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.
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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.
Koo GH, Park YS. Vibration reduction by using periodic supports in a piping system. J Sound Vib. 1998;210:53–68.
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.
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.
Chen SS. Vibration and stability of a uniformly curved tube conveying fluid. JASA. 1972;51:223–32.
Doll RW, Mote CD. On the dynamic analysis of curved and twisted cylinders transporting fluids. J Press Vess Trans ASME. 1976;98:143–50.
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.
Liu Z, Zhang X, Mao Y, Zhu YY, Yang Z, Chan CT, Sheng P. Locally resonant sonic materials. Science. 2000;289:1734–6.
Kushwaha MS. Acoustic band structure of periodic elastic composites. Phys Rev Lett. 1993;71:2022–5.
Kushwaha MS, Halevi P, Martinez G, Dobrzynski L. Theory of acoustic band structure of periodic elastic composite. Phys Rev B. 1994;49:2313–22.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Qian Q, Wang L, Ni Q. Instability of simply supported pipes conveying fluid under thermal loads. Mech Res Commun. 2009;36:413–7.
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.
Lee U, Oh H. The spectral element model for pipelines conveying internal steady flow. Eng Struct. 2003;25:1045–55.
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.
Wen XS. Photonic/phononic crystals theory and thechnology. Beijing: Science Press; 2006.
Banerjee JR. Free vibration of axially loaded composite timoshenko beams using the dynamic stiffness matrix method. Comput Struct. 1998;69:197–208.
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 51275519 and 11372346).
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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
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DOI: https://doi.org/10.1007/s10338-018-0070-2