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Flow-induced buckling statics and dynamics of imperfect pipes

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Abstract

The dynamic characteristics of imperfect pipes conveying fluid in the pre-buckling and post-buckling states are investigated. In this paper, the novel motion equation of fluid-conveying imperfect pipe supported at both ends is derived by considering the geometric imperfection and the geometric nonlinearity induced by mid-plane stretching. The imperfect configurations are chosen as the first bucked modes of pined–pined and clamped–clamped pipes. The exactly analytical solutions for static response are obtained due to the fluid flow. In the linear vibration analysis, the equation is discretized by the Galerkin method and solved as a linear eigenvalues problem. Excellent agreement is observed between the present solution and the available literature. Compared with the supercritical pitchfork bifurcation of the perfect pipe conveying fluid, the results show that the cusp bifurcation occurs in the imperfect pipe when increasing the flow velocity. In the post-buckling state, there are three equilibrium configurations composed of two asymmetry stable branches and an unstable branch. The critical velocity firstly increases and then decreases when the imperfect amplitude increases. The numerical results indicate that initial imperfect amplitude and flow velocity have a complex influence on the natural frequency of the imperfect pipe. The first natural frequency increases when the initial imperfect amplitude increases. The three branches of the imperfect pipe in the post-buckling state provide more interesting and essential dynamic behaviors.

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Abbreviations

\(L\) :

The pipe length

\(m_{{\text{p}}}\) :

Mass per unit length of pipe

\(E\) :

Young’s modulus

\(E^{ * }\) :

Viscoelastic damping

\(I\) :

Second moment of area

\(A_{{\text{p}}}\) :

Cross-sectional area

\(m_{{\text{f}}}\) :

Mass per unit length of pipe

\(U\) :

Flow velocity of fluid

\(T\) :

External applied tension

\(W_{{0}} (x)\) :

The initial deformation

\(W(x,t)\) :

The lateral displacements

\(\varepsilon_{{{\text{xx}}}}\) :

Axial strain induced by bending deformation

\(V_{{\text{p}}}\) :

The strain energy of the pipe

\(T_{{\text{p}}}\) :

The kinetic energy of the pipe

\(T_{{\text{f}}}\) :

The fluid kinetic energy

\(W_{{{\text{vis}}}}\) :

The virtual work done by the damping force

\(W_{{\text{T}}}\) :

The work done by the externally applied tension

\(\varepsilon_{{\text{H}}}\) :

Averaged axial strain induced by lateral displacement

\(T_{{\text{H}}}\) :

The axial force induced by lateral displacement

References

  1. Paidoussis, M.P.: Fluid-Structure Interactions: Slender Structures and Axial Flow, Volume1. Academic Press, London (1998)

    Google Scholar 

  2. Ibrahim, R.A.: Overview of mechanics of pipes conveying fluids—part I: fundamental studies. J. Pressure Vessel Technol. 132(3), 034001 (2010)

    Article  Google Scholar 

  3. Holmes, P.J.: Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis. J. Sound Vib. 53(4), 471–503 (1977). https://doi.org/10.1016/0022-460X(77)90521-1

    Article  MathSciNet  MATH  Google Scholar 

  4. Païdoussis, M.P., Issid, N.T.: Dynamic stability of pipes conveying fluid. J. Sound Vib. 33(3), 267–294 (1974)

    Article  Google Scholar 

  5. Sinir, B.G.: Bifurcation and chaos of slightly curved pipes. Math. Comput. Appl. 15(3), 490–502 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Sınır, B.G.: Pseudo-nonlinear dynamic analysis of buckled pipes. J. Fluids Struct. 37(37), 151–170 (2013)

    Article  Google Scholar 

  7. Dai, H.L., Wang, L., Abdelkefi, A., Ni, Q.: On nonlinear behavior and buckling of fluid-transporting nanotubes. Int. J. Eng. Sci. 87, 13–22 (2015)

    Article  Google Scholar 

  8. She, G.-L., Yuan, F.-G., Ren, Y.-R., Xiao, W.-S.: On buckling and postbuckling behavior of nanotubes. Int. J. Eng. Sci. 121, 130–142 (2017). https://doi.org/10.1016/j.ijengsci.2017.09.005

    Article  MathSciNet  MATH  Google Scholar 

  9. Tan, X., Mao, X.-Y., Ding, H., Chen, L.-Q.: Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid. J. Sound Vib. 428, 104–118 (2018). https://doi.org/10.1016/j.jsv.2018.04.041

    Article  Google Scholar 

  10. Tang, Y., Yang, T.: Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Compos. Struct. 185, 393–400 (2018). https://doi.org/10.1016/j.compstruct.2017.11.032

    Article  Google Scholar 

  11. Farajpour, A., Farokhi, H., Ghayesh, M.: Mechanics of fluid-conveying microtubes: Coupled buckling and post-buckling. Vibration 2(1), 102–115 (2019)

    Article  MATH  Google Scholar 

  12. Mohammadi, K., Mostafa Barouti, M., Safarpour, H., Ghadiri, M.: Effect of distributed axial loading on dynamic stability and buckling analysis of a viscoelastic DWCNT conveying viscous fluid flow. J. Braz. Soc. Mech. Sci. Eng. 41(2), 93 (2019)

    Article  Google Scholar 

  13. Nayfeh, A.H., Emam, S.A.: Exact solution and stability of postbuckling configurations of beams. Nonlinear Dyn. 54(4), 395–408 (2008)

    Article  MathSciNet  Google Scholar 

  14. Shafiei, N., Mirjavadi, S.S., Afshari, B.M., Rabby, S., Hamouda, A.M.S.: Nonlinear thermal buckling of axially functionally graded micro and nanobeams. Compos. Struct. 168, 428–439 (2017)

    Article  Google Scholar 

  15. Dai, H.L., Ceballes, S., Abdelkefi, A., Hong, Y.Z., Wang, L.: Exact modes for post-buckling characteristics of nonlocal nanobeams in a longitudinal magnetic field. Appl. Math. Model. 55, 758–775 (2018). https://doi.org/10.1016/j.apm.2017.11.025

    Article  MathSciNet  MATH  Google Scholar 

  16. Ding, H., Li, Y., Chen, L.-Q.: Effects of rotary inertia on sub- and super-critical free vibration of an axially moving beam. Meccanica 53(13), 3233–3249 (2018). https://doi.org/10.1007/s11012-018-0891-6

    Article  MathSciNet  Google Scholar 

  17. Chen, X., Zhang, X., Lu, Y., Li, Y.: Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams. Int. J. Mech. Sci. 151, 424–443 (2019). https://doi.org/10.1016/j.ijmecsci.2018.12.001

    Article  Google Scholar 

  18. Chen, X., Lu, Y., Li, Y.: Free vibration, buckling and dynamic stability of bi-directional FG microbeam with a variable length scale parameter embedded in elastic medium. Appl. Math. Model. 67, 430–448 (2019). https://doi.org/10.1016/j.apm.2018.11.004

    Article  MathSciNet  MATH  Google Scholar 

  19. Hong, Y., Wang, L.: Stability and nonplanar buckling analysis of a current-carrying mircowire in three-dimensional magnetic field. Microsyst. Technol. (2019). https://doi.org/10.1007/s00542-019-04330-5

    Article  Google Scholar 

  20. Wang, Y., Feng, C., Santiuste, C., Zhao, Z., Yang, J.: Buckling and postbuckling of dielectric composite beam reinforced with Graphene Platelets (GPLs). Aerosp. Sci. Technol. (2019). https://doi.org/10.1016/j.ast.2019.05.008

    Article  MATH  Google Scholar 

  21. Farshidianfar, A., Soltani, P.: Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection. Comput. Mater. Sci. 53(1), 105–116 (2012). https://doi.org/10.1016/j.commatsci.2011.08.014

    Article  Google Scholar 

  22. Wang, L., Dai, H.L., Qian, Q.: Dynamics of simply supported fluid-conveying pipes with geometric imperfections. J. Fluids Struct. 29(4), 97–106 (2012)

    Article  Google Scholar 

  23. Dehrouyeh-Semnani, A.M., Nikkhah-Bahrami, M., Yazdi, M.R.H.: On nonlinear stability of fluid-conveying imperfect micropipes. Int. J. Eng. Sci. 120, 254–271 (2017). https://doi.org/10.1016/j.ijengsci.2017.08.004

    Article  MathSciNet  MATH  Google Scholar 

  24. Li, Y.D., Yang, Y.R.: Nonlinear vibration of slightly curved pipe with conveying pulsating fluid. Nonlinear Dyn. 88(4), 2513–2529 (2017)

    Article  Google Scholar 

  25. Owoseni OD, Orolu KO, Oyediran A (2017) Dynamics of slightly curved pipe conveying hot pressurized fluid resting on Linear and Nonlinear Viscoelastic Foundations. J. Vibr. Acoust. Trans. ASME 140(2) (2018)

  26. Czerwiński, A., Łuczko, J.: Non-planar vibrations of slightly curved pipes conveying fluid in simple and combination parametric resonances. J. Sound Vib. 413, 270–290 (2018). https://doi.org/10.1016/j.jsv.2017.10.026

    Article  Google Scholar 

  27. Ghayesh, M.H., Farokhi, H., Farajpour, A.: Chaos in fluid-conveying NSGT nanotubes with geometric imperfections. Appl. Math. Model. (2019). https://doi.org/10.1016/j.apm.2019.04.053

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu, H., Lv, Z., Tang, H.: Nonlinear vibration and instability of functionally graded nanopipes with initial imperfection conveying fluid. Appl. Math. Model. (2019). https://doi.org/10.1016/j.apm.2019.06.011

    Article  MathSciNet  MATH  Google Scholar 

  29. Orolu, K.O., Fashanu, T.A., Oyediran, A.A.: Cusp bifurcation of slightly curved tensioned pipe conveying hot pressurized fluid. J. Vib. Control 25(5), 1109–1121 (2019). https://doi.org/10.1177/1077546318813401

    Article  MathSciNet  Google Scholar 

  30. Farokhi, H., Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory. Int. J. Eng. Sci. 68, 11–23 (2013). https://doi.org/10.1016/j.ijengsci.2013.03.001

    Article  MathSciNet  MATH  Google Scholar 

  31. Farokhi, H., Ghayesh, M.H.: Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams. Int. J. Eng. Sci. 91, 12–33 (2015). https://doi.org/10.1016/j.ijengsci.2015.02.005

    Article  MathSciNet  MATH  Google Scholar 

  32. Dehrouyeh-Semnani, A.M., Mostafaei, H., Nikkhah-Bahrami, M.: Free flexural vibration of geometrically imperfect functionally graded microbeams. Int. J. Eng. Sci. 105, 56–79 (2016)

    Article  MathSciNet  Google Scholar 

  33. Farokhi, H., Ghayesh, M.H.: Size-dependent parametric dynamics of imperfect microbeams. Int. J. Eng. Sci. 99, 39–55 (2016)

    Article  MathSciNet  Google Scholar 

  34. Farokhi, H., Ghayesh, M.H.: Nonlinear resonant response of imperfect extensible Timoshenko microbeams. Int. J. Mech. Mater. Des. 13(1), 43–55 (2017). https://doi.org/10.1007/s10999-015-9316-z

    Article  Google Scholar 

  35. Ghayesh, M.H., Farokhi, H.: Global dynamics of imperfect axially forced microbeams. Int. J. Eng. Sci. 115, 102–116 (2017)

    Article  MathSciNet  Google Scholar 

  36. Chen, X., Li, Y.: Size-dependent post-buckling behaviors of geometrically imperfect microbeams. Mech. Res. Commun. 88, 25–33 (2018). https://doi.org/10.1016/j.mechrescom.2017.12.005

    Article  Google Scholar 

  37. Mohamed, N., Eltaher, M.A., Mohamed, S.A., Seddek, L.F.: Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations. Int. J. Non-Linear Mech. 101, 157–173 (2018). https://doi.org/10.1016/j.ijnonlinmec.2018.02.014

    Article  Google Scholar 

  38. Dodds, H., Runyan, H.: Effect of high-velocity fluid flow on the bending vibrations and static divergence of a simply supported pipe (1965)

  39. Eltaher, M.A., Mohamed, N., Mohamed, S.A., Seddek, L.F.: Periodic and nonperiodic modes on postbuckling and nonlinear vibration of beams attached with nonlinear foundations. Appl. Math. Model. (2019). https://doi.org/10.1016/j.apm.2019.05.026

    Article  MathSciNet  MATH  Google Scholar 

  40. Li, Q., Liu, W., Lu, K., Yue, Z.: Nonlinear parametric vibration of the geometrically imperfect pipe conveying pulsating fluid. Int. J. Appl. Mech. 12(06), 2050064 (2020). https://doi.org/10.1142/S1758825120500647

    Article  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (Grant No. 11802235), National Key Basic Research Program of China (Grant No. 613268) and Aeronautics Power Foundation Program of China (Grant No. 6141B090320).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710129, People’s Republic of China

    Qian Li, Wei Liu, Kuan Lu & Zhufeng Yue

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  1. Qian Li
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Correspondence to Wei Liu.

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Li, Q., Liu, W., Lu, K. et al. Flow-induced buckling statics and dynamics of imperfect pipes. Arch Appl Mech 91, 4553–4569 (2021). https://doi.org/10.1007/s00419-021-02023-y

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