Cusp bifurcation of slightly curved tensioned pipe conveying hot pressurized fluid

Abstract

In the course of operation of pipes conveying high temperature-high pressure fluid, unexpected behaviors leading to catastrophic failures have been observed. These have been attributed to uncertainties arising from issues not adequately addressed in the design. Sources of such uncertainties include geometric imperfection of the pipe and temperature variation. The perfectly straight pipe is assumed in most designs, but it is an idealization that does not exist in practice. In a bid to reduce the number of uncertainties in design and operation, a model governing nonlinear vibration of tensioned pipes conveying hot pressurized fluid that accounts for the geometric imperfection of the pipe is developed in this work. Coupled nonlinear equations of motion in both axial and transverse directions are obtained and solved using the eigenfunction expansion method. The influence of initial curvature, temperature, and the longitudinal vibration on the pipe are investigated. The results obtained show that a pipe with geometric imperfection exhibits cusp bifurcation and not supercritical pitchfork bifurcation.

Keywords

Buckling cusp bifurcation geometric imperfection initial curvature out of straightness

Get full access to this article

View all access options for this article.

References

Ashley

Haviland

(1950) Bending vibrations of a pipeline containing flowing fluid. Journal of Applied Mechanics – Transactions of the ASME 17(3): 229–232.

Askari

Esmailzadeh

(2017) Forced vibration of fluid conveying carbon nanotubes considering thermal effect and nonlinear foundations. Composites Part B: Engineering 113(1): 31–43.

Carr M, Sinclair F and Bruton D (2006) Pipeline Walking – Understanding the field Layout Challenges and analytical solutions Developed for the SAFEBUCK JIP. In: Proceedings of Offshore Technology Conference, Houston, Texas, U.S.A., 1–4 May 2006.

Dodds HL and Runyan HL (1965) Effect of High-Velocity Fluid Flow on the Bending Vibrations and Static Divergence of a Simply Supported Pipe. Report No. NASA-TN-2870, 1–13. Available at: http://www.dtic.mil/dtic/tr/fulltext/u2/a393464.pdf (accessed 15 June 2018).

Gan

Jing

Yang

et al. (2015) Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid. Applied Mathematics and Mechanics – English Edition 36(6): 729–746.

Ghazavi

Molki

Ali Beigloo

(2018) Nonlinear analysis of the micro/nanotube conveying fluid based on second strain gradient theory. Applied Mathematical Modelling 60(1): 77–93.

Guo

Xie

Wang

(2018) Three-dimensional vibration of cantilevered fluid-conveying micropipes – Types of periodic motions and small-scale effect. International Journal of Non-Linear Mechanics 102(1): 112–135.

Hill AJ and Jacob H (2008) In-situ measurement of pipe–soil interaction in deep water. In: Proceedings of Offshore Technology Conference, Houston, Texas, U.S.A., 5–8 May 2008.

Hobbs

(1984) In-service buckling of heated pipelines. Journal of Transportation Engineering 110(2): 175–189.

10.

Holmes

(1977) Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis. Journal of Sound and Vibration 53(4): 471–503.

11.

Housner

(1952) Bending vibrations of a pipe line containing flowing fluid. ASME Journal of Applied Mechanics 19(2): 205–208.

12.

Huang YM, Ge S, Wu W, et al. (2012) A direct method of natural frequency analysis on pipe conveying fluid with both ends supported. Nuclear Engineering and Design 253(1): 12–22.

13.

Ibrahim

(2010) Overview of mechanics of pipes conveying fluids – Part I: Fundamental studies. Journal of Pressure Vessel Technology 132(3): 1–32.

14.

Jianxing

Mengning

Zhenzhou

et al. (2016) Research progress of buckling propagation experiments in deep water pipelines. Transactions of Tianjin University 22(4): 285–293.

15.

Kyriakides

(1988) Thermal buckling of offshore pipelines. Journal of Offshore Mechanics and Arctic Engineering 110(4): 355–364.

16.

Kaewunruen

Chiravatchradej

Chucheepsakul

(2005) Nonlinear free vibrations of marine risers/pipes transporting fluid. Ocean Engineering 32(3): 417–440.

17.

Kaye D (1996) Lateral buckling of subsea pipelines: Comparison between design and operation. In: Advances in Subsea Pipeline Engineering and Technology, Society of Underwater Technology, Aberdeen, UK, 27–28 November 1996.

18.

Liang

Yang

Zhang

et al. (2018) Dynamical modeling and free vibration analysis of spinning pipes conveying fluid with axial deployment. Journal of Sound and Vibration 417(1): 65–79.

19.

Liu

Mote

(1974) Dynamic response of pipes transporting fluids. ASME Journal of Engineering and Industry 96(2): 591–596.

20.

Mnassri

El Baroudi

(2017) Vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid. Acta Mechanica Solida Sinica 30(4): 435–444.

21.

Modarres-Sadeghi

Païdoussis

(2009) Nonlinear dynamics of extensible fluid-conveying pipes supported at both ends. Journal of Fluids and Structures 25(3): 535–543.

22.

Öz

Pakdemirli

Özkaya

et al. (1998) Non-linear vibrations of a slightly curved beam resting on a non-linear elastic foundation. Journal of Sound and Vibration 212(2): 295–309.

23.

Païdoussis

(1998) Fluid–Structure Interactions: Slender Structures and Axial Flow, London, UK: Academic Press.

24.

Peng

Xiong

Gao

et al. (2018) Non-linear dynamics of a simply supported fluid-conveying pipe subjected to motion-limiting constraints: Two-dimensional analysis. Journal of Sound and Vibration 435(1): 192–204.

25.

Qian

Wang

(2009) Instability of simply supported pipes conveying fluid under thermal loads. Mechanics Research Communications 36(3): 413–417.

26.

Rehfield

(1974) Nonlinear flexural oscillations of shallow arches. AIAA Journal 12(1): 91–93.

27.

Semler

Païdoussis

(1994) The non-linear equations of motion of pipes conveying fluid. Journal of Sound and Vibration 169(5): 577–599.

28.

Shi R, Wang K, Long F, et al. (2013) Vertical buckling of offshore pipelines with geometrical imperfection on soft seabed. Electronic Journal of Geotechnical Engineering 18(1): 5491–5508.

29.

Sinir

(2010) Bifurcation and chaos of slightly curved pipes. Mathematical and Computational Applications 15(3): 490–502.

30.

Sriskandarajah T, Ragupathy P and Wilkins R (2001) Dynamic versus static lateral buckling of subsea pipelines. In: 11th International Onshore and Polar Engineering Conference, International Society of Onshore and Polar Engineers, Stavanger, Norway, 17–22 June 2001.

31.

Strogatz SH (2000) Nonlinear Dynamics and Chaos: With Applications To Physics, Biology, Chemistry, And Engineering. New York, NY: Perseus Books Publishing.

32.

Timoshenko

(1956) Strength of Materials, New York, NY: Van Nostrand.

33.

Wang L and Ni Q (2009) Vibration of slender structures subjected to axial flow or axially towed in quiescent fluid. Advances in Acoustics and Vibration 2009: 1–19. Available at: https://www.hindawi.com/journals/aav/2009/432340/(accessed 11 June 2018).

34.

Wang

Dai

Qian

(2012) Dynamics of simply supported fluid-conveying pipes with geometric imperfections. Journal of Fluids and Structures 29(1): 97–106.

35.

Watson RD, Sinclair F and Bruton DAS (2011) SAFEBUCK JIP: Operational integrity of deepwater flowlines. In: Proceedings of Offshore Technology Conference, Houston, Texas, USA, 2–5 May 2011.