Skip to main content
SpringerLink
Log in

Flow-induced internal resonances and mode exchange in horizontal cantilevered pipe conveying fluid (I)

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3:1, 2:1 and 1:1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3:1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Long R H. Experimental and theoretical study of trans-verse vibration of a tube containing flowing fluid[J]. Journal of Applied Mechanics, 1955, 77(1):65–68.

    Google Scholar 

  2. Handelman G H. A note on the transverse vibration of a tube containing flowing fluid[J]. Quarterly of Applied Mathematics, 1955, 13(3):326–330.

    MATH  MathSciNet  Google Scholar 

  3. Naguleswaran S, Williams C J H. Lateral vibrations of a pipe conveying a fluid[J]. Journal of Mechanical Engineering Science, 1968, 10(2):228–238.

    Google Scholar 

  4. Stein R A, Torbiner W M. Vibrations of pipes containing flowing fluids[J]. Journal of Applied Mechanics, 1970, 37(6):906–916.

    MATH  Google Scholar 

  5. Païdoussis M P, Laithier B E. Dynamics of Timoshenko beams conveying fluid[J]. Journal of Mechanical Engineering Science, 1976, 18(2):210–220.

    Google Scholar 

  6. Païdoussis M P, Luu T P, Laithier B E. Dynamics of finite-length tubular beams conveying fluid[J]. Journal of Sound and Vibration, 1986, 106(2):311–331.

    Article  Google Scholar 

  7. Lee U, Pak C H, Hong S C. The dynamics of piping system with internal unsteady flow[J]. Journal of Sound and Vibration, 1995, 180(2):297–311.

    Article  Google Scholar 

  8. Holmes P J. Bifurcations to divergence and flutter in flow-induced oscillations: a finite-dimensional analysis[J]. Journal of Sound and Vibration, 1977, 53(4):471–503.

    Article  MATH  MathSciNet  Google Scholar 

  9. Rousselet J, Hermann G. Dynamic behaviour of continuous cantilevered pipes conveying fluid near critical velocities[J]. Journal of Applied Mechanics, 1981, 48(6):943–947.

    Article  Google Scholar 

  10. Païdoussis M P, Li G X. Pipes conveying fluid: a model dynamical problem[J]. Journal of Fluid and Structures, 1993, 7(2):137–204.

    Article  Google Scholar 

  11. Huang Yuying, Zhou Shizhi, Xu Jian, Qian Qin, Li Lin. Advances and trends of nonlinear dynamics of pipes conveyingfluid[J]. Advances in Mechanics, 1998, 28(1):30–42 (in Chinese).

    Google Scholar 

  12. Xu Jian, Yang Qianbiao. Recent development on models and nonlinear dynamics of pipes conveying fluid[J]. Advances in Mechanics, 2004, 34(2):1–13 (in Chinese).

    MATH  Google Scholar 

  13. Semler C, Li X, Païdoussis M P. The non-linear equations of motion of pipes conveying fluid[J]. Journal of Sound and Vibration, 1994, 169(3):577–599.

    Article  MATH  Google Scholar 

  14. Païdoussis M P. Fluid-Structure Interactions: Slender Structures and Axial Flow[M]. Academic Press, San Diego, 1998, 415–430.

    Google Scholar 

  15. Ryu S U, Sugiyama Y, Ryu B J. Eigenvalue branches and modes for flutter of cantileverd pipes conveying fluid[J]. Computers and Structures, 2002, 80(14/15):1231–1241.

    Article  Google Scholar 

  16. Seyranian A P. Collision of eigenvalues in linear oscillatory systems[J]. PMM-Journal of Applied Mathematics and Mechanics, 1994, 58(5):805–813.

    Article  Google Scholar 

  17. Xu Jian, Chung Kwowwai, Chan Henry Shuiying. Co-dimension 2 bifurcation and chaos in cantilevered pipe conveying time varying fluid with three-to-one in internal resonances[J]. Acta Mechanics Solid Sinica, 2003, 6(3), 245–255.

    Article  Google Scholar 

  18. Xu Jian, Yang Qianbiao. Flow-induced internal resonances and mode exchange in horizontal cantilevered pipe conveying fluid (II)[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(7):943–951.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, P. R. China

    Xu Jian Doctor  (徐鉴) (Professor) & Yang Qiao-biao  (杨前彪)

Authors
  1. Xu Jian Doctor  (徐鉴)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Qiao-biao  (杨前彪)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xu Jian Doctor  (徐鉴).

Additional information

Communicated by LIU Zeng-rong

Project supported by the National Natural Science Foundation of China (No.10472083) and the National Natural Science Key Foundation of China (No.10532050)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, J., Yang, Qb. Flow-induced internal resonances and mode exchange in horizontal cantilevered pipe conveying fluid (I). Appl Math Mech 27, 935–941 (2006). https://doi.org/10.1007/s10483-006-0709-z

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-006-0709-z

Key words

Chinese Library Classification

2000 Mathematics Subject Classification

Search

Navigation