不同截面杆件轴力识别的理论与试验验证
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摘要
基于修正Timoshenko梁理论,考虑剪切变形及其产生的转动惯量的影响,建立改进的动力方程进行杆件轴力识别。通过建立实心圆杆,空心圆杆,矩形空心杆等的有限元模型,计算其在不同轴力作用时的频率和振型,模拟不同截面形状和尺寸、不同传感器位置和不同阶次模态对轴力识别的影响。之后在万能材料试验机上进行了杆件轴力识别试验,将识别结果与实际加载轴力对比,验证了该方法对不同截面杆件轴力识别的准确性以及实用性。理论和试验结果表明该方法具有识别精度高,不受边界条件影响和适用范围广等优点。
An improved dynamic governing equation including the influence of shear deformation based on modified Timoshenko beam theory is established.The finite element models of various bars,such as circular solid bars,circular hollow bars and rectangular hollow bars,are simulated to obtain the natural frequencies and mode shapes,which are then used to estimate the axial forces based on modified Timoshenko beam theory.The influence of different cross sections and dimensions,sensor positions,and modal orders is analyzed.Laboratory experiments are conducted to validate the proposed method and simulation results.The first five natural frequencies and mode parameter shapes of the bars are obtained by the LMS software and are used for axial force estimate.It is found that the axial forces can be identified accurately and the method is not affected by boundary conditions and can be widely applied to different bar members.
An improved dynamic governing equation including the influence of shear deformation based on modified Timoshenko beam theory is established.The finite element models of various bars,such as circular solid bars,circular hollow bars and rectangular hollow bars,are simulated to obtain the natural frequencies and mode shapes,which are then used to estimate the axial forces based on modified Timoshenko beam theory.The influence of different cross sections and dimensions,sensor positions,and modal orders is analyzed.Laboratory experiments are conducted to validate the proposed method and simulation results.The first five natural frequencies and mode parameter shapes of the bars are obtained by the LMS software and are used for axial force estimate.It is found that the axial forces can be identified accurately and the method is not affected by boundary conditions and can be widely applied to different bar members.
引文
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[12]Li S,Reynders E,Maes K,et al.Vibration-based estimation of axial force for a beam member with uncertain boundary conditions[J].Journal of Sound and Vibration,2013,332(4):795-806.
[13]Maes K,Peeters J,Reynders E,et al.Identification of axial forces in beam members by local vibration measurements[J].Journal of Sound and Vibration,2013,332(21):5417-5432.
[14]陈镕,万春风,薛松涛,等.Timoshenko梁运动方程的修正及其影响[J].同济大学学报(自然科学版),2005,33(6):711-715.Chen Rong,Wan Chun-feng,Xue Song-tao.The modification and influence of kinematic equation for Timoshenko beam[J].Journal of Tongji University(Natural Science),2005,33(6):711-715.
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[16]边东洋.Timoshenko梁理论的缺陷及其运动方程的修正[D].上海:同济大学,2008.Bian Dong-yang.The defect of the Timoshenko beam theory and amendment of equation of motion[D].Shanghai:Tongji University,2008.
[17]Timoshenko S P,Gere J M.Mechanics of Materials[M].New York:Van Nostrand Reinhold Company,1972.
[18]张昭,蔡志勤.有限元方法与应用[M].大连:大连理工大学出版社,2011.
[19]李青霞,任焱晞,安宏伟.PolyMax方法在桥梁工作模态分析中的应用[J].新技术新工艺,2008,(07):21-23.Li Qing-xia,Ren Yan-xi,An Hong-wei.Application of PolyMax Method in Operating Modal Analysis of Bridge[J].New Technology&New Process,2008,(07):21-23.
[2]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.
[3]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 Feng-quan,Zhou Xing-de.Wavebased study for cable tension measurement of cablestayed bridge[J].Journal of Applied Sciences,2005,23(1):90-93.
[4]陈鲁,宋杰,张其林.EM法测量索张力的理论与工程实践研究[J].施工技术,2008,37(5):144-148.Chen Lu,Song Jie,Zhang Qilin.Theory and engineering practice research on cable tension measurement with EM method[J].Construction Technology,2008,37(5):144-148.
[5]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 Zhiyong.Overview on measuring method of forces in main cable of cable-stayed bridge[J].Railway Engineering,2007,(4):18-20.
[6]李素贞.杆件轴力的一种识别方法[J].振动.测试与诊断,2012,31(6):694-699.Li Su-zhen.A method of identification of axial forces in beam members[J].Journal of Vibration,Test and Diagnosis,2012,31(6):694-699.
[7]方同,薛璞.振动理论及应用[M].西安:西北工业大学出版社,1998.
[8]倪振华.振动力学[M].西安:西安交通大学出版社,1989.
[9]Timoshenko S P.On the correction for shear of the differential equation for transverse vibration of prismatic bars[J].Domestic Animal Endocrinology,1990,7(2):239-250.
[10]Timoshenko S P,Goodier J N,Abramson H N.Theory of elasticity[J].Journal of Applied Mechanics,1970,37:888.
[11]袁永强.基于动力方法的杆件轴力识别技术研究[D].大连:大连理工大学,2015.Yuan Yong-qiang.Investigations on identification of axial forces in bar members by dynamical vibration tests[D].Dalian:Dalian University of Technology,2015.
[12]Li S,Reynders E,Maes K,et al.Vibration-based estimation of axial force for a beam member with uncertain boundary conditions[J].Journal of Sound and Vibration,2013,332(4):795-806.
[13]Maes K,Peeters J,Reynders E,et al.Identification of axial forces in beam members by local vibration measurements[J].Journal of Sound and Vibration,2013,332(21):5417-5432.
[14]陈镕,万春风,薛松涛,等.Timoshenko梁运动方程的修正及其影响[J].同济大学学报(自然科学版),2005,33(6):711-715.Chen Rong,Wan Chun-feng,Xue Song-tao.The modification and influence of kinematic equation for Timoshenko beam[J].Journal of Tongji University(Natural Science),2005,33(6):711-715.
[15]Friedman Z,Kosmatka J B.An improved two-node Timoshenko beam finite element[J].Computers&Structures,1993,47(3):473-481.
[16]边东洋.Timoshenko梁理论的缺陷及其运动方程的修正[D].上海:同济大学,2008.Bian Dong-yang.The defect of the Timoshenko beam theory and amendment of equation of motion[D].Shanghai:Tongji University,2008.
[17]Timoshenko S P,Gere J M.Mechanics of Materials[M].New York:Van Nostrand Reinhold Company,1972.
[18]张昭,蔡志勤.有限元方法与应用[M].大连:大连理工大学出版社,2011.
[19]李青霞,任焱晞,安宏伟.PolyMax方法在桥梁工作模态分析中的应用[J].新技术新工艺,2008,(07):21-23.Li Qing-xia,Ren Yan-xi,An Hong-wei.Application of PolyMax Method in Operating Modal Analysis of Bridge[J].New Technology&New Process,2008,(07):21-23.