boundary constraints
LI Dongsheng1,2,CHEN Qizhou1,2,WEI Da3,GUO Xin3,JIANG Tao1,2
1.Department of Civil and Environmental Engineering, Shantou University, Shantou 515063, China;
2.Guangdong Engineering Center for Structure Safety and Health Monitoring, Shantou University, Shantou 515063, China;
3.State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
Abstract：As the main force component of bridge and long-span spatial structure in civil engineering, the measurement of axial force is very important. At present, axial force identification of truss structures is mostly based on the known boundary constraint conditions and stiffness of struts. However, a large number of studies have shown that the boundary constraint conditions of pull struts in practical engineering are complex with the change of loads and environmental conditions, and their actual stiffness is different from the design stiffness. Based on the dynamic equation of the classical Timoshenko beam theory, it is found that there is a certain functional relationship between the axial force and the flexural rigidity of the rods when the modal information is known. Therefore, a method for identifying the axial force and flexural rigidity of the rods under unknown boundary constraints is proposed. The validity of the method is verified by numerical simulation of a simply supported beam and axial force identification tests of three kinds of bars with different sections on a drawing machine.
Key words: Timoshenko beam; identification of axial force; bending stiffness; boundary conditions; modal information
李东升1,2，陈琪舟1,2，魏达3，郭鑫3，姜涛1,2. 不确定刚度和边界约束条件下的轴力识别[J]. 振动与冲击, 2022, 41(20): 208-215.
LI Dongsheng1,2,CHEN Qizhou1,2,WEI Da3,GUO Xin3,JIANG Tao1,2. Axial force identification for uncertain stiffness and boundary constraints. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(20): 208-215.
［1］李宏男，李东升. 土木工程结构安全性评估健康监测及诊断述评 [J]. 地震工程与工程振动，2002，22 (3): 82-90.
Li Hong-nan, Li Dong-sheng. Safety assessment, health monitoring and damage diagnosis for structures in civil engineering[J]. Earthquake Engineering and Engineering Vibration, 2002,22(3):82-90. (in Chinese)
［2］吴康雄, 刘克明, 杨金喜. 基于频率法的索力测量系统[J]. 中国公路学报, 2006(02):62-66.
Wu Kangxiong, Liu Keming, Yang Jinxi. Measuring System of Cable Tension Based on Frequency Method. [J] China Journal of Highway and Transport, 2006 (02): 62-66. (in Chinese)
［3］R. 克拉夫, J. 彭津. 结构动力学 第二版（修订版）（中译本）[M]. 高等教育出版社, 2006, p293.
R. Kraft, J. Peng Jin. Structural dynamics, Second Edition (Revised Edition) [M]. Higher education press, 2006, p293
［4］刘志勇．斜拉桥斜拉索索力测试方法综述[J]．铁道建筑，2007,(4):18-20.
Liu Zhiyoug. Overview on measuring method of forces in main cable of cable-stayed bridge [J]. Railway Engineering,2007,(4):18-20. (in Chinese)
［5］陈强,黎永索.短吊杆频率法索力系数修正的研究[J].公路工程,2007(05):98-100.
Chen Qiang, Li yongsuo. Research into revising of coefficient of pulling force of short bar by frequency method. [J]. Highway engineering, 2007 (05): 98-100. (in Chinese)
［6］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，振动与冲击，2003，04期（4）：12-4.
Liu Wenfeng, Ying Huaiqiao, Liu chuntu. Precise solution of cable tensile force in consideration of cable stiffness and its boundary conditions. Journal of Vibration and Shock, 2003, 04 (4): 12-4. (in Chinese)
［7］秦杰，高政国，钱英欣，等．预应力钢结构拉索索力测试理论与技术[M]．北京：中国建筑工业出版社，2010.
Qin Jie, Gao Zhengguo, Qian Yingxin, et al. Theory and technology of cable tension test for prestressed steel structures [M]. Beijing: China Construction Industry Press, 2010. (in Chinese)
［8］武晓凤．拉索弯曲性能研究［Ｄ］．天津：天津大学，2014．
Wu Xiaofeng. Research on bending behavior of cables. [D]. Tianjin: Tianjin University, 2014. (in Chinese)
［9］李素贞 , G.D.Roeck, E.Reynders. 杆件轴力的一种识别方法[J]. 振动、测试与诊断 , 2011,31(6):694-699.
Li Suzhen, D.Roeck,E.Reynders. Identification Method for Axial Force of Beam Membe. [J]. Journal of Vibration,Measurement and Diagnosis, 2011,31 (6): 694-699. (in Chinese)
［10］陈强，黎永索. 短吊杆频率法索力系数修正的研究[J]. 公路工程, 2007(05):98-100.
CHEN Qiang,LI Yongsuo. Research into revising of coefficient of pulling force of short bar by frequency method[J]. Highway Engineering, 2007, 32(5): 98-100.
［11］袁永强, 李东升, 李宏男. 基于动力方法的改进杆件轴力识别[J]. 大连理工大学学报,2015,55(05):511-517.
Yuan Yongqiang, Li Dongsheng, Li Hongnan. Investigations on identification of axial forces in bar members by dynamical vibration tests. [J]. Journal of Dalian University of Technology ,2015, 55(05): 511-517. (in Chinese)
［12］李东升, 李坤朋, 魏达. 不同截面杆件轴力识别的理论与试验验证[J]. 振动工程学报,2019,32(01):151-159.
Li Dongsheng, Li Kunpeng, Wei Da. Theory and experimental verification of axial force identification of members with different cross sections [J]. Journal of Vibration Engineering, 2019, 32 (01): 151-159. (in Chinese)
［13］Chen CC, Wu WH, Chen SY, et al. A novel tension estimation approach for elastic cables by elimination of complex boundary condition effects employing mode shape functions[J]. Engineering Structures. 2018;166:152-66.
［14］张戌社, 杜彦良, 孙宝臣,等. 光纤光栅压力传感器在斜拉索索力监测中的应用研究[J]. 铁道学报, 2002, 24(6):47-49.
Zhang Xu she, Du Yan Liang, sun Bao Chen, et al. Application of optical fiber grating pressure sensor on monitoring of cables' tension. [J]. Journal of The China Railway Society, 2002, 24 (6): 47-49. (in Chinese)
［15］王 俊，汪凤泉，周星德．基于波动法的斜拉桥索力测试研究[J]．应用科学学报，2005, 23(1):90-93.
Wang Jun, Wang Fengquan, Zhou Xingde. Wave-Based Study for Cable Tension Measurement of Cable-Stayed Bridge. [J]. Journal of Applied Sciences, 2005, 23 (1): 90-93. (in Chinese)
［16］张海东, 田章华, 段元锋,等. 基于磁弹效应的拱桥吊杆索力监测[J]. 结构工程师, 2016, 32(4).
Zhang Haidong, Tian Zhanghua, Duan Yuanfeng, et al. Elasto-magnetic Effect Based Suspender Force Monitoring of an Arch Bridge. [J]. Structural engineer, 2016, 32 (4). (in Chinese)
［17］Yan B, Li D, Chen W, Deng L et al. Mode shape–aided cable force determination using digital image correlation[J]. Structural Health Monitoring, 2020: 1475921720952163.
［18］李宏男, 李东升, 赵柏东. 光纤健康监测方法在土木工程中的研究与应用进展[J]. 地震工程与工程振动, 2002, 22(6):76-83.
Zhang Haidong, Tian Zhanghua, Duan Yuanfeng, et al. Progress in study and application of smart health monitoring method by fiber optic sensor in civil engineering. [J]. Earthquake engineering and engineering vibration, 2002, 22 (6): 76-83. (in Chinese)
［19］Geier R,De Roeck G, Petz J. Cable force determination for the Danube channel bridge in Vienna[J]. Structural engineering international,2005,15(3):181-185.
［20］Mehrabi. A, Tabatabai,Unified finite difference formulation for free vibration of cables[J].Journal of Structural Engineering.1998.124(11):1313-1322
［21］Chen Z H, Yu Y J, Wang X D, er al . “Experimental research on bending performance of structural cable.” Construction and Building Materials. 2015, 96: 279–288.
［22］余玉洁. 基于拉索半精细化有限元模型的拉索弯曲及断丝研究[D]. 2016.
Yu Yujie. Semi-refined Finite Element Model of Cable and its Application on Bending Behavior and Wire Break. [D]. 2016. (in Chinese)
［23］Papailiou K O, Bending of Helically Twisted Cables Under Variable Bending Stiffness Due to Internal Friction, Tensile Force and Cable Curvature, Ph.D thesis, Zurich, Switzerland: Swiss Federal Institute of Technology(ETH), 1995.
［24］苏成, 徐郁峰, 韩大建. 频率法测量索力中的参数分析与索抗弯刚度的识别[J]. 公路交通科技, 2005,22(5): 75―78.
Su Cheng, Xu Yufeng, Han Dajian. Parameter analysis and identification of bending stiffness of cables during tension measurements by frequency method [J]. Journal of Highway and Transportation Research and Development, 2005, 22(5): 75―78. (in Chinese)
［25］谢晓峰，索的抗弯刚度识别方法研究，硕士学位论文，中南大学，2012.
Xie Xiaofeng, The flexural rigidity of cable identification method research, master's dissertation, Central South University, 2012. (in Chinese)
［26］Zhang Y P, Wang J F, Ye G R, et al. Bending stiffness of cables of parallel wires including interfacial slips among wires [J]. Journal of Structural Engineering, 2018,144(10): 04018164-1―04018164-9
［27］孟少平, 杨睿, 王景全. 一类精确考虑抗弯刚度影响的系杆拱桥索力测量新公式[J]. 公路交通科技(6):91-95+102.Vibration, 2002,22(3):82-90.
Meng Shaoping, Yang Rui, Wang Jingquan. Novel formula of tension measurement for tied arch bridge in precise consideration of flexural rigidity [J]. Journal of Highway and Transportation Research and Development (6): 91-95 + 102. Vibration, 2002,22 (3): 82-90. (in Chinese)
