Explanation for paradox in natural frequency calculation of cantilever fluid-conveying pipe system with an end-mass

PDF(701 KB)

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (7) : 18-24.

ZHAO Guixin, MENG Shuai, CHE Chidong, CHEN Li

Author information +

History +

Abstract

Once emergency disconnection occurs for a deep-water drilling system, drilling mud should be released to avoid undesired axial loading from resonance while seawater must be refilled in case of riser collapse. The riser system following an emergency disconnection is a typical flow-conveying pipe system attached with an end-mass (Low Marine Riser Package). There are typically two methods utilized to calculate the natural frequencies of the pipe system via Galerkin method: (1) the end-mass is accounted for in the boundary conditions; (2) the end-mass is included in the equation of motion via a Dirac delta function. Although Paidoussis have pointed out that the first method is incorrect when the internal flow velocity is nonzero, a reasonable explanation has not been given. The orthogonality relations of a beam accounting for the end-mass in the boundary conditions is re-derived. Then the natural frequencies of the aforementioned pipe system is calculated employing first method and verified by comparing with the results adopting the second method. Then an experiment employing a cantilevered fluid-conveying pipe under gravity is introduced. The refined method can predict the critical internal flow velocity and the vibration frequency when the pipe loses stability. This new finding can not only explain the paradox in natural frequency calculation of the pipe system under consideration, but also provide as a workbench for dynamic analysis of fluid-conveying pipe systems with various boundary conditions.

Key words

fluid-conveying pipe / end-mass / Galerkin method / modal orthogonality / natural frequency

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHAO Guixin, MENG Shuai, CHE Chidong, CHEN Li. Explanation for paradox in natural frequency calculation of cantilever fluid-conveying pipe system with an end-mass[J]. Journal of Vibration and Shock, 2023, 42(7): 18-24

References

[1] Ashley H, Haviland G. Bending vibrations of a pipeline containing flowing fluid[J]. Journal of Applied Mechanics, 1952, 19(2):205-208.
[2] 徐鉴, 杨前彪. 输液管模型及其非线性动力学近期研究进展[J]. 力学进展, 2004, 34(2): 182-194
Xu Jian, Yang Qian-biao. Recent development on models and nonlinear dynamics of pipes conveying fluid[J]. Advances in Mechamics, 2004, 34(2): 182-194
[3] Païdoussis M P. Fluid-Structure Interactions: Slender Structures and Axial Flow (Vol.1) [M]. Second Ed. San Diego: Academic Press, 2014
[4] Folley C N, Bajaj A K. Spatial nonlinear dynamics near principal parametric resonance for a fluid-conveying cantilever pipe[J]. Journal of Fluids and Structures, 2005,21:459-484.
[5] Modarres-sadeghi Y, Païdoussis M P, Semler C. Three-dimensional oscillations of a cantilever pipe conveying fluid[J]. International Journal of Non-Linear Mechanics, 2008,43(01):18-25.
[6] Meng S, Kajiwara H, Zhang W J. Internal flow effect on the cross-flow vortex-induced vibration of a cantilevered pipe discharging fluid[J]. Ocean Engineering, 2017,137:120-128.
[7] Chen W, Dai HL, Wang L. Three-dimensional dynamical model for cantilevered pipes conveying fluid under large deformation[J].Journal of Fluids and Structures, 2021,105:1-27.
[8] 唐冶,方勃,张业伟,等.非线性弹簧支承悬臂输液管道的分岔与混沌分析[J].振动与冲击,2011,(08):269-274.
Tang Ye, Fang Bo, Zhang Ye-wei, et al. Bifurcation and Chaos Analysis of Nonlinear Spring-Supported Cantilever Infusion Pipelines [J]. Journal of vibration and shock, 2011, (08): 269-274.
[9] 黄茜,臧峰刚,张毅雄,等.带滞变支撑悬臂输流管的动力响应分析[J].振动与冲击,2011,30(11):8-12
Hang Qian, Zang Feng-gang, Zhang Yi-xiong, et al. Nonlinear dynamic analysis of cantilevered pipes conveying fluid with hysteretic supports [J]. Journal of vibration and shock, 2011, 30(11):8-12
[10] 张紫龙，唐敏，倪樵. 非线性弹性地基上悬臂输流管的受迫振动[J]. 振动与冲击, 2013, 32(10):17-21
Zhang Zi-long, Tang Min, Ni Qiao. Forced vibration of a cantilever fluid-conveying pipe on nonlinear elastic foundation [J]. Journal of vibration and shock, 2013, 32(10):17-21
[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[J]. 力学学报, 2020, 52(6): 1800-1810
Yi Hao-ran, Zhou Kun, Dai Hu-liang, et al. Study on stability and modal evolution characteristics of the cantilevered fluid-conveying pipe attached with the lumped mass[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1800-1810
[12] Copeland G S, Moon F C. Chaotic flow-induced vibration of a flexible tube with end mass[J]. Journal of Fluids and Structures, 1992,6:705-718.
[13] Semler C, Païdoussis M P. Intermittency Route to Chaos of a Cantilevered Pipe Conveying Fluid With a Mass Defect at the Free End[J]. Journal of Applied Mechanics, 1995, 62(4):903-907.
[14] Hirose Y, Yamashita K, Ajiro J. Experiments on the mixed-mode vibration of a fluid conveying cantilevered pipe with an end mass[C]//ASME 2008 International Mechanical Engineering Congress and Exposition, Boston, USA: ASME,2008: 1-10.
[15] 刘超,刘传岩,刘健,等.水下油气生产系统概述及其发展现状[J].石油工程建设,2021,47(06):29-34
Liu Chao, Liu Chuan-yan, Liu Jian, et,al.Overview and development status of subsea oil and gas production system[J]. Petroleum Engineering Construction, 2021,47(06):29-34
[16] 柳博瀚,陈正寿,鲍健等.管道内流对海洋弹性管振动影响的数值仿真研究[J].振动与冲击,2020,(17): 177-185+202.
Liu Bohan, Chen Zhengshou, Bao Jian, et al. Numerical simulation research on the effect of pipeline internal flow on vibration of marine elastic pipe [J]. Journal of vibration and shock, 2020, (17): 177-185+202.
[17] Meng S, Karjiwara H. VIV Analysis of a Cantilevered Pipe Discharging Fluid with a Nozzle in the Sea[J]. IFAC Proceedings Volumes, 2013, 33(46):374-379.
[18] Meng S, Karjiwara H. Dynamics of a Cantilevered Pipe Discharging Fluid with a Nozzle. Part 1: Nonlinear Equations of Three-Dimensional Motion[C]//ISOPE International Ocean and Polar Engineering Conference. Alaska:USA:ISOPE, 2013:194-201.
[19] Meng S, Karjiwara H. Dynamics of a cantilevered pipe discharging fluid with a nozzle. Part 2: Three-dimensional dynamic analysis and parametric study[C] //ISOPE International Ocean and Polar Engineering Conference. Alaska:USA:ISOPE, 2013:202-209.
[20] 孙明远, 张明贺, 刘双莹,等.浮式钻井平台隔水管应急解脱分析.浮式钻井平台隔水管应急解脱分析[J]. 钻探工程, 2021,48(10):82-87
Sun Ming-yuan, Zhang Ming-he, Liu Shuang-ying, et,al. Emergency release analysis of the riser on semi-submersible drilling rig[J]. Drilling Engineering, 2021,48(10):82-87
[21] Liu J, Zhao H L, Liu Q Y, et al. Dynamic behavior of a deepwater hard suspension riser under emergency evacuation conditions[J]. Ocean Engineering, 2018, 150:138-151.
[22] Mao L J, Zeng S, Liu Q Y, et al. Dynamical mechanics behavior and safety analysis of deep water riser considering the normal drilling condition and hang-off condition[J]. Ocean Engineering, 2020, 199:106996.
[23] Wu Q, Yang J M, Lu H N, et al. Effects of heave motion on the dynamic performance of vertical transport system for deep sea mining[J]. Applied Ocean Research, 2020,101: 102188.
[24] Dai Y, Su Q, Zhang Y Y. A new dynamic model and trajectory tracking control strategy for deep ocean mining vehicle[J]. Ocean Engineering, 2020, 216: 108162.
[25] Wu Q, Yang J M, Guo X X, et al. Influence of irregular waves on the dynamic response of a vertical transport system for deep sea mining[J] .Ocean Engineering, 2021, 229: 108443.
[26] 苏伟, 孟帅, 王俊雄. 深海钻井立管系统紧急脱离反冲耦合效应研究[J]. 装备环境工程, 2018,15(12),40-44
Su Wei, Meng Shuai, Wang Jun-xiong. Coupling Effect of Deep-water Drilling Riser in Recoil after Emergency Disconnection[J]. Equipment Environmental Engineering, 2018,15(12),40-44
[27] Milier J E, Young R D. Influence of mud column dynamics on top tension of suspended deepwater drilling risers[C]//Offshore Technology Conference. Houston, USA: OTC–5015, 1985:1-6.
[28] Grønevik A. Simulation of drilling riser disconnection-recoil analysis. [D]. Norwegian University of Science and Technology, Norway, 2013.
[29] Grvtøyr G, Sharma P, Vishnubotla S. Marine drilling riser disconnect and recoil analysis[C]//The 2011 AADE National Technical Conference and Exhibition, Houston,USA: AADE–11–NTCE–80, 2011:1-9.
[30] Meng S, Che CD, Zhang WJ. Discharging flow effect on the recoil response of a deep-water drilling riser after an emergency disconnect[J]. Ocean Engineering, 151, 199-205.
[31] Modarres-sadeghi Y, Semler C, Wadham-gagnon M, et al. Dynamics of cantilevered pipes conveying fluid. Part 3: Three-dimensional dynamics in the presence of an end-mass[J]. Journal of Fluids and Structures, 2007,23: 589–603.
[32] Meng S, Zhang XQ, Che C D, et al. Cross-flow vortex-induced vibration of a flexible riser transporting an internal flow from subcritical to supercritical[J]. Ocean Engineering, 2017, 139,74-84.
[33] Semler C, Gentleman WC, Païdoussis MP. Numerical solutions of second order implicit nonlinear ordinary differential equation[J]. Journal of Sound and Vibration, 1996, 195, 553–574.