基于动力刚度法的体外预应力梁自振频率分析
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摘要
用预应力梁-杆组合结构模拟体外预应力梁,以体外预应力简支梁为例,建立了预应力梁杆单元动力刚度矩阵。采用动力刚度法,进一步推导出预应力梁-杆组合结构的整体动力刚度矩阵,利用Williams-Wittrick算法求解频率。本文以理论推导为基础,引入了动力刚度法。最后通过算例,讨论了各种因素对梁横向的振动特性的影响,并与试验值比较。计算结果表明:动力刚度法能够精确有效的求解体外预应力混凝土梁的横向振动问题。
A prestressed beam-bar composite structure model was introduced to simulate an external prestressed beam.A simply-supported external prestressed beam was studied.The dynamic stiffness matrix method was used to establish the element and the global dynamic stiffness matrices for the beam-bar composite structure model of the external prestressed beam.As a result,the frequency solution was obtained by means of Williams-Wittrick algorithm.Based on the theoretical derivation,the dynamic stiffness method was introduced.The influence on the natural frequencies of the beam were also discussed.Numerical results showed that the dynamic stiffness matrix method is reliable,efficient,and well applicable to this kind of problems.
A prestressed beam-bar composite structure model was introduced to simulate an external prestressed beam.A simply-supported external prestressed beam was studied.The dynamic stiffness matrix method was used to establish the element and the global dynamic stiffness matrices for the beam-bar composite structure model of the external prestressed beam.As a result,the frequency solution was obtained by means of Williams-Wittrick algorithm.Based on the theoretical derivation,the dynamic stiffness method was introduced.The influence on the natural frequencies of the beam were also discussed.Numerical results showed that the dynamic stiffness matrix method is reliable,efficient,and well applicable to this kind of problems.
引文
[1]熊学玉.体外预应力结构设计[M].北京:中国建筑工业出版社,2005.
[2]易伟建,周云,曹冰.无粘结预应力钢筋混凝土梁的静动力实验研究及刚度识别[J].振动与冲击,2008,27(1):71-75.
[3]夏樟华,宗周红.预应力对混凝土梁动力特性的影响分析[J].振动与冲击,2007,26(7):129-134.
[4]林贤坤,张令弥,郭勤涛,等.预应力连续箱梁桥的基准动力有限元模型研究[J].振动与冲击,2009,28(11):38-42.
[5]孙宝俊,周国华.体外预应力结构技术及应用综述[J].东南大学学报(自然科学版),2001,31(1):109-113.
[6]张耀庭,邱继生,黄恒卫.体外预应力混凝土梁的研究现状综述[J].华中科技大学学报(城市科学版),2002,19(4):86-91.
[7]胡志坚,郭友,谭金华.体外预应力混凝土结构研究现状与展望[J].公路交通科技,2006,23(2):94-97.
[8]Ayaho Miyamoto,Katsuji Tei.Behavior of prestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE,2000,126(9):1000-1044.
[9]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.
[10]楼梦麟,洪婷婷.体外预应力梁动力特性的分析方法[J].同济大学学报(自然科学版),2006,34(10):1284-1288.
[11]张耀庭,张长跑.体外预应力简支混凝土梁基频的理论与实验研究[J].华中科技大学学报(城市科学版),2005,22(1):13-15.
[12]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(自然科学版),2006,34(6):118-121.
[13]周平,赵德有.动态刚度阵法的研究概况[J].振动与冲击,2006,25(4):104-108.
[14]袁驷.程序结构力学[M].北京:高等教育出版社,2008.
[15]袁驷,叶康生,Williams F W,等.杆系结构自由振动精确求解的理论和算法[J].工程力学,2005,22(6):1-6.
[16]Paz M,Dung l.Power series expansions of the general stiff-ness matrix for beam element Intl.J.Methods Engrg.1975,9:449-459.
[2]易伟建,周云,曹冰.无粘结预应力钢筋混凝土梁的静动力实验研究及刚度识别[J].振动与冲击,2008,27(1):71-75.
[3]夏樟华,宗周红.预应力对混凝土梁动力特性的影响分析[J].振动与冲击,2007,26(7):129-134.
[4]林贤坤,张令弥,郭勤涛,等.预应力连续箱梁桥的基准动力有限元模型研究[J].振动与冲击,2009,28(11):38-42.
[5]孙宝俊,周国华.体外预应力结构技术及应用综述[J].东南大学学报(自然科学版),2001,31(1):109-113.
[6]张耀庭,邱继生,黄恒卫.体外预应力混凝土梁的研究现状综述[J].华中科技大学学报(城市科学版),2002,19(4):86-91.
[7]胡志坚,郭友,谭金华.体外预应力混凝土结构研究现状与展望[J].公路交通科技,2006,23(2):94-97.
[8]Ayaho Miyamoto,Katsuji Tei.Behavior of prestressed beam strengthened with external tendons[J].Journal of Structural Engineering,ASCE,2000,126(9):1000-1044.
[9]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.
[10]楼梦麟,洪婷婷.体外预应力梁动力特性的分析方法[J].同济大学学报(自然科学版),2006,34(10):1284-1288.
[11]张耀庭,张长跑.体外预应力简支混凝土梁基频的理论与实验研究[J].华中科技大学学报(城市科学版),2005,22(1):13-15.
[12]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(自然科学版),2006,34(6):118-121.
[13]周平,赵德有.动态刚度阵法的研究概况[J].振动与冲击,2006,25(4):104-108.
[14]袁驷.程序结构力学[M].北京:高等教育出版社,2008.
[15]袁驷,叶康生,Williams F W,等.杆系结构自由振动精确求解的理论和算法[J].工程力学,2005,22(6):1-6.
[16]Paz M,Dung l.Power series expansions of the general stiff-ness matrix for beam element Intl.J.Methods Engrg.1975,9:449-459.
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