油气管道非线性振动基频分析
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摘要
为了揭示外部激励、油气介质对管道非线性自由振动基频的影响规律,首先基于Euler-Bernoulli非线性几何方程和Hamilton原理,建立油气管道非线性动力学控制方程,然后通过伽辽金法和同伦摄动法,求得油气管道频幅关系、位移-时间曲线的一阶近似解和基频理论解。计算结果表明:推导的理论解与相关文献和实验数据相吻合。管道基频与外激励初始振幅正相关,与介质流速和密度负相关。过高的流体流速或密度易引起管道基频急剧降低。当有适当的扰力出现时,管道系统易发生较大受迫振动乃至共振失效。
In order to reveal the rule of external excitation and oil & gas medium's influences on the fundamental frequency of nonlinear free vibration of pipelines, having Euler-Bernoulli nonlinear geometric equation and the Hamilton principle based to establish the nonlinear dynamic governing equation of oil and gas pipelines was implemented, including having Galerkin's and homotopy perturbation method based to obtain frequency-amplitude relationship and the first-order approximate solution and the fundamental frequency theoretical solution of the displacement-time curve. The results show that, the derived theoretical solution of fundamental frequency is in good agreement with the experimental data and related literature. In addition, the fundamental frequency of the pipeline is positively correlated with the initial amplitude of the external excitation and negatively correlated with the flow velocity and density of the medium. Excessive flow velocity or fluid density tends to cause a sharp decrease of the fundamental frequency. In this case, the pipeline system is prone to failure due to large forced vibration or even resonance.
In order to reveal the rule of external excitation and oil & gas medium's influences on the fundamental frequency of nonlinear free vibration of pipelines, having Euler-Bernoulli nonlinear geometric equation and the Hamilton principle based to establish the nonlinear dynamic governing equation of oil and gas pipelines was implemented, including having Galerkin's and homotopy perturbation method based to obtain frequency-amplitude relationship and the first-order approximate solution and the fundamental frequency theoretical solution of the displacement-time curve. The results show that, the derived theoretical solution of fundamental frequency is in good agreement with the experimental data and related literature. In addition, the fundamental frequency of the pipeline is positively correlated with the initial amplitude of the external excitation and negatively correlated with the flow velocity and density of the medium. Excessive flow velocity or fluid density tends to cause a sharp decrease of the fundamental frequency. In this case, the pipeline system is prone to failure due to large forced vibration or even resonance.
引文
[1] Kjolsing E J,Todd M D.Damping of a Fluid-Conveying Pipe Surrounded by a Viscous Annulus Fluid[J].Journal of Sound and Vibration,2017,394:575～592.
[2] Saki F,Bhattacharya A,Kehtarnavaz N.Real-Time Simulink Implementation of Noise Adaptive Speech Processing Pipeline of Cochlear Implants[J].Speech Communication,2018,96:197～206.
[3] Singh K,Mallik A K.Wave Propagation and Vibration Response of a Periodically Supported Pipe Conveying Fluid[J].Journal of Sound and Vibration,1977,54(1):55～66.
[4] Lee U,Park J.Spectral Element Modelling and Analysis of a Pipeline Conveying Internal Unsteady Fluid[J].Journal of Fluids and Structures,2006,22(2):273～292.
[5] Zhang Y L,Gorman D G,Reese J M.A Finite Element Method for Modelling the Vibration of Initially Tensioned Thin-Walled Orthotropic Cylindrical Tubes Conveying Fluid[J].Journal of Sound and Vibration,2001,245(1):93～112.
[6] 张立翔,黄文虎.输流管道非线性流固耦合振动的数学建模[J].水动力学研究与进展,2000,15(1):116～128.
[7] 包日东,金志浩,闻邦椿.分析一般支承输流管道的非线性动力学特性[J].振动与冲击,2008,27(7):87～90.
[8] 梅树立,张森文.基于精细积分技术的非线性动力学方程的同伦摄动法[J].计算力学学报,2005,22(6):665～670.
[9] Housner G W.Bending Vibrations of a Pipe Line Containing Flowing Fluid[J].Journal of Applied Mechanics-Transactions of the ASME,1952,19(2):205～208.
[10] Xu M R,Xu S P,Guo H Y.Determination of Natural Frequencies of Fluid-Conveying Pipes Using Homotopy Perturbation Method[J].Computers & Mathematics with Applications,2010,60(3):520～527.
[11] Dodds H L,Runyan H L.Effect of High-Velocity Fluid Flow in the Bending Vibrations and Static Divergence of a Simply Supported Pipe[M].Washington DC:National Aeronautics and Space Administration,1965.
[2] Saki F,Bhattacharya A,Kehtarnavaz N.Real-Time Simulink Implementation of Noise Adaptive Speech Processing Pipeline of Cochlear Implants[J].Speech Communication,2018,96:197～206.
[3] Singh K,Mallik A K.Wave Propagation and Vibration Response of a Periodically Supported Pipe Conveying Fluid[J].Journal of Sound and Vibration,1977,54(1):55～66.
[4] Lee U,Park J.Spectral Element Modelling and Analysis of a Pipeline Conveying Internal Unsteady Fluid[J].Journal of Fluids and Structures,2006,22(2):273～292.
[5] Zhang Y L,Gorman D G,Reese J M.A Finite Element Method for Modelling the Vibration of Initially Tensioned Thin-Walled Orthotropic Cylindrical Tubes Conveying Fluid[J].Journal of Sound and Vibration,2001,245(1):93～112.
[6] 张立翔,黄文虎.输流管道非线性流固耦合振动的数学建模[J].水动力学研究与进展,2000,15(1):116～128.
[7] 包日东,金志浩,闻邦椿.分析一般支承输流管道的非线性动力学特性[J].振动与冲击,2008,27(7):87～90.
[8] 梅树立,张森文.基于精细积分技术的非线性动力学方程的同伦摄动法[J].计算力学学报,2005,22(6):665～670.
[9] Housner G W.Bending Vibrations of a Pipe Line Containing Flowing Fluid[J].Journal of Applied Mechanics-Transactions of the ASME,1952,19(2):205～208.
[10] Xu M R,Xu S P,Guo H Y.Determination of Natural Frequencies of Fluid-Conveying Pipes Using Homotopy Perturbation Method[J].Computers & Mathematics with Applications,2010,60(3):520～527.
[11] Dodds H L,Runyan H L.Effect of High-Velocity Fluid Flow in the Bending Vibrations and Static Divergence of a Simply Supported Pipe[M].Washington DC:National Aeronautics and Space Administration,1965.