考虑剪切变形及转动惯量的H型钢梁自由振动
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摘要
以3种典型热轧H型钢截面简支梁为研究对象,分别采用初等梁理论模型和考虑剪切变形及转动惯量影响的高等梁理论模型,分析在不同长细比情况下H型钢截面简支梁前3阶自由振动频率的差异,得出了初等梁理论进行H型钢梁自由振动分析的适用条件,该结论可供结构动力分析及动力设计参考。
With three kinds of typical hot-rolled H-shape steel section free beam as research objective,the difference of former third-order free vibration frequency with different slenderness ratio was analyzed by elementary beam theory model and higher beam theory model which considering the shearing deformation and the inertia effect.The applicable conditions of free vibration analysis by the elementary beam theory on H-shape steel beam is obtained.This conclusion provids reference for dynamic analysis and the dynamic design.
With three kinds of typical hot-rolled H-shape steel section free beam as research objective,the difference of former third-order free vibration frequency with different slenderness ratio was analyzed by elementary beam theory model and higher beam theory model which considering the shearing deformation and the inertia effect.The applicable conditions of free vibration analysis by the elementary beam theory on H-shape steel beam is obtained.This conclusion provids reference for dynamic analysis and the dynamic design.
引文
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[6]王力力,易伟健,何庆峰.考虑剪切变形和转动惯量影响的梁的固有频率计算[J].铁道科学与工程学报,2007,4(5):6-10.WANG Li-li,YI Wei-jian,HE Qing-feng.Eigenfrequen-cies of beams considering the effects of shear distortionand rotary inertia[J].Journal of Railway Science and En-gineering,2007,4(5):6-10.
[7]葛素娟,李静斌.简支梁横向振动固有频率的误差分析[J].郑州大学学报:工学版,2010,31(5):48-51.GE Su-juan,LI Jing-bin.Error anslysis of transverse vi-bration natural frequency of simply supported beam[J].Journal of Zhengzhou University:Engineering Science,2010,31(5):48-51.
[8]Chopra A K.结构动力学理论及其在地震工程中的应用[M].谢礼立,吕大刚,等译.北京:高等教育出版社,2007.Chopra A K.Dynamics of structures-theory and applica-tions to earthquake engineering[M].XIE Li-li,LDa-gang,translate.Beijing:Higher Education Press,2007.
[9]王伟,赖永星,苗同臣,等.振动力学与工程应用[M].郑州:郑州大学出版社,2008.WANG Wei,LAI Yong-xing,MIAO Tong-chen,et al.Vibration mechanics and engineering application[M].Zhengzhou:Zhengzhou University Press,2008.
[10]GB/T11263—2010,热轧H型钢和剖分T型钢[S].GB/T 11263—2010,Hot-rolled H and cut T sectionsteel[S].
[2]李进军,李国强.考虑轴力和剪切变形影响的楔形梁自由振动分析[J].钢结构,2000,15(1):31-34.LI Jin-jun,LI Guo-qiang.Anslysis of free vibration for ta-pered beam including effects of axial force and shear de-formation[J].Steel Construction,2000,15(1):31-34.
[3]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,2002,30(8):911-916.LOU Meng-lin,REN Zhi-gang.Precise solution to modalcharacteristics of Timoshenko Pin-ended beams[J].Journal of Tongji University,2002,30(8):911-916.
[4]龚善初.轴向荷载、转动惯量和剪切变形对简支梁固有频率的影响[J].河南科学,2004,22(5):592-596.GONG Shan-chu.The influence of axial load moment ofintertia and shear deformation of the natural freauency ofsimply supported beam[J].Henan Science,2004,22(5):592-596.
[5]马连生,欧志英.经典理论与一阶理论之间简支梁特征值的解析关系[J].应用力学学报,2006,23(3):447-450.MA Lian-sheng,OU Zhi-ying.Analytical relationships ofeigenvalue for a simply supported beam between EBT andTBT[J].Chinese Journal of Applied Mechanics,2006,23(3):447-450.
[6]王力力,易伟健,何庆峰.考虑剪切变形和转动惯量影响的梁的固有频率计算[J].铁道科学与工程学报,2007,4(5):6-10.WANG Li-li,YI Wei-jian,HE Qing-feng.Eigenfrequen-cies of beams considering the effects of shear distortionand rotary inertia[J].Journal of Railway Science and En-gineering,2007,4(5):6-10.
[7]葛素娟,李静斌.简支梁横向振动固有频率的误差分析[J].郑州大学学报:工学版,2010,31(5):48-51.GE Su-juan,LI Jing-bin.Error anslysis of transverse vi-bration natural frequency of simply supported beam[J].Journal of Zhengzhou University:Engineering Science,2010,31(5):48-51.
[8]Chopra A K.结构动力学理论及其在地震工程中的应用[M].谢礼立,吕大刚,等译.北京:高等教育出版社,2007.Chopra A K.Dynamics of structures-theory and applica-tions to earthquake engineering[M].XIE Li-li,LDa-gang,translate.Beijing:Higher Education Press,2007.
[9]王伟,赖永星,苗同臣,等.振动力学与工程应用[M].郑州:郑州大学出版社,2008.WANG Wei,LAI Yong-xing,MIAO Tong-chen,et al.Vibration mechanics and engineering application[M].Zhengzhou:Zhengzhou University Press,2008.
[10]GB/T11263—2010,热轧H型钢和剖分T型钢[S].GB/T 11263—2010,Hot-rolled H and cut T sectionsteel[S].
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