Skip to main content
Log in

Flexural Wave Bandgap Property of a Periodic Pipe with Axial Load and Hydro-Pressure

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

A periodical composite material pipe is proposed based on the Bragg scattering mechanism of phononic crystals (PCs). The band gap (BG) properties of the flexural wave in this PC pipe under axial load and hydro-pressure are calculated using the transfer matrix (TM) method. The frequency response functions (FRFs) of the PC pipe under axial load and hydro-pressure are calculated using the finite element approach, and the mechanism is elucidated to illustrate the phenomenon. The results show that axial load and hydro-pressure and their combination all have a great influence on the flexural vibration properties. This research offers theoretical support for research on PC pipes with complex conditions and is of great significance in solving the problem of high pressure.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Koo GH, Park YS. Vibration analysis of a 3-dimensional piping system conveying fluid by wave approach. Int J Pres Ves Pip. 1996;67:249–56.

    Article  Google Scholar 

  2. Koo GH, Park YS. Vibration reduction by using periodic supports in a piping system. J Sound Vib. 1998;210:53–68.

    Article  Google Scholar 

  3. Kang MG. The influence of rotary inertia of concentrated masses on the natural vibrations of fluid-conveying pipes. J Sound Vib. 2000;238:179–87.

    Article  Google Scholar 

  4. Lee SY, Mote CD. A generalized treatment of the energetic of translating continua, part II: beams and fluid conveying pipes. J Sound Vib. 1997;204:735–53.

    Article  Google Scholar 

  5. Chen SS. Vibration and stability of a uniformly curved tube conveying fluid. JASA. 1972;51:223–32.

    Article  MATH  Google Scholar 

  6. Doll RW, Mote CD. On the dynamic analysis of curved and twisted cylinders transporting fluids. J Press Vess Trans ASME. 1976;98:143–50.

    Article  Google Scholar 

  7. Gopalakrishnan S, Martin M, Doyle JF. A matrix methodology for spectral analysis of wave propagation in multiple connected timoshenko beams. J Sound Vib. 1992;158:11–24.

    Article  MATH  Google Scholar 

  8. Liu Z, Zhang X, Mao Y, Zhu YY, Yang Z, Chan CT, Sheng P. Locally resonant sonic materials. Science. 2000;289:1734–6.

    Article  Google Scholar 

  9. Kushwaha MS. Acoustic band structure of periodic elastic composites. Phys Rev Lett. 1993;71:2022–5.

    Article  Google Scholar 

  10. Kushwaha MS, Halevi P, Martinez G, Dobrzynski L. Theory of acoustic band structure of periodic elastic composite. Phys Rev B. 1994;49:2313–22.

    Article  Google Scholar 

  11. Wen JH, Wang G, Yu DL, Zhao HG, Liu YZ. Theoretical and experimental investigation of flexural wave propagation in straight beams with periodic structures: application to a vibration isolation structure. J Appl Phys. 2005;97(11):114907.

    Article  Google Scholar 

  12. Yu DL, Liu YZ, Zhao HG, Wang G, Qiu J. Flexural vibration band gaps in Euler-Bernoulli beams with two-degree-of-freedom locally resonant structures. Phys Rev B. 2006;73:064301.

    Article  Google Scholar 

  13. Yu DL, Wen JH, Zhao HG, Liu YZ, Wen XS. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid. J Sound Vib. 2008;318:193–205.

    Article  Google Scholar 

  14. Shen HJ, Wen JH, Yu DL, Wen XS. Flexural vibration property of periodic pipe system conveying fluid base on Timoshenko beam equation. Acta Phys Sin. 2009;58:8357–63.

    Google Scholar 

  15. Yu DL, Wen JH, Shen HJ, Wen XS. Flexural vibration band gaps in periodic pipe system conveying fluid with external loads. In: Proceedings of the 16th international congress on sound and vibration Kraków, Poland, 2009; p. 5–9.

  16. Sorokin SV, Ershova OA. Analysis of the energy transmission in compound cylindrical shell with and without internal heavy fluid loading by boundary integral equations and by Floquet theory. J Sound Vib. 2006;291:81–99.

    Article  Google Scholar 

  17. Shen HJ, Wen JH, Yu DL, Wen XS. Control of flexural vibration in a periodic pipe conveying fluid based on a Bragg scattering mechanism coupled with a locally resonant mechanism. In: The 2011 IEEE international conference on mechatronics and automation, Beijing, 2011; p. 1700–1705.

  18. Wen JH, Shen HJ, Yu DL, Wen XS. Theoretical and experimental investigation of flexural wave propagating in a periodic pipe with fluid-filled loading. Chin Phys Lett. 2010;27:114301.

    Article  Google Scholar 

  19. Sorokin SV, Olhoff N, Ershov OA. Analysis of the energy transmission in spatial piping systems with heavy internal fluid loading. J Sound Vib. 2008;310:1141–66.

    Article  Google Scholar 

  20. Qian Q, Wang L, Ni Q. Instability of simply supported pipes conveying fluid under thermal loads. Mech Res Commun. 2009;36:413–7.

    Article  MATH  Google Scholar 

  21. Wei ZD, Li BR, Du JM, Yang G. Theoretical and experimental investigation of flexural vibration transfer properties of high-pressure periodic pipe. Chin Phys Lett. 2016;33:1–4.

    Google Scholar 

  22. Lee U, Oh H. The spectral element model for pipelines conveying internal steady flow. Eng Struct. 2003;25:1045–55.

    Article  Google Scholar 

  23. Lee U, Jang I, Go H. Stability and dynamic analysis of oil pipelines by using spectral element method. J Loss Prevent Proc. 2009;6(22):873–8.

    Article  Google Scholar 

  24. Wen XS. Photonic/phononic crystals theory and thechnology. Beijing: Science Press; 2006.

    Google Scholar 

  25. Banerjee JR. Free vibration of axially loaded composite timoshenko beams using the dynamic stiffness matrix method. Comput Struct. 1998;69:197–208.

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51275519 and 11372346).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jihong Wen.

Ethics declarations

Conflicts of interest

The authors declare 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

Liu, J., Yu, D., Zhang, Z. et al. Flexural Wave Bandgap Property of a Periodic Pipe with Axial Load and Hydro-Pressure. Acta Mech. Solida Sin. 32, 173–185 (2019). https://doi.org/10.1007/s10338-018-0070-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-018-0070-2

Keywords

Navigation