Analysis of Flow-induced Vibration of Fluid Conveying Pipe with Elastic Support

doi:10.12068/j.issn.1005-3026.2016.08.013

Abstract

Abstract: The flow-induced vibration of cantilevered fluid-conveying pipes with elastic support was analyzed by differential transformation method (DTM). Firstly， the motion equation was non-dimensionalized， then， the recurrence relation among each derivative was derived by DTM. Furthermore， the former four dimensionless frequencies and the general expression for mode shapes were obtained without consideration of fluid flow. On this basis， the relationship between frequency and flow velocity， elastic coefficient was worked out， and the critical velocity and stability condition were investigated simultaneously. DTM was verified to be of high accuracy and practicability by comparison and analysis. Besides， DTM could be referred when support format for pipes are designed.

Key words: fluid conveying pipe, fluid-structure interaction vibration, differential transformation method, elastic support, stability

CLC Number:

O353

ZHAO Qian-li， SUN Zhi-li， CHAI Xiao-dong， TONG Cao. Analysis of Flow-induced Vibration of Fluid Conveying Pipe with Elastic Support[J]. Journal of Northeastern University Natural Science, 2016, 37(8): 1122-1126.

References

[1]Paidoussis M P.Fluid-structure interactions:slender structures and axial flow:vol.1［M］.London:Academic Press，1998.
[2]Paidoussis M P，Li G X.Pipes conveying fluid:a model dynamical problem［J］.Journal of Fluids and Structure，1993，7(2):137-204.
[3]Paidoussis M P.The canonical problem of the fluid conveying pipe and radiation of the knowledge gained to other dynamics problems across applied mechanics［J］.Journal of Sound and Vibration，2008，310(3):462-492.
[4]赵凤群，王忠民.具有可移动弹性支承输流管道的稳定性分析［J］.机械工程学报，2004，40(9):38-41.(Zhao Feng-qun，Wang Zhong-min.Stability analysis of pipes conveying fluid with removable elastic support［J］.Journal of Mechanical Engineering，2004，40(9):38-41.)
[5]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［J］.计算力学学报，2000，18(2):146-149.(Ni Qiao，Huang Yu-ying，Chen Yi-ping.Analysis of critical velocity of fluid conveying pipes by differential quadrature method［J］.Chinese Journal of Computational Mechanics，2000，18(2):146-149.)
[6]包日东，闻邦椿.微分求积法分析弹性支承输流管道的稳定性［J］.东北大学学报(自然科学版)，2007，28(7):1017-1020.(Bao Ri-dong，Wen Bang-chun.Differential quadrature method to analyze stability of elastically supported fluid conveying pipelines［J］.Journal of Northeastern University (Natural Science)，2007，28(7):1017-1020.)
[7]赵家奎.微分变换及其在电路中的应用［M］.武汉:华中工学院出版社，1986.(Zhao Jia-kui.Differential transformation and its application for electrical circuits［M］.Wuhan:Huazhong College of Technology Press，1986.)
[8]Ni Q，Zhang Z L，Wang L.Application of the differential transformation method to vibration analysis of pipes conveying fluid［J］.Applied Mathematics and Computation，2011，217(16):7028-7038.
[9]金基铎，杨晓东，邹光胜.两端支承输流管道的稳定性和临界流速分析［J］.机械工程学报，2006，42(11):131-136.(Jin Ji-duo，Yang Xiao-dong，Zou Guang-sheng.Stability and critical flow velocity of supported pipes conveying fluid［J］.Journal of Mechanical Engineering，2006，42(11):131-136.)

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