两端支承式输流管路的强迫振动分析
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摘要
研究水平放置的两端支承式输流管路的强迫振动问题,将欧拉-伯努利梁模型视为管路的简化力学模型.利用格林函数法对无量纲的强迫振动微分方程进行推导,得到一般支承形式管路的格林函数,并最终得到挠度的一般表达式.在此基础上研究一端固定、另一端弹性支承输流管路的振动响应,分别利用微分变换法和伽辽金法验证其正确性与准确性,并研究了集中载荷和分布载荷情况下的振动响应.利用该方法可以得到封闭的精确解,比其他数值方法具有较大的优势.
The forced vibration of fluid conveying pipe with elastic support was investigated.Euler-Bernoulli beam was adopted to simplify the mechanical model of the pipe. Green's Function method was used to deduce the dimensionless differential equation of forced vibration and Green's Function of pipes with general supporting formats was obtained. Finally,the general expression of the deflection was obtained. On this basis,dynamic responses of the pipe with one end fixed and the other elastically supported was studied. Differential Transformation method and Galerkin's Method were utilized to verify the validity and accuracy of the proposed method,and the responses of the pipe under concentrated and distributed force were investigated. The proposed model has advantages compared with other numerical methods because it is capable for offering precise closed solutions.
The forced vibration of fluid conveying pipe with elastic support was investigated.Euler-Bernoulli beam was adopted to simplify the mechanical model of the pipe. Green's Function method was used to deduce the dimensionless differential equation of forced vibration and Green's Function of pipes with general supporting formats was obtained. Finally,the general expression of the deflection was obtained. On this basis,dynamic responses of the pipe with one end fixed and the other elastically supported was studied. Differential Transformation method and Galerkin's Method were utilized to verify the validity and accuracy of the proposed method,and the responses of the pipe under concentrated and distributed force were investigated. The proposed model has advantages compared with other numerical methods because it is capable for offering precise closed solutions.
引文
[1]Dai H L,Wang L,Qian Q,et al.Vibration analysis of threedimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method[J].Applied Mathematics and Computation,2012,219(5):2453-2464.
[2]Faal R T,Derakhshan D.Flow-induced vibration of pipeline on elastic support[J].Procedia Engineering,2011,14:2986-2993.
[3]Paidoussis M P,Li G X.Pipes conveying fluid:a model dynamical problem[J].Journal of Fluids and Structures,1993,7(2):137-204.
[4]Li S J,Liu G M,Kong W T.Vibration analysis of pipes conveying fluid by transfer matrix method[J].Journal of Fluids and Structures,2014,266(1):78-88.
[5]Guo C Q,Zhang C H,Paidoussis M P.Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles[J].Journal of Fluids and Structures,2010,26(5):793-803.
[6]Karami H,Farid M.A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid[J].Journal of Vibration and Control,2015,21(12):2360-2371.
[7]Foda M A,Abduljabber Z.A dynamic Green function formulation for the response of a beam structure to a moving mass[J].Journal of Sound and Vibration,1998,210(3):295-306.
[8]Abu-Hilal M.Forced vibration of Euler-Bernoulli beams by means of dynamic Green functions[J].Journal of Sound and Vibration,2003,267(2):191-207.
[9]Abu-Hilal M.Dynamic response of a double Euler-Bernoulli beam due to a moving constant load[J].Journal of Sound and Vibration,2006,297(3):477-491.
[10]Li X Y,Zhao X,Li Y H.Green’s functions of the forced vibration of Timoshenko beams with damping effect[J].Journal of Sound and Vibration,2014,333(6):1781-1795.
[11]Lee S I,Chung J.New non-linear modeling for vibration analysis of a straight pipe conveying fluid[J].Journal of Sound and Vibration,2002,254(2):313-325.
[2]Faal R T,Derakhshan D.Flow-induced vibration of pipeline on elastic support[J].Procedia Engineering,2011,14:2986-2993.
[3]Paidoussis M P,Li G X.Pipes conveying fluid:a model dynamical problem[J].Journal of Fluids and Structures,1993,7(2):137-204.
[4]Li S J,Liu G M,Kong W T.Vibration analysis of pipes conveying fluid by transfer matrix method[J].Journal of Fluids and Structures,2014,266(1):78-88.
[5]Guo C Q,Zhang C H,Paidoussis M P.Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles[J].Journal of Fluids and Structures,2010,26(5):793-803.
[6]Karami H,Farid M.A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid[J].Journal of Vibration and Control,2015,21(12):2360-2371.
[7]Foda M A,Abduljabber Z.A dynamic Green function formulation for the response of a beam structure to a moving mass[J].Journal of Sound and Vibration,1998,210(3):295-306.
[8]Abu-Hilal M.Forced vibration of Euler-Bernoulli beams by means of dynamic Green functions[J].Journal of Sound and Vibration,2003,267(2):191-207.
[9]Abu-Hilal M.Dynamic response of a double Euler-Bernoulli beam due to a moving constant load[J].Journal of Sound and Vibration,2006,297(3):477-491.
[10]Li X Y,Zhao X,Li Y H.Green’s functions of the forced vibration of Timoshenko beams with damping effect[J].Journal of Sound and Vibration,2014,333(6):1781-1795.
[11]Lee S I,Chung J.New non-linear modeling for vibration analysis of a straight pipe conveying fluid[J].Journal of Sound and Vibration,2002,254(2):313-325.