周期性输流管道的非线性动力学特性研究

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (10) : 75-80.

论文

周期性输流管道的非线性动力学特性研究

周坤1,2，倪樵1,2，代胡亮1,2，王琳1,2，熊夫睿3，姜乃斌3

作者信息 +

Analysis of nonlinear dynamic characteristics of periodic pipe conveying fluid

ZHOU Kun1,2，NI Qiao1,2，DAI Huliang1,2，WANG Lin1,2，XIONG Furui3，JIANG Naibin3

Author information +

文章历史 +

摘要

基于绝对节点坐标法，推导出不同材料组成的周期性悬臂输流管道在定常内流作用下的非线性动力学方程，通过数值求解的方式对两种不同形式的周期性输流管道，即，铝-钢及钢-铝周期性悬臂输流管道的稳定性和非线性动力学行为进行了研究。研究结果表明，单位长度内，当管道周期数大于8时，两种周期性输流管道的临界流速均趋于定值。非线性分析结果显示，铝-钢周期性输流管道的非线性动力学行为随着周期数目的减小变得越来越复杂，从单周期行为演变为多周期、倍周期、概周期和混沌等多种运动的复杂动力学行为，而对于钢-铝周期输流管道而言，管道一直处于单周期运动状态。

Abstract

Based on the absolute nodal coordinate formulation, the nonlinear dynamic equations of the periodic cantilevered pipe conveying fluid with different materials under steady flow were derived.Numerical solution method was employed to investigate the stability and nonlinear dynamic behaviors of periodic fluid-conveying pipe with two different materials: aluminum-steel and steel-aluminum periodic variation.Stability analysis shows that when the pipe per unit length has more than 8 period numbers, the critical flow velocity for these two kinds of periodic pipe tends to be constant.The nonlinear analysis indicates that the nonlinear dynamic behavior of aluminum-steel periodic pipe conveying fluid becomes more complicated with the decrease of period number, from periodic response to complicated dynamic responses including multi-periodic, periodic-doubling, quasiperiodic, and chaotic behaviors.While for steel-aluminum periodic pipe, the pipe is always displaying a single-period motion state.

导出引用

周坤1,2，倪樵1,2，代胡亮1,2，王琳1,2，熊夫睿3，姜乃斌3. 周期性输流管道的非线性动力学特性研究[J]. 振动与冲击, 2020, 39(10): 75-80

ZHOU Kun1,2，NI Qiao1,2，DAI Huliang1,2，WANG Lin1,2，XIONG Furui3，JIANG Naibin3. Analysis of nonlinear dynamic characteristics of periodic pipe conveying fluid[J]. Journal of Vibration and Shock, 2020, 39(10): 75-80

参考文献

[1] Paidoussis M P. Fluid-Structure Interactions: Slender Structures and Axial Flow (Vol. 1). London: Academic Press, 1998.

[2] Paidoussis M P. Fluid-Structure Interactions: Slender Structures and Axial Flow (Vol. 2). London: Academic Press, 2004.

[3] Semler C , Li G X , Paidoussis M P . The Non-linear Equations of Motion of Pipes Conveying Fluid[J]. Journal of Sound and Vibration, 1994, 169(5):577-599.

[4] Wadham-Gagnon M , M.P. Paidoussis, Semler C . Dynamics of cantilevered pipes conveying fluid. Part 1: Nonlinear equations of three-dimensional motion[J]. Journal of Fluids and Structures, 2007, 23(4):545-567.

[5] Stangl M, Gerstmayr J, Irschik H. A large deformation planar finite element for pipes conveying fluid based on the absolute nodal coordinate formulation[J]. Journal of Computational and Nonlinear Dynamics, 2009, 4(3): 031009.

[6] 蔡逢春, 臧峰刚, 叶献辉, 等. 基于绝对节点坐标法的输流管道非线性动力学分析[J]. 振动与冲击, 2011, 30(6):143-146.
CAI Feng-chun, ZANG Feng-gang, YE Xian-hui, et al. Analysis of nonlinear dynamic behavior of pipe conveying fluid based on absolute nodal coordinate formulation[J]. Journal of vibration and shock, 2011, 30(6):143-146.

[7] Stangl M, Gerstmayr J, Irschik H. An alternative approach for the analysis of nonlinear vibrations of pipes conveying fluid[J]. Journal of Sound and Vibration, 2008, 310(3): 493-511.

[8] Zhou K, Xiong F R, Jiang N B, et al. Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink[J]. Nonlinear Dynamics, 2018: 1-22.

[9] Ni Q, Wang Y, Tang M, et al. Nonlinear impacting oscillations of a fluid-conveying pipe subjected to distributed motion constraints[J]. Nonlinear Dynamics, 2015, 81(1-2): 893-906.

[10] Yan H, Dai H, Ni Q, et al. Nonlinear dynamics of a sliding pipe conveying fluid[J]. Journal of Fluids and Structures, 2018, 81: 36-57.

[11] Shabana A A. An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. No. MBS96-1-UIC, University of Illinois at Chicago, 1996.

[12] Shabana A A. Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation[J]. Multibody System Dynamics, 1997, 1(3):339-348.

[13] Yu D, Païdoussis M P, Shen H, et al. Dynamic stability of periodic pipes conveying fluid[J]. Journal of Applied Mechanics, 2014, 81(1): 011008.

[14] Dai H L, Wang L, Ni Q. Dynamics of a fluid-conveying pipe composed of two different materials[J]. International Journal of Engineering Science, 2013, 73: 67-76.

[15] Li Q, Liu W, Zhang Z, et al. Parametric Resonance of Pipes with Soft and Hard Segments Conveying Pulsating Fluids[J]. International Journal of Structural Stability and Dynamics, 2018, 18(10): 1850119.