Skip to main content
SpringerLink
Log in

Frequency band preservation: pipe design strategy away from resonance

频带禁区: 远离共振的管道设计策略

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, a design strategy to keep a pipe away from resonance by adjusting retaining clips is presented. The pipe natural frequency is within the band of vibration frequencies generated by mechanical operation, which can cause the resonance phenomenon. The resonance of pipes could bring serious disaster to the mechanical operation. Therefore, the band of vibration frequencies generated by the mechanical operation is defined as the preserved frequency band (PFB). The pipe in engineering has been simplified to a multispan pipe conveying fluid. An integral pipe model of a multispan pipe conveying fluid is established by simplifying the retaining clips. The natural frequencies of a pipe with clips are obtained. The resonance range and safety range of pipe length are defined as the natural frequencies inside and outside the PFB, respectively. The absolute safety length and the absolute resonance length with respect to clip number are derived. Moreover, the influence of the clip stiffness and location on the safety range is determined. The results show that the safety range is significantly changed by adjusting the vertical stiffness, torsional stiffness, and location of the clips. Based on the results, a pipe design strategy is proposed to stay away from resonance and make for a smaller number of clips. Subsequently, a design for an aircraft pipe is carried out as an example. As a result of the design, the natural frequencies of the aircraft pipe are kept away from the PFB. In summary, a design strategy is obtained to avoid resonance for pipes by adjusting the clip stiffness and/or location.

摘要

本文介绍了一种通过调整卡箍使得管道避免发生共振的设计策略. 当管道的固有频率在机械设备运作时产生的振动频率范围内, 会引发共振现象, 给机械设备的正常操作带来严重的灾难. 因此, 把机械设备操作产生的振动频率范围定义为频带禁区. 通常, 工程中的管道被简化为多跨输流管道: 通过将卡箍简化为线性和扭转刚度, 建立了多跨输流管道的整体管道模型. 通过采用Galerkin截断方法并应用广义特征值方法, 获得了多跨输流管道的固有频率. 通过对比不同长度的管道固有频率和频带禁区, 定义了管长的安全范围和共振范围分别为频带禁区的外和内, 并且通过分析卡箍的影响推导得出了绝对安全长度和绝对共振长度. 此外, 还确定了卡箍刚度和位置对安全范围的影响. 结果表明, 通过调整卡箍的线性刚度、 扭转刚度和位置, 管道的安全范围会发生显著地变化. 根据这些结果, 提出了一种管道设计策略, 从而避免了管道的共振发生, 并减少了使用卡箍的数量. 最后, 以飞机上的一段管道为例进行了设计, 结果表明: 通过调整卡箍, 管道的固有频率成功地远离了频带禁区, 因而在飞机的运行过程中不会发生共振. 总而言之, 通过调整卡箍的刚度或位置, 可以获得避免多跨输流管道发生共振的设计策略.

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

References

  1. Y. Shi, and S. Li, An inverse modification method for assigning antiresonant frequencies, Appl. Acoust. 170, 107524 (2020).

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Y. Yan, and M. Chai, Sealing failure and fretting fatigue behavior of fittings induced by pipeline vibration, Int. J. Fatigue 136, 105602 (2020).

    Article  Google Scholar 

  4. P. Gao, T. Yu, Y. Zhang, J. Wang, and J. Zhai, Vibration analysis and control technologies of hydraulic pipeline system in aircraft: A review, Chin. J. Aeronaut. 34, 83 (2020).

    Article  Google Scholar 

  5. Z. Mehmood, A. Hameed, A. Javed, and A. Hussain, Analysis of premature failure of aircraft hydraulic pipes, Eng. Fail. Anal. 109, 104356 (2020).

    Article  Google Scholar 

  6. P. Gao, J. Zhai, Y. Yan, Q. Han, F. Qu, and X. Chen, A model reduction approach for the vibration analysis of hydraulic pipeline system in aircraft, Aerosp. Sci. Tech. 49, 144 (2016).

    Article  Google Scholar 

  7. Q. Chai, J. Zeng, H. Ma, K. Li, and Q. Han, A dynamic modeling approach for nonlinear vibration analysis of the L-type pipeline system with clamps, Chin. J. Aeronaut. 33, 3253 (2020).

    Article  Google Scholar 

  8. T. A. El-Sayed, and H. H. El-Mongy, Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method, Appl. Math. Model. 71, 173 (2019).

    Article  MathSciNet  Google Scholar 

  9. J. Lin, Y. Zhao, Q. Zhu, S. Han, H. Ma, and Q. Han, Nonlinear characteristic of clamp loosing in aero-engine pipeline system, IEEE Access 9, 64076 (2021).

    Article  Google Scholar 

  10. Y. Gao, and W. Sun, Inverse identification of the mechanical parameters of a pipeline hoop and analysis of the effect of preload, Front. Mech. Eng. 14, 358 (2019).

    Article  Google Scholar 

  11. Y. Yang, and Y. Zhang, Random vibration response of three-dimensional multi-span hydraulic pipeline system with multipoint base excitations, Thin-Walled Struct. 166, 108124 (2021).

    Article  Google Scholar 

  12. B. Dou, H. Ding, X. Y. Mao, H. R. Feng, and L. Q. Chen, Modeling and parametric studies of retaining clips on pipes, Mech. Syst. Signal Process. 186, 109912 (2023).

    Article  Google Scholar 

  13. M. Li, Q. Xu, X. C. Chen, X. L. Zhang, and Y. H. Li, Modeling and modal analysis of non-uniform multi-span oil-conveying pipes with elastic foundations and attachments, Appl. Math. Model. 88, 661 (2020).

    Article  MathSciNet  Google Scholar 

  14. Q. Guo, J. X. Zhou, and X. L. Guan, Fluid-structure interaction in Z-shaped pipe with different supports, Acta Mech. Sin. 36, 513 (2020).

    Article  MathSciNet  Google Scholar 

  15. L. Zhang, T. Zhang, H. Ouyang, T. Li, and S. Zhang, Receptance-based natural frequency assignment of a real fluid-conveying pipeline system with interval uncertainty, Mech. Syst. Signal Process. 179, 109321 (2022).

    Article  Google Scholar 

  16. G. Tong, Y. Liu, Q. Cheng, J. Dai, Y. Zhao, and Y. Wang, Stability analysis of multi-span aluminum-based functionally graded material fluid-conveying pipe reinforced by carbon nanotubes, Int. J. Pressure Vessels Piping 176, 103971 (2019).

    Article  Google Scholar 

  17. H. B. Wen, Y. Yang, and Y. Li, Study on the stability of multi-span U-shaped pipe conveying fluid with complex constraints, Int. J. Pressure Vessels Piping 203, 104911 (2023).

    Article  Google Scholar 

  18. C. Cai, J. Zhou, K. Wang, Q. Lin, D. Xu, and G. Wen, Quasi-zero-stiffness metamaterial pipe for low-frequency wave attenuation, Eng. Struct. 279, 115580 (2023).

    Article  Google Scholar 

  19. X. Li, W. Li, J. Shi, Q. Li, and S. Wang, Pipelines vibration analysis and control based on clamps’ locations optimization of multi-pump system, Chin. J. Aeronaut. 35, 352 (2022).

    Article  Google Scholar 

  20. M. Iqbal, A. Kumar, M. M. Jaya, and O. S. Bursi, Vibration control of periodically supported pipes employing optimally designed dampers, Int. J. Mech. Sci. 234, 107684 (2022).

    Article  Google Scholar 

  21. L. Zhang, T. Zhang, H. Ouyang, T. Li, and M. You, Natural frequency assignment of a pipeline through structural modification in layout optimization of elastic supports, J. Sound Vib. 561, 117702 (2023).

    Article  Google Scholar 

  22. Y. Yang, Y. Xiang, and C. Gao, Vehicle-SFT-current coupling vibration of multi-span submerged floating tunnel, Part II: comparative analysis of finite difference method and parametric study, Ocean Eng. 249, 110951 (2022).

    Article  Google Scholar 

  23. F. Liang, A. Gao, and X. D. Yang, Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans, Appl. Math. Model. 83, 454 (2020).

    Article  MathSciNet  Google Scholar 

  24. A. Czerwiński, and J. Łuczko, Experimental and numerical study on vibrations of ahelical pipe with fluid flow, J. Sound Vib. 535, 117116 (2022).

    Article  Google Scholar 

  25. X. Tan, X. Y. Mao, H. Ding, and L. Q. Chen, Vibration around nontrivial equilibrium of a supercritical Timoshenko pipe conveying fluid, J. Sound Vib. 428, 104 (2018).

    Article  Google Scholar 

  26. Y. Cao, X. Guo, H. Ma, H. Ge, H. Li, J. Lin, D. Jia, B. Wang, and Y. Ma, Dynamic modelling and natural characteristics analysis of fluid conveying pipeline with connecting hose, Mech. Syst. Signal Process. 193, 110244 (2023).

    Article  Google Scholar 

  27. L. Wang, T. L. Jiang, and H. L. Dai, Three-dimensional dynamics of supported pipes conveying fluid, Acta Mech. Sin. 33, 1065 (2017).

    Article  MathSciNet  Google Scholar 

  28. A. R. Askarian, M. R. Permoon, M. Zahedi, and M. Shakouri, Stability analysis of viscoelastic pipes conveying fluid with different boundary conditions described by fractional Zener model, Appl. Math. Model. 103, 750 (2022).

    Article  MathSciNet  Google Scholar 

  29. Y. Wang, M. Tang, M. Yang, and T. Qin, Three-dimensional dynamics of a cantilevered pipe conveying pulsating fluid, Appl. Math. Model. 114, 502 (2023).

    Article  MathSciNet  Google Scholar 

  30. T. C. Deng, H. Ding, and L. Q. Chen, Critical velocity and supercritical natural frequencies of fluid-conveying pipes with retaining clips, Int. J. Mech. Sci. 222, 107254 (2022).

    Article  Google Scholar 

  31. W. D. Xie, X. F. Gao, and W. H. Xu, Stability and nonlinear vibrations of a flexible pipe parametrically excited by an internal varying flow density, Acta Mech. Sin. 36, 206 (2020).

    Article  MathSciNet  Google Scholar 

  32. A. Xu, Y. Chai, F. Li, and Y. Chen, Nonlinear vortex-induced vibrations of slightly curved pipes conveying fluid in steady and oscillatory flows, Ocean Eng. 270, 113623 (2023).

    Article  Google Scholar 

  33. B. Zhu, X. Zhang, and T. Zhao, Nonlinear planar and non-planar vibrations of viscoelastic fluid-conveying pipes with external and internal resonances, J. Sound Vib. 548, 117558 (2023).

    Article  Google Scholar 

  34. Y. Li, C. Feng, S. Bo, and O. Guiyu, Three-dimensional vibration analysis in extensible pipes conveying fluid with different initial geometrical configurations, Appl. Math. Model. 115, 470 (2023).

    Article  MathSciNet  Google Scholar 

  35. M. Mohammadimehr, and M. Mehrabi, Electro-thermo-mechanical vibration and stability analyses of double-bonded micro composite sandwich piezoelectric tubes conveying fluid flow, Appl. Math. Model. 60, 255 (2018).

    Article  MathSciNet  Google Scholar 

  36. S. Q. Ye, H. Ding, S. Wei, J. C. Ji, and L. Q. Chen, Non-trivial equilibriums and natural frequencies of a slightly curved pipe conveying supercritical fluid, Ocean Eng. 227, 108899 (2021).

    Article  Google Scholar 

  37. K. Zhou, Q. Ni, Z. L. Guo, H. Yan, H. L. Dai, and L. Wang, Nonlinear dynamic analysis of cantilevered pipe conveying fluid with local rigid segment, Nonlinear Dyn. 109, 1571 (2022).

    Article  Google Scholar 

  38. J. Zhou, X. Chang, Z. Xiong, and Y. Li, Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions, Thin-Walled Struct. 179, 109597 (2022).

    Article  Google Scholar 

  39. M. Heshmati, F. Daneshmand, and Y. Amini, Corrugated pipes conveying fluid: Vibration and instability analysis, Ocean Eng. 271, 113507 (2023).

    Article  Google Scholar 

  40. J. R. Yuan, and H. Ding, An out-of-plane vibration model for in-plane curved pipes conveying fluid, Ocean Eng. 271, 113747 (2023).

    Article  Google Scholar 

  41. K. Zhou, H. R. Yi, H. L. Dai, H. Yan, Z. L. Guo, F. R. Xiong, Q. Ni, P. Hagedorn, and L. Wang, Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation, Nonlinear Dyn. 107, 391 (2022).

    Article  Google Scholar 

  42. R. Ebrahimi, and S. Ziaei-Rad, Nonplanar vibration and flutter analysis of vertically spinning cantilevered piezoelectric pipes conveying fluid, Ocean Eng. 261, 112180 (2022).

    Article  Google Scholar 

  43. W. Chen, K. Zhou, L. Wang, and Z. Yin, Geometrically exact model and dynamics of cantilevered curved pipe conveying fluid, J. Sound Vib. 534, 117074 (2022).

    Article  Google Scholar 

  44. A. O. Oyelade, P. J. V. Ponte, and A. A. Oyediran, Dynamic stability of slightly curved tensioned pipe conveying pressurized hot two phase fluid resting on non uniform foundation, Eng. Struct. 286, 116138 (2023).

    Article  Google Scholar 

  45. H. Ghadirian, S. Mohebpour, P. Malekzadeh, and F. Daneshmand, Nonlinear free vibrations and stability analysis of FG-CNTRC pipes conveying fluid based on Timoshenko model, Compos. Struct. 292, 115637 (2022).

    Article  Google Scholar 

  46. Q. Jin, and Y. Ren, Contact dynamics of graphene reinforced composite nanotubes conveying high-speed nanofluid: size-dependence and local/global transient response, Acta Mech. Sin. 39, 122235 (2023).

    Article  MathSciNet  Google Scholar 

  47. B. Zhu, X. Chen, Y. Dong, and Y. Li, Stability analysis of cantilever carbon nanotubes subjected to partially distributed tangential force and viscoelastic foundation, Appl. Math. Model. 73, 190 (2019).

    Article  MathSciNet  Google Scholar 

  48. B. Karami, M. Janghorban, and T. Rabczuk, Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory, Compos. Part B-Eng. 182, 107622 (2020).

    Article  Google Scholar 

  49. B. Zhu, X. C. Chen, Y. Guo, and Y. H. Li, Static and dynamic characteristics of the post-buckling of fluid-conveying porous functionally graded pipes with geometric imperfections, Int. J. Mech. Sci. 189, 105947 (2020).

    Article  Google Scholar 

  50. B. Zhu, Q. Xu, M. Li, and Y. Li, Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation, Compos. Struct. 252, 112672 (2020).

    Article  Google Scholar 

  51. Y. Guo, B. Zhu, B. Yang, and Y. Li, Flow-induced buckling and post-buckling vibration characteristics of composite pipes in thermal environment, Ocean Eng. 243, 110267 (2022).

    Article  Google Scholar 

  52. Q. Yin, X. Wei, H. Nie, and J. Deng, Study on modal characteristics and vibration reduction of an aircraft rotor-stator brake-induced squeal system, Acta Mech. Sin. 36, 1350 (2020).

    Article  Google Scholar 

  53. T. H. Patel, and A. K. Darpe, Experimental investigations on vibration response of misaligned rotors, Mech. Syst. Signal Process. 23, 2236 (2009).

    Article  Google Scholar 

  54. M. H. Ranginkaman, A. Haghighi, and P. J. Lee, Frequency domain modelling of pipe transient flow with the virtual valves method to reduce linearization errors, Mech. Syst. Signal Process. 131, 486 (2019).

    Article  Google Scholar 

  55. X. Tan, H. Ding, and L. Q. Chen, Nonlinear frequencies and forced responses of pipes conveying fluid via a coupled Timoshenko model, J. Sound Vib. 455, 241 (2019).

    Article  Google Scholar 

  56. J. Luo, S. Zhu, and W. Zhai, Exact closed-form solution for free vibration of Euler-Bernoulli and Timoshenko beams with intermediate elastic supports, Int. J. Mech. Sci. 213, 106842 (2022).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Science Funds for Distinguished Young Scholars (Grant No. 12025204), and the Shanghai Municipal Education Commission (Grant No. 2019-01-07-00-09-E00018).

Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Tian-Chang Deng  (邓天昌) & Hu Ding  (丁虎)

  2. Shanghai Institute of Aircraft Mechanics and Control, Shanghai, 200092, China

    Hu Ding  (丁虎)

Authors
  1. Tian-Chang Deng  (邓天昌)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hu Ding  (丁虎)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Author contributions Hu Ding designed the research and proposed the concept. Tian-Chang Deng and Hu Ding wrote the first draft of the manuscript, set-up and processed the investigation. Tian-Chang Deng participated in data collection. Hu Ding helped organize the manuscript. Tian-Chang Deng and Hu Ding revised and edited the final version, reviewed and approved the final version of the article, taking responsibility for its accuracy and integrity. In conclusion, Tian-Chang Deng and Hu Ding have made substantial contributions to the development and completion of this article. Our collaboration and combined expertise have resulted in a comprehensive and valuable piece of research.

Corresponding author

Correspondence to Hu Ding  (丁虎).

Ethics declarations

Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, TC., Ding, H. Frequency band preservation: pipe design strategy away from resonance. Acta Mech. Sin. 40, 523201 (2024). https://doi.org/10.1007/s10409-023-23201-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-023-23201-x

Search

Navigation