STUDY ON NATURAL CHARACTERISTICS OF FLUID-CONVEYING PIPES WITH ELASTIC SUPPORTS AT BOTH ENDS

Yan Xiong; Wei Sha; Mao Xiaoye; Ding Hu; Chen Liqun

doi:10.6052/0459-1879-21-566

Volume 54 Issue 5

May 2022

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(5): 1341-1352

Yan Xiong, Wei Sha, Mao Xiaoye, Ding Hu, Chen Liqun. Study on natural characteristics of fluid-conveying pipes with elastic supports at both ends. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1341-1352 doi: 10.6052/0459-1879-21-566

Citation:

Yan Xiong, Wei Sha, Mao Xiaoye, Ding Hu, Chen Liqun. Study on natural characteristics of fluid-conveying pipes with elastic supports at both ends. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1341-1352 doi: 10.6052/0459-1879-21-566

Citation:

PDF( 3035 KB)

STUDY ON NATURAL CHARACTERISTICS OF FLUID-CONVEYING PIPES WITH ELASTIC SUPPORTS AT BOTH ENDS

doi: 10.6052/0459-1879-21-566

School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China

Received Date: 2021-11-02
Accepted Date: 2022-03-14

Available Online: 2022-03-15

Publish Date: 2022-05-01

Abstract

Abstract

Fluid-conveying pipes have been widely used in aerospace, petrochemical, offshore and other important engineering fields. The vibration characteristics of the fluid-conveying pipes, especially the natural characteristics of the system, have been an important issue in the research of scholars around the world. This study investigates the natural characteristics of transverse vibration of a fluid-conveying pipe with elastic supports at both ends. In particular, the natural characteristics of the fluid-conveying pipe with asymmetric elastic supports at both ends are discussed. The governing equation and boundary conditions of the fluid-conveying pipe system are derived by the Hamilton’s principle. The modal functions of the static pipe are obtained by the complex modal method, and then they are used as the potential function and weight function for the Galerkin method to truncate the control equation of the linear derived system. The effects of symmetrical support stiffness at both ends, asymmetric support stiffness at both ends, pipe length and fluid mass ratio on the natural frequencies of the system are discussed. The discussion focuses on the variation of natural frequencies under the condition of asymmetric supports that may happen at both ends of the pipe. Results show that a fast decrease in the first natural frequency for large symmetrical support stiffness. When the support stiffness at both ends of the pipe changes, the natural frequencies of each order of the pipe obtain the maximum or minimum value when the support stiffness at both ends is equal. For the pipe with asymmetric supports at both ends, the closer the support stiffness at both ends, the faster the first natural frequency decreases, and the smaller the corresponding critical flow velocity. The greater the flow velocity of the fluid, the more significant is the effect on the natural frequency of the pipe supported by asymmetric supports at both ends.
- fluid-conveying pipes,
- natural frequency,
- elastic supports,
- transverse vibration,
- asymmetric boundary

FullText(HTML)

References(34)

References

[1]	Chatjigeorgiou IK. On the effect of internal flow on vibrating catenary risers in three dimensions. Engineering Structures, 2010, 32(10): 3313-3329 doi: 10.1016/j.engstruct.2010.07.004
[2]	Huang BW, Chen GS, Yu CT. Parametric resonance of a fluctuation fluid flow heat exchanger system. International Journal of Mechanical Sciences, 2018, 146: 386-395
[3]	Gao PX, Zhai JY, Qu FZ, et al. Vibration and damping analysis of aerospace pipeline conveying fluid with constrained layer damping treatment. Journal of Aerospace Engineering, 2018, 232(8): 1529-1541 doi: 10.1177/0954410017692367
[4]	Lu HF, Asce SM, Huang K, et al. Vibration and stress analyses of positive displacement pump pipeline systems in oil transportation stations. Journal of Pipeline Systems Engineering and Practice, 2016, 7(1): 0000205 doi: https://doi.org/10.1061/(ASCE)PS.1949-1204.0000205
[5]	Ashley H, Haviland G. Bending vibration of a pipe line containing flowing fluid. Journal of Applied Mechanics, 1950, 17(3): 229-232 doi: 10.1115/1.4010122
[6]	Gregory RW, Paidoussis MP. Unstable oscillation of tubular cantilevers conveying fluid Ⅰ. Theory. Proceedings of the Royal Society of London, 1966, 293(1435): 512-527
[7]	Gregory RW, Paidoussis MP. Unstable oscillation of tubular cantilevers conveying fluid Ⅱ. Experiments. Proceedings of the Royal Society of London, 1966, 293(1435): 528-542
[8]	Paidoussis MP, Issid N. Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration, 1974, 33(3): 267-294 doi: 10.1016/S0022-460X(74)80002-7
[9]	杨晓东, 金基铎. 输流管道流-固耦合振动的固有频率分析. 振动与冲击, 2008, 27(3): 80-81, 86 (Yang Xiaodong, Jin Jiduo. Comparison of Galerkin method and complex mode method in natural frequency analysis of tube conveying fluid. Journal of Vibration and Shock, 2008, 27(3): 80-81, 86 (in Chinese) doi: 10.3969/j.issn.1000-3835.2008.03.020
[10]	周永兆, 杨晓东, 金基铎. 输流管道非线性横向振动固有频率分析. 振动、测试与诊断, 2012, 32: 66-68, 150 (Zhou Yongzhao, Yang Xiaodong, Jin Jiduo. Natural frequency analysis of nonlinear transverse vibration for pipes conveying fluid. Journal of Vibration,Measurement &Diagnosis, 2012, 32: 66-68, 150 (in Chinese)
[11]	易浩然, 周坤, 代胡亮等. 含集中质量悬臂输流管的稳定性与模态演化特性研究. 力学学报, 2020, 52(6): 1800-1810 (Yi Haoran, Zhou Kun, Dai Huliang, et al. Study on stability and modal evolution characteristics of the cantilevered fluid-conveying pipe attached with the lumped mass. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1800-1810 (in Chinese) doi: 10.6052/0459-1879-20-280
[12]	刘昌领, 罗晓兰, 叶道辉等. 一端固定一端简支输流管道流固耦合振动分析. 机械与电子, 2013, 7: 19-23 (Liu Changling, Luo Xiaolan, Ye Daohui, et al. Vibration analysis of liquid-filled pipes with fixed-hinged under fluid structure interaction. Machinery & Electronics, 2013, 7: 19-23 (in Chinese)
[13]	郭梓龙, 王琳, 倪樵等. 接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究. 力学学报, 2021, 53(6): 1769-1780 (Guo Zilong, Wang Lin, Ni Qiao, et al. Research on the influence of grounded inerter-based absorber on the stability and dynamic response of cantilevered pipe conveying fluid. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1769-1780 (in Chinese) doi: 10.6052/0459-1879-21-105
[14]	张挺, 林震寰, 郭晓梅等. 基于广义有限差分法的输流直管振动响应特性研究. 振动与冲击, 2019, 38(24): 165-171 (Zhang Ting, Lin Zhenhuan, Guo Xiaomei, et al. Numerical simulation of vibration response of pipe conveying fluid based on a generalized finite difference method. Journal of Vibration and Shock, 2019, 38(24): 165-171 (in Chinese)
[15]	金基铎, 邹光胜, 张宇飞. 悬臂输流管道的运动分岔现象和混沌运动. 力学学报, 2002, 34(6): 863-873 (Jin Jiduo, Zou Guangsheng, Zhang Yufei. Bifurcations and chaotic motions of a cantilevered pipe conveying fluid. Chinese Journal of Theoretical and Applied Mechanics, 2002, 34(6): 863-873 (in Chinese) doi: 10.3321/j.issn:0459-1879.2002.06.004
[16]	匡华军, 刘永寿, 岳珠峰. 温度对两端固支管道振动特性影响分析. 机械设计与制造, 2010, 5: 207-208 (Kuang Huajun, Liu Yongshou, Yue Zhufeng. Analysis the temperature to the vibration characteristics of pipeline with both ends clamped lmpact. Machinery Design & Manufacture, 2010, 5: 207-208 (in Chinese) doi: 10.3969/j.issn.1001-3997.2010.03.087
[17]	邢静忠, 柳春图. 线弹性土壤中埋设悬跨管道的弯曲和振动特性. 海洋工程, 2008, 2: 78-82 (Xing Jingzhong, Liu Chuntu. Bending and vibration characteristics of spanning pipe buried in linear elastic soil. The Ocean Engineering, 2008, 2: 78-82 (in Chinese) doi: 10.3969/j.issn.1005-9865.2008.02.010
[18]	随岁寒, 李成. 输流管道弯曲和振动的有限元分析. 动力学与控制学报, 2021, 出版中, https://kns.cnki.net/kcms/detail/43.1409.O3.20211111.1552.002.html Sui Suihan, Li Cheng. The finite element analysis on bending and vibration of the fluid-conveying pipes. Journal of Dynamics and Control, 2021, in press, https://kns.cnki.net/kcms/detail/43.1409.O3.20211111.1552.002.html (in Chinese))
[19]	Ye SQ, Ding H, Wei S, et al. Non-trivial equilibriums and natural frequencies of a slightly curved pipe conveying supercritical fluid. Ocean Engineering, 2021, 227: 108899 doi: 10.1016/j.oceaneng.2021.108899
[20]	江建祥, 黄幼玲. 弹性支承输流管道固有频率计算. 振动工程学报, 1992, 5(4): 396-402 (Jiang Jianxiang, Huang Youling. Calculation of the eigenfrequency of the fluid-conveying pipes on spring-support. Journal of Vibration Engineering, 1992, 5(4): 396-402 (in Chinese)
[21]	倪樵, 黄玉盈, 陈贻平. 微分求积法分析具有弹性支承输液管的临界流速. 计算力学学报, 2001, 18(2): 146-149 (Ni Qiao, Huang Yuying, Chen Yiping. Differential quadrature method for analyzing critical flow velocity of the pipe conveying fluid with spring support. Journal of Computational Mechanics, 2001, 18(2): 146-149 (in Chinese) doi: 10.3969/j.issn.1007-4708.2001.02.004
[22]	李琳, 唐冶, 任正义等. 具有弹性支承输流管道的稳定性和临界流速分析. 哈尔滨工程大学学报, 2010, 31(11): 1509-1513 (Li Lin, Tang Ye, Ren Zhengyi, et al. Stability and critical flow velocity analysis on a fluid-conveying pipeline with elastic support. Journal of Harbin Engineering University, 2010, 31(11): 1509-1513 (in Chinese)
[23]	Qian Q, Wang L, Ni Q. Nonlinear responses of a fluid-conveying pipe embedded in nonlinear elastic foundations. Acta Mechanica Solida Sinica, 2008, 21(2): 170-176 doi: 10.1007/s10338-008-0820-7
[24]	包日东, 金志浩, 闻邦椿. 端部约束悬臂输流管道的动力学特性. 工程力学, 2009, 26(1): 209-215 (Bao Ridong, Jin Zhihao, Wen Bangchun. Dynamic behaviors of restrained cantilever pipe conveying fluid. Engineering Mechanics, 2009, 26(1): 209-215 (in Chinese)
[25]	包日东, 冯颖, 毕文军. 弹性支承输流管道的动力学特性. 机械设计与制造, 2010, 3(3): 129-131 (Bao Ridong, Feng Ying, Bi Wenjun. Dynamic characteristic of pipeline conveying fluid with elastic supports. Machinery Design & Manufacture, 2010, 3(3): 129-131 (in Chinese) doi: 10.3969/j.issn.1001-3997.2010.03.055
[26]	刘俊卿, 王克林. 弹性支承输液管道的临界流速. 应用力学学报, 2003, 20(1): 133-135, 168 (Liu Junqing, Wang Kelin. Critical flow velocity of pipes coneying fluid with elastic supports. Chinese Journal of Applied Mechanics, 2003, 20(1): 133-135, 168 (in Chinese) doi: 10.3969/j.issn.1000-4939.2003.01.030
[27]	吴男, 金基铎. 弹性地基两端铰支输流管的模态和固有频率. 沈阳航空工业学院学报, 2008, 1: 42-46 (Wu Nan, Jin Jiduo. The mode and nature frequency of pinned-pinned pipes conveying fluid with elastic foundations. Journal of Shengyang Institute of Aeronautical Engineering, 2008, 1: 42-46 (in Chinese)
[28]	Ni Q, Tang M, Luo YY, et al. Internal-external resonance of a curved pipe conveying fluid resting on a nonlinear elastic foundation. Nonlinear Dynamics, 2013, 76(1): 867-886
[29]	Ni Q, Wang L, Qian Q. Bifurcations and chaotic motions of a curved pipe conveying fluid with nonlinear constraints. Computers and Structures, 2006, 84(10-11): 708-717 doi: 10.1016/j.compstruc.2005.11.006
[30]	许锋, 郭长青, 黄建红. 弹性支承输流弹性支承输液管道在分布随从力作用下的稳定性. 工程力学, 2014, 31(7): 234-238, 256 (Xu Feng, Guo Changqing, Huang Jianhong. Stability of elastically supported pipes conveying fluid with distributed follower force. Engineering Mechanics, 2014, 31(7): 234-238, 256 (in Chinese) doi: 10.6052/j.issn.1000-4750.2012.10.0763
[31]	Li Q, Liu W, Lu K, et al. Nonlinear parametric vibration of a fluid-conveying pipe flexibly restrained at the ends. Acta Mechanica Solida Sinica, 2019, 33(3): 327-346
[32]	Ding H, Ji JC, Chen LQ. Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics. Mechanical Systems and Signal Processing, 2019, 121: 675-688 doi: 10.1016/j.ymssp.2018.11.057
[33]	Semler C, Li GX, Paidoussis MP. The non-linear equations of motion of pipes conveying fluid. Journal of Sound and Vibration, 1994, 169(5): 577-599 doi: 10.1006/jsvi.1994.1035
[34]	刘延柱, 陈立群, 陈文良. 振动力学, 第3版. 北京: 高等教育出版社, 2019: 206-207 Liu Yanzhu, Chen Liqun, Chen Wenliang. Mechanics of Vibrations, 3rd edition. Beijing: Higher Education Press, 2019: 206-207 (in Chinese)