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Nonlinear Dynamics

, Volume 93, Issue 2, pp 505–524 | Cite as

Non-planar responses of cantilevered pipes conveying fluid with intermediate motion constraints

  • Yikun Wang
  • Lin Wang
  • Qiao Ni
  • Huliang Dai
  • Hao Yan
  • Yangyang Luo
Original Paper
  • 170 Downloads

Abstract

In this paper, the nonlinear responses of a loosely constrained cantilevered pipe conveying fluid in the context of three-dimensional (3-D) dynamics are investigated. The pipe is allowed to oscillate in two perpendicular principal planes, and hence its 3-D motions are possible. Two types of motion constraints are considered. One type of constraints is the tube support plate (TSP) which comprises a plate with drilled holes for the pipe to pass through. A second type of constraints consists of two parallel bars (TPBs). The restraining force between the pipe and motion constraints is modeled by a smoothened-trilinear spring. In the theoretical analysis, the 3-D version of nonlinear equations is discretized via Galerkin’s method, and the resulting set of equations is solved using a fourth-order Runge–Kutta integration algorithm. The dynamical behaviors of the pipe system for varying flow velocities are presented in the form of bifurcation diagrams, time traces, power spectra diagrams and phase plots. Results show that both types of motion constraints have a significant influence on the dynamic responses of the cantilevered pipe. Compared to previous work dealing with the loosely constrained pipe with motions restricted to a plane, both planar and non-planar oscillations are explored in this 3-D version of pipe system. With increasing flow velocity, it is shown that both periodic and quasi-periodic motions can occur in the system of a cantilever with TPBs constraints. For a cantilevered pipe with TSP constraints, periodic, chaotic, quasi-periodic and sticking behaviors are detected. Of particular interest of this work is that quasi-periodic motions may be induced in the pipe system with either TPBs or TSP constraints, which have not been observed in the 2-D version of the same system. The results obtained in this work highlight the importance of consideration of the non-planar oscillations in cantilevered pipes subjected to loose constraints.

Keywords

Cantilevered pipe conveying fluid 3-D nonlinear dynamics Non-planar response Motion constraints Quasi-periodic motion 

Notes

Acknowledgements

The financial support of the National Natural Science Foundation of China (Nos. 11672115 and 11622216) to this work is gratefully acknowledged.

References

  1. 1.
    Paidoussis, M.P.: Pipes conveying fluid: a model dynamical problem. J. Fluid Struct. 7(2), 137–204 (1993)CrossRefGoogle Scholar
  2. 2.
    Ni, Q., Wang, Y., Tang, M., Luo, Y., Yan, H., Wang, L.: Nonlinear impacting oscillations of a fluid-conveying pipe subjected to distributed motion constraints. Nonlinear Dyn. 81(893–904), 14 (2015)Google Scholar
  3. 3.
    Modarres-Sadeghi, Y., Paidoussis, M.P., Semler, C.: Three-dimensional oscillations of a cantilever pipe conveying fluid. Int. J. Non-Linear Mech. 43(43), 18–25 (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Jayaraman, K., Narayanann, S.: Chaotic oscillations in pipes conveying pulsating fluid. Nonlinear Dyn. 10(4), 333–357 (1996)CrossRefGoogle Scholar
  5. 5.
    Wadham-Gagnon, M., Paidoussis, M.P., Semler, C.: Dynamics of cantilevered pipes conveying fluid. Part 1: nonlinear equations of three-dimensional motion. J. Fluids Struct. 23(4), 545–567 (2007)CrossRefGoogle Scholar
  6. 6.
    Hu, K., Wang, Y.K., Dai, H.L., Wang, L., Qian, Q.: Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory. Int. J. Eng. Sci. 105, 93–107 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, L., Hong, Y.Z., Dai, H.L., Ni, Q.: Natural frequency and stability tuning of cantilevered CNTs conveying fluid in magnetic field. Acta Mech. Solida Sin. 29(6), 567–576 (2016)CrossRefGoogle Scholar
  8. 8.
    Paidoussis, M.P.: Fluid-Structure Interactions: Slender Structures and Axial Flow. Academic Press, London (1998)Google Scholar
  9. 9.
    Gregory, R.W., Paidoussis, M.P.: Unstable oscillations of tubular cantilevers conveying fluid—I. Theory. Proc. R. Soc. A 293(1435), 512–527 (1966)CrossRefzbMATHGoogle Scholar
  10. 10.
    Bajaj, A.K., Sethna, P.R., Lundgren, T.S.: Hopf bifurcation phenomena in tubes carrying fluid. SIAM J. Appl. Math. 39(2), 213–230 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Tang, D.M., Dowell, E.H.: Chaotic oscillations of a cantilevered pipe conveying fluid. J. Fluids Struct. 2(3), 263–283 (1988)CrossRefGoogle Scholar
  12. 12.
    Dai, H.L., Wang, L.: Dynamics and stability of magnetically actuated pipes conveying fluid. Int. J. Struct. Stab. Dyn. 16(06), 1550026 (2016)CrossRefGoogle Scholar
  13. 13.
    Sugiyama, Y., Tanaka, Y., Kishi, T., Kawagoe, H.: Effect of a spring support on the stability of pipes conveying fluid. J. Sound Vib. 100(2), 257–270 (1985)CrossRefGoogle Scholar
  14. 14.
    Païdoussis, M.P., Semler, C: Nonlinear dynamics of a fluid-conveying cantilevered pipe with an intermediate spring support. Journal of Fluids and Structures. 7(7), 269–298; addendum in 7, 565–566 (1993)Google Scholar
  15. 15.
    Sugiyama, Y., Katayama, T., Akesson, B., Sallström, J.H.: Stability of cantilevered pipes conveying fluid and having intermediate spring support. In: Transactions 11th International Conference on Structural Mechanics in Reactor Technology (SMiRT). Tokyo, Paper J10/1 (1991)Google Scholar
  16. 16.
    Païdoussis, M.P., Moon, F.C.: Nonlinear and chaotic fluidelastic vibrations of a flexible pipe conveying fluid. J. Fluids Struct. 2(6), 567–591 (1988)CrossRefGoogle Scholar
  17. 17.
    Païdoussis, M.P., Li, G.X., Rand, R.H.: Chaotic motions of a constrained pipe conveying fluid: comparison between simulation, analysis and experiment. J. Appl. Mech. 58(2), 559–565 (1991)CrossRefGoogle Scholar
  18. 18.
    Païdoussis, M.P., Li, G.X., Moon, F.C.: Chaotic oscillations of the autonomous system of a constrained pipe conveying fluid. J. Sound Vib. 135(1), 1–19 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Paidoussis, M.P., Semler, C.: Nonlinear and chaotic oscillations of a constrained cantilevered pipe conveying fluid: a full nonlinear analysis. Nonlinear Dyn. 4(6), 655–670 (1993)CrossRefGoogle Scholar
  20. 20.
    Makrides, G.A., Edelstein, W.S.: Some numerical studies of chaotic motions in tubes conveying fluid. J. Sound Vib. 152(152), 517–530 (1992)CrossRefzbMATHGoogle Scholar
  21. 21.
    Jin, J.D.: Stability and chaotic motion of a restrained pipe conveying fluid. J. Sound Vib. 208(3), 427–439 (1997)CrossRefGoogle Scholar
  22. 22.
    Fredriksson, M.H., Borglund, D., Nordmark, A.B.: Experiments on the onset of impacting motion using a pipe conveying fluid. Nonlinear Dyn. 19(3), 261–271 (1999)CrossRefzbMATHGoogle Scholar
  23. 23.
    Lim, J.-H., Jung, G.-C., Choi, Y.-S.: Nonlinear dynamic analysis of cantilever tube conveying fluid with system identification. KSME Int. J. 17(12), 1994–2003 (2003)CrossRefGoogle Scholar
  24. 24.
    Païdoussis, M.P.: Fluid Structure Interactions: Slender Structures and Axial Flow, 1st edn. Academic Press, London (1998)Google Scholar
  25. 25.
    Lundgren, T.S., Sethna, P.R., Bajaj, A.K.: Stability boundaries for flow induced motions of tubes with an inclined terminal nozzle. J. Sound Vib. 64(4), 553–571 (1979)CrossRefzbMATHGoogle Scholar
  26. 26.
    Bajaj, A.K., Sethna, P.R.: Flow induced bifurcations to three-dimensional oscillatory motions in continuous tubes. SIAM J. Appl. Math. 44(2), 270–286 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Païdoussis, M.P., Semler, C., Wadham-Gagnon, M., Saaid, S.: Dynamics of cantilevered pipes conveying fluid. Part 2: dynamics of the system with intermediate spring support. J. Fluids Struct. 23(4), 569–587 (2007)CrossRefGoogle Scholar
  28. 28.
    Ghayesh, M.H., Paidoussis, M.P., Modarres-Sadeghi, Y.: Three-dimensional dynamics of a fluid-conveying cantilevered pipe fitted with an additional spring-support and an end-mass. J. Sound Vib. 330(12), 2869–2899 (2011)CrossRefGoogle Scholar
  29. 29.
    Ghayesh, M.H., Païdoussis, M.P.: Three-dimensional dynamics of a cantilevered pipe conveying fluid, additionally supported by an intermediate spring array. Int. J. Non-Linear Mech. 45(5), 507–524 (2010)CrossRefGoogle Scholar
  30. 30.
    Mureithi, N.W., Paidoussis, M.P., Price, S.J.: Intermittency transition to chaos in the response of a loosely supported cylinder in an array in cross-flow. Chaos, Solitons Fractal. 5(5), 847–867 (1995)CrossRefzbMATHGoogle Scholar
  31. 31.
    Wadham-Gagnon, M., Païdoussis, M.P., Semler, C.: Dynamics of cantilevered pipes conveying fluid. Part 1: nonlinear equations of three-dimensional motion. J. Fluids Struct. 23(4), 545–567 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Yikun Wang
    • 1
    • 2
  • Lin Wang
    • 1
    • 2
  • Qiao Ni
    • 1
    • 2
  • Huliang Dai
    • 1
    • 2
  • Hao Yan
    • 1
    • 2
  • Yangyang Luo
    • 1
    • 2
  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Hubei Key Laboratory for Engineering Structural Analysis and Safety AssessmentWuhanChina

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