Skip to main content
SpringerLink
Log in

Dynamics of fluid-conveying piping system containing a short threaded joint

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The dynamics of a cantilevered fluid-conveying straight piping system composed of a left pipe, a right pipe and a short threaded joint implemented intermediately is investigated. First of all, the flow-induced equation of motion is deduced with the consideration of rotatory inertia as well as flexural stiffness of the joint, where the joint is treated as a segment of pipe according to the principle of equivalent substitution and a regulatory factor is introduced to represent the reduction of flexural stiffness at the joint. Secondly, DTM-Galerkin (Galerkin’s method whose shape functions are derived by differential transformation) is employed to discretize the above equation of motion, and the eigenfunction for calculating the piping system’s natural frequency is obtained. Finally, influences of some vital parameters including regulatory factor, length of the left pipe and rotatory inertia of the joint on the piping system’s dynamics are studied under given conditions. The research proposes an equivalent method to study the influence of short threaded joint on the pipe dynamics, which has reference meaning on the experimental research about the impact of threaded joint on pipe dynamics, especially in curve fitting when studying the dynamic characteristics of pipes, and can be radiated to study other connection forms in piping system.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Abbreviations

d i :

Inner radius of two pipes and the equivalent joint

d o :

Outer radius of two pipes

D o :

Outer radius of the equivalent joint

w :

Lateral displacement

x :

Horizontal coordinate

t :

Time

L 1 :

Length of the left pipe

L 2 :

Total length of the left pipe and the joint

L :

Total length of the whole piping system

E p :

Elastic modulus of two pipes

ρ p :

Density of two pipes

A p :

Cross-section area of two pipes, \(A_{{\text{p}}} = \pi (d_{{\text{o}}}^{2} - d_{{\text{i}}}^{2} )/4\)

m p :

Mass per unit length of two pipes, \(m_{{\text{p}}} = \rho_{{\text{p}}} A_{{\text{p}}}\)

I p :

Cross-section moment of inertia of two pipes, \(I_{{\text{p}}} = \pi (d_{{\text{o}}}^{4} - d_{{\text{i}}}^{4} )/64\)

E j :

Elastic modulus of the equivalent joint

ρ j :

Density of the equivalent joint

A j :

Cross-section area of the equivalent joint, \(A_{{\text{j}}} = \pi (D_{{\text{o}}}^{2} - d_{{\text{i}}}^{2} )/4\)

m j :

Mass per unit length of the equivalent joint, \(m_{{\text{j}}} = \rho_{{\text{j}}} A_{{\text{j}}}\)

I j :

Cross-section moment of inertia of the equivalent joint, \(I_{{\text{j}}} = \pi (D_{{\text{o}}}^{4} - d_{{\text{i}}}^{4} )/64\)

J j :

Rotatory inertia per unit length of the equivalent joint

ρ f :

Density of fluid

A f :

Cross-section area of fluid, \(A_{{\text{f}}} = \pi d_{{\text{i}}}^{2} /4\)

m f :

Mass per unit length of fluid, \(m_{{\text{f}}} = \rho_{{\text{f}}} A_{{\text{f}}}\)

U :

Cross-section average flow velocity

References

  1. Wang YK, Tang M, Yang M, Qin T (2023) Three-dimensional dynamics of a cantilevered pipe conveying pulsating fluid. Appl Math Model 114:502–524

    Article  MathSciNet  MATH  Google Scholar 

  2. Ma YQ, You YX, Chen K, Hu LL, Feng AC (2023) Application of harmonic differential quadrature (HDQ) method for vibration analysis of pipes conveying fluid. Appl Math Comput 439:127613

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhao LY, Yang XW, Wang JX, Chai YJ, Li YM, Wang CM (2023) Improved frequency-domain Spectral Element Method for vibration analysis of nonuniform pipe conveying fluid. Thin Wall Struct 182:110254

    Article  Google Scholar 

  4. Liang F, Chen Y, Kou HJ, Qian Y (2023) Hybrid Bragg-locally resonant bandgap behaviors of a new class of motional two-dimensional meta-structure. Eur J Mech A-Solid 97:104832

    Article  MathSciNet  MATH  Google Scholar 

  5. Mirhashemi S, Saeidiha M, Ahmadi H (2023) Dynamics of a harmonically excited nonlinear pipe conveying fluid equipped with a local nonlinear energy sink. Commun Nonlinear Sci 118:107035

    Article  MathSciNet  MATH  Google Scholar 

  6. Oyelade AO, Ehigie JO, Oyediran AA (2021) Nonlinear forced vibrations of a slightly curved nanotube conveying fluid based on the nonlocal strain gradient elasticity theory. Microfluid Nanofluid 25:95

    Article  Google Scholar 

  7. Dou B, Ding H, Mao XY, Feng HR, Chen LQ (2023) Modeling and parametric studies of retaining clips on pipes. Mech Syst Signal Pr 186:109912

    Article  Google Scholar 

  8. Zhang Y, Sun W, Ma HW, Ji WH, Ma H (2023) Semi-analytical modeling and vibration analysis for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps. Eur J Mech A-Solid 97:104797

    Article  MathSciNet  MATH  Google Scholar 

  9. Ding XM, Luan LB, Zheng CJ, Zhou W (2017) Influence of the second-order effect of axial load on lateral dynamic response of a pipe pile in saturated soil layer. Soil Dyn Earthq Eng 103:86–94

    Article  Google Scholar 

  10. Li SJ, Liu GM, Kong WT (2014) Vibration analysis of pipes conveying fluid by transfer matrix method. Nucl Eng Des 266:78–88

    Article  Google Scholar 

  11. Zhao QL, Sun ZL (2018) Flow-induced vibration of curved pipe conveying fluid by a new transfer matrix method. Eng Appl Comp Fluid 12(1):780–790

    Google Scholar 

  12. Reza E, Saeed ZR (2022) Nonplanar vibration and flutter analysis of vertically spinning cantilevered piezoelectric pipes conveying fluid. Ocean Eng 261:112180

    Article  Google Scholar 

  13. Guo Y, Li JA, Zhu B, Li YH (2022) Flow-induced instability and bifurcation in cantilevered composite double-pipe systems. Ocean Eng 258:111825

    Article  Google Scholar 

  14. Lu ZQ, Chen J, Ding H, Chen LQ (2022) Energy harvesting of a fluid-conveying piezoelectric pipe. Appl Math Model 107:165–181

    Article  MathSciNet  MATH  Google Scholar 

  15. Hu JY, Zhu WD (2018) Vibration analysis of a fluid-conveying curved pipe with an arbitrary undeformed configuration. Appl Math Model 64:624–642

    Article  MathSciNet  MATH  Google Scholar 

  16. Luo YY, Tang M, Ni Q, Wang YK, Wang L (2016) Nonlinear vibration of a loosely supported curved pipe conveying pulsating fluid under principal parametric resonance. Acta Mech Solida Sin 29(5):468–478

    Article  Google Scholar 

  17. Wang L, Ni Q (2008) In-plane vibration analyses of curved pipes conveying fluid using the generalized differential quadrature rule. Comput Struct 86:133–139

    Article  Google Scholar 

  18. Li YD, Yang YR (2014) Forced vibration of pipe conveying fluid by the Green function method. Arch Appl Mech 84:1811–1823

    Article  Google Scholar 

  19. Zhao X, Chen B, Li YH, Zhu WD, Nkiegaing FJ, Shao YB (2020) Forced vibration analysis of Timoshenko double-beam system under compressive axial load by means of Green’s functions. J Sound Vib 464:115001

    Article  Google Scholar 

  20. Ni Q, Zhang ZL, Wang L (2011) Application of the differential transformation method to vibration analysis of pipes conveying fluid. Appl Math Comput 217:7028–7038

    Article  MathSciNet  MATH  Google Scholar 

  21. Païdoussis MP (2008) The canonical problem of the fluid-conveying pipe and radiation of the knowledge gained to other dynamics problems across Applied Mechanics. J Sound Vib 310:462–492

    Article  Google Scholar 

  22. Païdoussis MP, Li GX (1993) Pipes conveying fluid: a model dynamical problem. J Fluid Struct 7:137–204

    Article  Google Scholar 

  23. Guo CQ, Zhang CH, Païdoussis MP (2010) Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles. J Fluid Struct 26:793–803

    Article  Google Scholar 

  24. Tang Y, Yang T (2018) Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material. Compos Struct 185:393–400

    Article  Google Scholar 

  25. Tang Y, Yang TZ, Fang B (2018) Fractional dynamics of fluid-conveying pipes made of polymer-like materials. Acta Mech Solida Sin 31:243–258

    Article  Google Scholar 

  26. Tang Y, Zhen Y, Fang B (2018) Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid. Appl Math Model 56:123–136

    Article  MathSciNet  MATH  Google Scholar 

  27. Misra AK, Païdoussis MP, Van KS (1988) On the dynamics of curved pipes transporting fluid, Part I: inextensible theory. J Fluid Struct 2:221–244

    Article  MATH  Google Scholar 

  28. Misra AK, Païdoussis MP, Van KS (1988) On the dynamics of curved pipes transporting fluid, Part II: extensible theory. J Fluid Struct 2:245–261

    Article  MATH  Google Scholar 

  29. Zhao QL, Sun ZL (2017) In-plane forced vibration of curved pipe conveying fluid by Green function method. Appl Math Mech-Engl 38(10):1397–1414

    Article  MathSciNet  MATH  Google Scholar 

  30. Łuczko J, Czerwiński A (2019) Three-dimensional dynamics of curved pipes conveying fluid. J Fluid Struct 91:102704

    Article  Google Scholar 

  31. Czerwiński A, Łuczko J (2021) Nonlinear vibrations of planar curved pipes conveying fluid. J Sound Vib 501:116054

    Article  Google Scholar 

  32. Zhu B, Guo Y, Chen B, Li YH (2022) Nonlinear nonplanar dynamics of porous functionally graded pipes conveying fluid. Commun Nonlinear Sci 117:106907

    Article  MathSciNet  MATH  Google Scholar 

  33. Guo X, Gao P, Ma H, Li H, Wang B, Han Q, Wen B (2023) Vibration characteristics analysis of fluid-conveying pipes concurrently subjected to base excitation and pulsation excitation. Mech Syst Signal Pr 189:110086

    Article  Google Scholar 

  34. Wang Y, Hu Z, Wang L, Qin T, Yang M, Ni Q (2022) Stability analysis of a hybrid flexible-rigid pipe conveying fluid. Acta Mech Sinica-Prc 38:521375

    Article  MathSciNet  Google Scholar 

  35. Cao YH, Liu GM, Hu Z (2023) Vibration calculation of pipeline systems with arbitrary branches by the hybrid energy transfer matrix method. Thin Wall Struct 183:110442

    Article  Google Scholar 

  36. Zhao QL, Liu W, Yu WW, Cai FH (2023) Dynamics of a fluid-conveying pipe by a hybrid method combining differential transformation and Galerkin discretization. Iran J Sci Tech-Trans Mech Eng. https://doi.org/10.1007/s40997-023-00680-8

    Article  Google Scholar 

  37. Faal RT, Derakhshan D (2011) Flow-induced vibration of pipeline on elastic support. Proc Eng 14:2986–2993

    Article  Google Scholar 

  38. Sato K, Saito H, Otomi K (1978) The parametric response of a horizontal beam carrying a concentrated mass under gravity. J Appl Mech 45:643–648

    Article  MATH  Google Scholar 

  39. Malik M, Dang HH (1998) Vibration analysis of continuous system by differential transformation. Appl Math Comput 96:17–26

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the General Project of Basic Science (Natural Science) Research in Colleges and Universities of Jiangsu Province (No. 22KJD130001); the Changzhou Science and Technology Plan Project (No. CJ20220017); Research Science and Technology Project of Special Equipment Safety Supervision Inspection Institute of Jiangsu Province (No. KJ(Y) 2023031) and the Changzhou University Higher Vocational Education Research Project (No. CDGZ2019010). The authors want to thank the anonymous referees for their valuable suggestions and comments.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Changzhou Vocational Institute of Mechatronic Technology, Changzhou, 213164, China

    Qianli Zhao, Wei Liu, Fuhai Cai, Yedi Chen & Wenwu Yu

Authors
  1. Qianli Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuhai Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yedi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wenwu Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qianli Zhao.

Ethics declarations

Conflict of interest

None of the authors have any financial or scientific conflicts of interest with regard to the research described in this manuscript.

Additional information

Technical Editor Samuel da Silva.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, Q., Liu, W., Cai, F. et al. Dynamics of fluid-conveying piping system containing a short threaded joint. J Braz. Soc. Mech. Sci. Eng. 45, 636 (2023). https://doi.org/10.1007/s40430-023-04547-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-023-04547-6

Keywords

Search

Navigation