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Applied Mathematics and Mechanics

, Volume 36, Issue 6, pp 729–746 | Cite as

Effects of supported angle on stability and dynamical bifurcations of cantilevered pipe conveying fluid

  • Chunbiao GanEmail author
  • Shuai Jing
  • Shixi Yang
  • Hua Lei
Article

Abstract

The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.

Key words

cantilevered pipe conveying fluid supported angle modal analysis response characteristics dynamical bifurcation 

Chinese Library Classification

TH113 

2010 Mathematics Subject Classification

70K50 74H45 

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References

  1. [1]
    Zhang, Y. L., Gorman, D. G., and Reese, J. M. Vibration of prestressed thin cylindrical shells conveying fluid. Thin-Walled Structures, 41, 1103–1127 (2003)CrossRefGoogle Scholar
  2. [2]
    Päidoussis, M. P., Price, S. J., and de Langre, E. Fluid-Structure Interactions: Cross-Flow-Induced Instabilities, Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  3. [3]
    Ashley, H. and Haviland, G. Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics-Transactions of the ASME, 17, 229–232 (1950)MathSciNetGoogle Scholar
  4. [4]
    Housner, G. W. Bending vibrations of a pipe line containing flowing fluid. Journal of Applied Mechanics-Transactions of the ASME, 19, 205–208 (1952)Google Scholar
  5. [5]
    Benjamin, T. B. Dynamics of a system of articulated pipes conveying fluid-parts, I: theory. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 261, 457–486 (1961)zbMATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Benjamin, T. B. Dynamics of a system of articulated pipes conveying fluid, II: experiments. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 261, 487–499 (1961)MathSciNetCrossRefGoogle Scholar
  7. [7]
    Gregory, R. W. and Päidoussis, M. P. Unstable oscillation of tubular cantilevers conveying fluid, I: theory. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 293, 512–527 (1966)CrossRefGoogle Scholar
  8. [8]
    Gregory, R. W. and Päidoussis, M. P. Unstable oscillation of tubular cantilevers conveying fluid, II: experiments. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 293, 528–545 (1966)CrossRefGoogle Scholar
  9. [9]
    Firouz-Abadi, R. D., Askarian A. R., and Kheiri, M. Bending-torsional flutter of a cantilevered pipe conveying fluid with an inclined terminal nozzle. Journal of Sound and Vibration, 332, 3002–3014 (2013)CrossRefGoogle Scholar
  10. [10]
    Päidoussis, M. P., Li, G. X., and Moon, F. C. Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. Journal of Sound and Vibration, 135, 1–19 (1989)MathSciNetCrossRefGoogle Scholar
  11. [11]
    Li, G. X. and Päidoussis, M. P. Stability, double degeneracy and chaos in cantilevered pipes conveying fluid. International Journal of Non-Linear Mechanics, 29, 83–107 (1994)zbMATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    Jin, J. D. Stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 208, 427–439 (1997)CrossRefGoogle Scholar
  13. [13]
    Wadham-Gagnon, M., Päidoussis, M. P., and Semler, C. Dynamics of cantilevered pipes conveying fluid, part 1: nonlinear equations of three-dimensional motion. Journal of Fluids and Structures, 23(4), 545–567 (2007)CrossRefGoogle Scholar
  14. [14]
    Modarres-Sadeghi, Y., Semler, C., and Wadham-Gagnon, M. Dynamics of cantilevered pipes conveying fluid, part 3: three-dimensional dynamics in the presence of an end-mass. Journal of Fluids and Structures, 23, 589–603 (2007)CrossRefGoogle Scholar
  15. [15]
    Modarres-Sadeghi, Y. and Päidoussis, M. P. Chaotic oscillations of long pipes conveying fluid in the presence of a large end-mass. Computers and Structures, 122, 192–201 (2013)CrossRefGoogle Scholar
  16. [16]
    Päidoussis, M. P. and Semler, C. Non-linear dynamics of a fluid-conveying cantilevered pipe with a small mass attached at the free end. International Journal of Non-Linear Mechanics, 33, 15–32 (1998)CrossRefGoogle Scholar
  17. [17]
    Bajaj, A. K. and Sethna, P. R. Effect of symmetry-breaking perturbations on flow-induced oscillations in tubes. Journal of Fluids and Structures, 5, 651–679 (1991)CrossRefGoogle Scholar
  18. [18]
    Wang, Z. L., Feng, Z. Y., Zhao, F. Q., and Liu, H. Z. Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation. Applied Mathematics and Mechanics, 21, 1177–1186 (2010)Google Scholar
  19. [19]
    Wang, L. Flutter instability of supported pipes conveying fluid subjected to distributed follower forces. Acta Mechanica Solida Sinica, 25, 46–52 (2012)CrossRefGoogle Scholar
  20. [20]
    Päidoussis, M. P. and Li, G. X. Pipes conveying fluid: a model dynamical problem. Journal of Fluids and Structures, 7, 137–204 (1993)CrossRefGoogle Scholar
  21. [21]
    Päidoussis, M. P. Fluid-Structure Interactions, Academic Press, Pittsburgh (2003)Google Scholar
  22. [22]
    Päidoussis, M. P. Dynamics of tubular cantilevers conveying fluid. Journal of Mechanical Engineering Science, 12, 85–103 (1970)CrossRefGoogle Scholar
  23. [23]
    Wang, L. and Ni, Q. A note on the stability and chaotic motions of a restrained pipe conveying fluid. Journal of Sound and Vibration, 296, 1079–1083 (2006)CrossRefGoogle Scholar
  24. [24]
    Panda, L. N. and Kar, R. C. Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances. Journal of Sound and Vibration, 309, 375–406 (2008)CrossRefGoogle Scholar
  25. [25]
    Zhang, Y. L. and Chen, L. Q. External and internal resonances of the pipe conveying fluid in the supercritical regime. Journal of Sound and Vibration, 332, 2318–2337 (2013)CrossRefGoogle Scholar
  26. [26]
    Nayfeh, A. H. and Balachandran, B. Modal interactions in dynamical and structural systems. Applied Mechanics Review, 42, 175–201 (1989)MathSciNetCrossRefGoogle Scholar
  27. [27]
    Päidoussis, M. P. and Moon, F. C. Nonlinear and chaotic fluid-elastic vibrations of a flexible pipe conveying fluid. Journal of Fluids and Structures, 2, 567–591 (1988)CrossRefGoogle Scholar
  28. [28]
    Qian, Q., Wang, L., and Ni, Q. Nonlinear responses of a fluid-conveying pipe embedded in nonlinear elastic foundations. Acta Mechanica Solida Sinica, 21, 170–176 (2008)CrossRefGoogle Scholar
  29. [29]
    Liang, F. and Wen, B. C. Forced vibrations with internal resonance of a pipe conveying fluid under external periodic excitation. Acta Mechanica Solida Sinica, 24, 477–483 (2011)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.The State Key Laboratory of Fluid Power Transmission and Control, School of Mechanical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Department of Engineering MechanicsZhejiang UniversityHangzhouChina

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