体外预应力钢-混凝土组合连续梁自振频率分析
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摘要
为研究预应力组合连续梁的自振频率,建立双折线型体外预应力钢-混凝土组合两跨连续梁振动特性的分析模型,并在Ayaho Miyamoto的基础上,推导出双折线型体外预应力组合连续梁振动方程。通过对振动方程进行拉普拉斯变换,得到了连续梁在对称振型和反对称振型下的全部频率计算公式,分析了等效轴向力对组合连续梁频率的影响规律。和现有的预应力组合连续梁的动力试验和有限元结果进行了比较分析,公式计算的组合梁基频结果与前两者吻合较好,理论公式所反映的预加力对频率的影响规律与有限元一致。所得公式可以用来计算体外预应力钢-混凝土组合连续梁的自振频率。
In order to investigate the natural frequency of a prestressed composite beam,an analytical model of a prestressed steel-concrete composite continuous beam is formulated.Based on the formula presented by Ayaho Miyamoto,the formulas for natural frequency of a double broken line prestressed composite continuous beam with external tendons are derived.The all natural frequency formulas for the continuous beam is derived through Laplace transform,meanwhile,the influence rule of the composite continuous beam due to an equivalent axial force is analyzed.The results of the formulas are compared with existing tests and FEA results,and the first calculated frequency of the continuous beam is consistent with the other results.Meanwhile,the influence rule of the theoretic formulas on the composite continuous beam due to the equivalent axial force is consistent with FEA.The natural frequency of a prestressed composite beam with external tendons can be calculated by the derived formula.
In order to investigate the natural frequency of a prestressed composite beam,an analytical model of a prestressed steel-concrete composite continuous beam is formulated.Based on the formula presented by Ayaho Miyamoto,the formulas for natural frequency of a double broken line prestressed composite continuous beam with external tendons are derived.The all natural frequency formulas for the continuous beam is derived through Laplace transform,meanwhile,the influence rule of the composite continuous beam due to an equivalent axial force is analyzed.The results of the formulas are compared with existing tests and FEA results,and the first calculated frequency of the continuous beam is consistent with the other results.Meanwhile,the influence rule of the theoretic formulas on the composite continuous beam due to the equivalent axial force is consistent with FEA.The natural frequency of a prestressed composite beam with external tendons can be calculated by the derived formula.
引文
[1]Ayaho Miyamoto,Katsuji Tei.Behaviour of prestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE,2000,126(9):1033―1044.
[2]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55―61.Xiong Xueyu,Wang Shousheng.Analysis and research of externally prestressed concrete beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55―61.(in Chinese)
[3]张耀庭,蔡利建.基于摄动法的体外预应力梁基频分析[J].华中科技大学学报,2006,34(6):118—121.Zhang Yaoting,Cai Lijian.Study on the basic frequency analysis of external prestressed concrete beams based on perturbation[J].Journal of Huazhong University of Science&Technology,2006,34(6):118―121.(in Chinese)
[4]熊辉霞,张耀庭.体外预应力混凝土梁自振频率分析[J].工程力学,2008,25(增刊Ⅱ):173―176.Xiong Huixia,Zhang Yaoting.Analysis of natural frequency of externally prestressed concrete beam[J].Engineering Mechanics,2008,25(SupplementⅡ):173―176.(in Chinese)
[5]王佳伟,贾艳敏.预应力简支钢箱梁自振频率研究[J].工程力学,2009,26(1):120―124.Wang Jiawei,Jia Yanmin.Study on natural frequency of simply supported steel box girder with prestressed tendons[J].Engineering Mechanics,2009,26(1):120―124.(in Chinese)
[6]王常雷.预应力钢-混凝土组合梁的动力特性研究[D].上海:同济大学,2008.Wang Changlei.Study on dynamic characteristics of composite beams with external tendons[D].Shanghai:Tongji University,2008.(in Chinese)
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[8]Henry Edwards C,Penney David E.Differential equations and boundary value problems:computing and modeling[M].American:Pearson Education,2004.
[9]李军强,方同.轴向力作用下连续梁固有振动分析[J].机械科学与技术,1998,17(4):541―547.Li Junqiang,Fang Tong.Analysis of natural transverse vibration of continuous beam subjected to axial force[J].Mechanical Science and Technology,1998,17(4):541―547.(in Chinese)
[10]唐友刚.高等结构动力学[M].天津:天津大学出版社,2002.Tang Yougang.Advanced structure dynamics[M].Tianjin:Tianjin University Press,2002.(in Chinese)
[2]熊学玉,王寿生.体外预应力梁振动特性的分析与研究[J].地震工程与工程振动,2005,25(2):55―61.Xiong Xueyu,Wang Shousheng.Analysis and research of externally prestressed concrete beam vibration behavior[J].Earthquake Engineering and Engineering Vibration,2005,25(2):55―61.(in Chinese)
[3]张耀庭,蔡利建.基于摄动法的体外预应力梁基频分析[J].华中科技大学学报,2006,34(6):118—121.Zhang Yaoting,Cai Lijian.Study on the basic frequency analysis of external prestressed concrete beams based on perturbation[J].Journal of Huazhong University of Science&Technology,2006,34(6):118―121.(in Chinese)
[4]熊辉霞,张耀庭.体外预应力混凝土梁自振频率分析[J].工程力学,2008,25(增刊Ⅱ):173―176.Xiong Huixia,Zhang Yaoting.Analysis of natural frequency of externally prestressed concrete beam[J].Engineering Mechanics,2008,25(SupplementⅡ):173―176.(in Chinese)
[5]王佳伟,贾艳敏.预应力简支钢箱梁自振频率研究[J].工程力学,2009,26(1):120―124.Wang Jiawei,Jia Yanmin.Study on natural frequency of simply supported steel box girder with prestressed tendons[J].Engineering Mechanics,2009,26(1):120―124.(in Chinese)
[6]王常雷.预应力钢-混凝土组合梁的动力特性研究[D].上海:同济大学,2008.Wang Changlei.Study on dynamic characteristics of composite beams with external tendons[D].Shanghai:Tongji University,2008.(in Chinese)
[7]Zill Dennis G,Cullen Michael R.Differential equations with boundary-value problems[M].American:Thomson Learning,2001.
[8]Henry Edwards C,Penney David E.Differential equations and boundary value problems:computing and modeling[M].American:Pearson Education,2004.
[9]李军强,方同.轴向力作用下连续梁固有振动分析[J].机械科学与技术,1998,17(4):541―547.Li Junqiang,Fang Tong.Analysis of natural transverse vibration of continuous beam subjected to axial force[J].Mechanical Science and Technology,1998,17(4):541―547.(in Chinese)
[10]唐友刚.高等结构动力学[M].天津:天津大学出版社,2002.Tang Yougang.Advanced structure dynamics[M].Tianjin:Tianjin University Press,2002.(in Chinese)
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