支承弹簧对输液曲管固有频率和极限流速的影响
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摘要
基于Hamilton变分原理,导出具有弹性支撑的1/4圆形输液曲管的变分—积分方程。采用多个函数组合的方法,选取满足边界条件的试函数,利用Galerkin直接法求出系统的固有频率和极限流速的近似解析公式。数值结果表明,弹簧对固有频率和极限流速都有显著影响。根据数值结果,用最小二乘法给出固有频率和极限流速与弹簧刚度的关系公式。
Based on Hamilton variation principle,the variation-integration equations of a quad-circle curved pipe conveying fluid with spring support were derived.Multi-function combination method was employed.The test function satisfied boundary conditions were selected.The approximate analytic formulae of natural frequency and limit velocity were presented by Galerkin direct method.The numerical results illustrate that the spring has be of notable influence on natural frequency and limit velocity.According to the upwards numerical results,relation formulae of natural frequency and limit velocity along with spring modulus are presented by use of the least square method.
Based on Hamilton variation principle,the variation-integration equations of a quad-circle curved pipe conveying fluid with spring support were derived.Multi-function combination method was employed.The test function satisfied boundary conditions were selected.The approximate analytic formulae of natural frequency and limit velocity were presented by Galerkin direct method.The numerical results illustrate that the spring has be of notable influence on natural frequency and limit velocity.According to the upwards numerical results,relation formulae of natural frequency and limit velocity along with spring modulus are presented by use of the least square method.
引文
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[14]张敦福,汤红卫.极限流速的Galerkin直接法和科氏惯性力的影响[J].山东大学学报,2005,35(1):110-114.ZHANG DunFu,TANG HongWei.Galerkin direct method for limit ve-locity andinfluence of coriolisinetial force[J].Journal of Shandong Uni-versity,2005,35(1):110-114(In Chinese).
[15]黄昭度,钟奉俄.工程系统分析力学[M].北京:高等教育出版社,1992:407-463.HUANG ZhaoDu,ZHONG FengE.Analysis mechanics of engineering system[M].Beijing:Higher Education Press,1992,407-461(In Chi-nese).
[2]Houser G.W.Bending vibrations of a pipe line containing flowing fluid[J].Appl.Mech.,1952,19(6):205-208.
[3]Weaver DS.Onthe flutter of thin cylindrical shells conveyingfluid[J].Journal of Sound and Vibration,1972,22(2):247-248.
[4]Chen S S.Vibration and stability of a uniformly curved tube conveying fliud[J].Acoust.Soc.Am.1972,51:223-232.
[5]Chen S S.Out-of-plane vibration and stability of curved tubes conveying fluid[J].J.Appl.Mech.,1973,40:362-368.
[6]王忠民,冯振宇,赵风群,等.弹性地基输液管道的耦合模态颤振分析[J].应用数学和力学,2000,21(10):1060-1068.WANGZhongMin,FENGZhenYu,ZHAO FengQun,et al.Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation[J].Applied Mathematics and Mechanics,2000,21(10):1060-1068(In Chinese).
[7]孙建刚,薛景宏,王振.架空输液管道系统动力响应分析[J].地震工程与工程振动,2000,20(2):129-133.SUNJianGang,XUEJingHong,WANGZhen.Dynamic response analys-is of pipeline systems conveyingfluid andsupported abovethe ground[J].Earthquake Engineering and Engineering Vibration,2000,20(2):129-133(In Chinese).
[8]王世忠,刘玉兰,黄文虎.输送流体管道的固—液耦合动力学研究[J].应用数学和力学,1998,19(11):987-993.WANGShiZhong,LIUYuLan,HUANG WenHu.Research on solid-liq-uid coupling dynamics of pipe conveying fluid[J].Applied Mathematics and Mechanics,1998,19(11):987-993(In Chinese).
[9]王本利,王世忠,安为民,等.用有限元法分析导管固—液耦合振动[J].哈尔滨工业大学学报,1984,16(2):8-14.WANGBenLi,WANG ShiZhong,AN Wei Ming,et al.An analysis of solidfluid couplingvibrationin piping byfinite element method[J].Jour-nal of Harbin Institute of Technology,1984,16(2):8-14(In Chinese).
[10]李琳.载流管系流—固耦合振动分析中的摄动法[J].振动与冲击,1993(2):48-52.LI Lin.The perturbation methodforfluid-solid couplingvibrationanalysis of pipe conveyingfluid[J].Vibration and Shock,1993(2):48-52(In Chinese).
[11]张敦福,王锡平,赵俊峰.悬臂输送管道流—固耦合动力学系统的直接解法[J].机械工程学报,2004,40(3):195-198.ZHANG DunFu,WANGXiPing,ZHAOJunFeng.Direct methodforliq-uid-solid coupled a dynamics analysis of camped pipe conveyingfluid[J].Journal of Mechanical Engineering,2004,40(3):195-198(In Chi-nese).
[12]魏发远,林长圣.分析输液曲管临界流速的迁移矩阵法[J].固体力学学报,2000,21(1):33-39.WEI FaYuan,LINChangSheng.Anew matrix method for solving prob-lems of curved pipes conveyingfluid[J].Acta Mechanica Solids Sinica,2000,21(1):33-39(In Chinese).
[13]张敦福,王锡平,张洪伟.半圆形输液曲管极限流速的直接法[J].机械工程学报,2005,41(5):221-224.ZHANG DunFu,WANG XiPing,ZHANG HongWei.Direct method for limit velocity of a semi-circle curved pipe conveyingfluid[J].Journal of Mechanical Engineering,2005,41(5):221-224(In Chinese).
[14]张敦福,汤红卫.极限流速的Galerkin直接法和科氏惯性力的影响[J].山东大学学报,2005,35(1):110-114.ZHANG DunFu,TANG HongWei.Galerkin direct method for limit ve-locity andinfluence of coriolisinetial force[J].Journal of Shandong Uni-versity,2005,35(1):110-114(In Chinese).
[15]黄昭度,钟奉俄.工程系统分析力学[M].北京:高等教育出版社,1992:407-463.HUANG ZhaoDu,ZHONG FengE.Analysis mechanics of engineering system[M].Beijing:Higher Education Press,1992,407-461(In Chi-nese).
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