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The effect of nanoparticle in reduction of critical fluid velocity in pipes conveying fluid

  • Ghaitani, M.M. (Department of Mechanical Engineering, Sari Branch, Islamic Azad University) ;
  • Majidian, A. (Department of Mechanical Engineering, Sari Branch, Islamic Azad University) ;
  • Shokri, V. (Department of Mechanical Engineering, Sari Branch, Islamic Azad University)
  • Received : 2019.10.09
  • Accepted : 2019.11.13
  • Published : 2020.01.25

Abstract

This paper deal with the critical fluid velocity response of nanocomposite pipe conveying fluid based on numerical method. The pressure of fluid is obtained based on perturbation method. The motion equations are derived based on classical shell theory, energy method and Hamilton's principle. The shell is reinforced by nanoparticles and the distribution of them are functionally graded (FG). The mixture rule is applied for obtaining the equivalent material properties of the structure. Differential quadrature method (DQM) is utilized for solution of the motion equations in order to obtain the critical fluid velocity. The effects of different parameters such asCNT nanoparticles volume percent, boundary conditions, thickness to radius ratios, length to radius ratios and internal fluid are presented on the critical fluid velocity response structure. The results show that with increasing the CNT nanoparticles, the critical fluid velocity is increased. In addition, FGX distribution of nanoparticles is the best choice for reinforcement.

Keywords

References

  1. Abdoun, T.H., Ha, D., O'Rourke, M., Symans, M., O'Rourke, T., Palmer, M. and Harry, E. (2009), "Factors influencing the behavior of buried pipelines subjected to earthquake faulting", Soil Dyn. Earthq. Eng., 29, 415-427. https://doi.org/10.1016/j.soildyn.2008.04.006.
  2. Alijani, F. and Amabili, M. (2014), "Nonlinear vibrations and multiple resonances of fluid filled arbitrary laminated circular cylindrical shells", Compos. Struct., 108, 951-962. https://doi.org/10.1016/j.compstruct.2013.10.029.
  3. Amabili, M. (2008), Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Cambridge.
  4. Benjamin, T.B. (1961), "Dynamics of a system of articulated pipes conveying fluid", Proc. Royal Soc. A., 261(130), 457-486. https://doi.org/10.1098/rspa.1961.0090.
  5. Brush, O. and Almorth, B. (1975), Buckling of Bars, Plates and Shells, Mc-Graw Hill.
  6. Chan, D.Q., Anh, V.T.T. and Duc, N.D. (2018), "Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells in thermal environments", Acta Mech., 230, 157-178. https://doi.org/10.1007/s00707-018-2282-4.
  7. Chen, W., Shih, B.J., Chen, Y.C., Hung, J.H. and Hwang, H.H. (2002), "Seismic response of natural gas and water pipelines in the Ji-Ji earthquake", Soil Dyn. Earthq. Eng., 22, 1209-1214. https://doi.org/10.1016/S0267-7261(02)00149-5.
  8. Chung, D.N., Dinh, N.N., Hui, D., Duc, N.D., Trung, T.Q. and Chipara, M. (2013), "Investigation of polymeric composite films using modified $TiO_2$ nanoparticles for organic light emitting diodes", J. Current Nanosci., 9, 14-20. https://doi.org/10.2174/157341313805118018.
  9. Dey, T. and Ramachandra, L.S. (2017), "Non-linear vibration analysis of laminated composite circular cylindrical shells", Compos. Struct., 163, 89-100. https://doi.org/10.1016/j.compstruct.2016.12.018.
  10. Duc, N.D. (2014a), Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi.
  11. Duc, N.D. (2014b), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", J. Compos. Struct., 102, 306-314. https://doi.org/10.1016/j.compstruct.2012.11.017.
  12. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. A/Solid., 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004.
  13. Duc, N.D. and Minh, D.K. (2010), "Bending analysis of three-phase polymer composite plates reinforced by glass fibers and Titanium oxide particles", J. Comput. Mater. Sci., 49, 194-198. https://doi.org/10.1016/j.commatsci.2010.04.016.
  14. Duc, N.D., Hadavinia, H., Thu, P.V. and Quan, T.Q. (2015), "Vibration and nonlinear dynamic response of imperfect three-phase polymer nanocomposite panel resting on elastic foundations under hydrodynamic loads", Compos. Struct., 131, 229-237. https://doi.org/10.1016/j.compstruct.2015.05.009.
  15. Duc, N.D., Khoa, N.D. and Thiem, H.T. (2018), "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory", Mech. Adv. Mat. Struct., 25, 1157-1167. https://doi.org/10.1080/15376494.2017.1341581.
  16. Duc, N.D., Quan, T.Q. and Nam, D. (2013), "Nonlinear stability analysis of imperfect three phase polymer composite plates", J. Mech. Compos. Mater., 49, 345-358. ttps://doi.org/10.1007/s11029-013-9352-4.
  17. Frikha, A., Hajlaoui, A., Wali, M. and Dammak, F. (2016), "A new higher order C0 mixed beam element for FGM beams analysis", Compos. Part B., 106, 181-189. https://doi.org/10.1016/j.compositesb.2016.09.024.
  18. Ghavanloo, E. and Fazelzadeh, A. (2011), "Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid", Physica E., 44, 17-24. https://doi.org/10.1016/j.physe.2011.06.024.
  19. GhorbanpourArani, A., Bagheri, M.R., Kolahchi, R. and KhodamiMaraghi, Z. (2013), "Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory", J. Mech. Sci. Tech., 27(9), 2645-2658. https://doi.org/10.1007/s12206-013-0709-3.
  20. Gong, S.W., Lam, K.Y. and Lu, C. (2000), "Structural analysis of a submarine pipeline subjected to underwater shock", Int. J. Pres. Ves. Pip., 77, 417-423. https://doi.org/10.1016/S0308-0161(00)00022-3.
  21. Hajlaoui, A., Chebbi, E., Wali, M. and Dammak, F. (2019a), "Geometrically nonlinear analysis of FGM shells using solid-shell element with parabolic shear strain distribution", Int. J. Mech. Mater. Des., 1-16. https://doi.org/10.1007/s10999-019-09465-x.
  22. Hajlaoui, A., Chebbi, E., Wali, M. and Dammak, F. (2019b), "Buckling analysis of carbon nanotube reinforced FG shells using an efficient solid-shell element based on a modified FSDT", Thin Wall. Struct., 144, 106254. https://doi.org/10.1016/j.tws.2019.106254.
  23. Hajlaoui, A., Chebbi, E., Wali, M. and Dammak, F. (2019c), "Static analysis of carbon nanotube-reinforced FG shells using an efficient solid-shell element with parabolic transverse shear strain", Eng. Comput. https://doi.org/10.1108/EC-02-2019-0075.
  24. Hajlaoui, A., Triki, E., Frikha, A., Wali, M. and Dammak, F. (2017), "Nonlinear dynamics analysis of FGM shell structures with a higher order shear strain enhanced solid-shell element", Latin. Am. J. Solid. Struct., 14, 72-91. http://dx.doi.org/10.1590/1679-78253323.
  25. Housner, G.W. (1952), "Bending vibrations of a pipe line containing flowing fluid", J. Appl. Mech., 19, 205-208. https://doi.org/10.1115/1.4010447
  26. Huang, Y.M., Liu, Y.S., Li, B.H., Li, Y.J. and Yue, Z.F. (2010), "Natural frequency analysis of fluid conveying pipeline with different boundary conditions", Nucl. Eng. Des., 240(3), 461-467. https://doi.org/10.1016/j.nucengdes.2009.11.038.
  27. Inozemtcev, A.S., Korolev, E.V. and Smirnov, V.A. (2017), "Nanoscale modifier as an adhesive for hollow microspheres to increase the strength of high-strength lightweight", Struct., 18(1), 67-74. https://doi.org/10.1002/suco.201500048.
  28. JafarianArani, A and Kolahchi, R. (2016), "Buckling Analysis of embedded columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567.
  29. Kim, D.H., Lee, G.N., Lee, Y. and Lee, I.K. (2015), "Dynamic reliability analysis of offshore wind turbine support structure under earthquake", Wind Struct., 21, 609-623. https://doi.org/10.12989/was.2015.21.6.609.
  30. Kolahchi, R., RabaniBidgoli, M., Beygipoor, G.H. and Fakhar, M.H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Tech., 29, 3669-3677. https://doi.org/10.1007/s12206-015-0811-9.
  31. Lam, K.Y., Zong, Z. and Wang, Q.X. (2003), "Dynamic response of a laminated pipeline on the seabed subjected to underwater shock", Compos. Part B-Eng., 34, 59-66. https://doi.org/10.1016/S1359-8368(02)00072-0.
  32. Lee, U. and Oh, H. (2003), "The spectral element model for pipelines conveying internal steady flow", Eng. Struct., 25, 1045-1055. https://doi.org/10.1016/S0141-0296(03)00047-6.
  33. Lin, W. and Qiao, N. (2008), "Vibration and stability of an axially moving beam immersed in fluid", Int. J. Solid. Struct., 45, 1445-1457. https://doi.org/10.1016/j.ijsolstr.2007.10.015.
  34. Liu, X., Zhang, H., Gu X., Chen, Y., Xia, M. and Wu, K. (2017), "Strain demand prediction method for buried X80 steel pipelines crossing oblique-reverse faults", Earthq. Struct., 12, 321-332. https://doi.org/10.12989/eas.2017.12.3.321.
  35. Liu, Z.G., Liu, Y. and Lu, J. (2012), "Fluid-structure interaction of single flexible cylinder in axial flow", Comput. Fluid., 56, 143-151. https://doi.org/10.1016/j.compfluid.2011.12.003.
  36. Mohammadian, H., Kolahchi, R. and Rabani Bidgoli, M. (2017), "Dynamic response of beams reinforced by $Fe_2O_3$ nanoparticles subjected to magnetic field and earthquake load", Earthq. Struct., 13, 589-598. https://doi.org/10.12989/eas.2017.13.6.589.
  37. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta. Metall. Mater., 21, 571-574. https://doi.org/10.1016/0001-6160(73)90064-3.
  38. Motezaker, M. and Kolahchi, R. (2017), "Seismic response of CNT nanoparticles-reinforced pipes based on DQ and newmark methods", Comput. Concrete, 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745.
  39. Nogueira, A.C. (2012), "Rationally modeling collapse due to bending and external pressure in pipelines", Earthq. Struct., 3, 473-494. https://doi.org/10.12989/eas.2012.3.3_4.473.
  40. Paidoussis, M.P. and Issid, N.T. (1974), "Dynamic stability of pipes conveying fluid", J. Sound Vib., 33, 267-294. https://doi.org/10.1016/S0022-460X(74)80002-7.
  41. RabaniBidgoli, M. and Saeidifar, M. (2017), "Time-dependent buckling analysis of CNT nanoparticles reinforced columns exposed to fire", Comput. Concrete, 20(2), 119-127. https://doi.org/10.12989/cac.2017.20.2.119.
  42. RabaniBidgoli, M., Karimi, M.S. and GhorbanpourArani, A. (2016), "Nonlinear vibration and instability analysis of functionally graded CNT-reinforced cylindrical shells conveying viscous fluid resting on orthotropic Pasternak medium", Mech. Adv. Mater. Struct., 23(7), 819-831. https://doi.org/10.1080/15376494.2015.1029170.
  43. Ray, M.C. and Reddy, J.N. (2013), "Active damping of laminated cylindrical shells conveying fluid using 1-3 piezoelectric composites", Compos. Struct., 98, 261-271. https://doi.org/10.1016/j.compstruct.2012.09.051.
  44. Safari Bilouei, B., Kolahchi, R. and Rabanibidgoli, M. (2016), "Buckling of columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053.
  45. Shamsuddoha, M., Islam, M.M., Aravinthan, T., Manalo, A. and Lau, K.T. (2013), "Effectiveness of using fibre-reinforced polymer composites for underwater steel pipeline repairs", Compos. Struct., 100, 40-54. https://doi.org/10.1016/j.compstruct.2012.12.019.
  46. Sharifi, M., Kolahchi, R. and Rabani Bidgoli, M. (2018), "Dynamic analysis of beams reinforced with $Tio_2$ nano particles under earthquake load", Wind Struct., 26, 1-9. https://doi.org/10.12989/was.2018.26.1.001.
  47. Shokravi, M. (2017), "Vibration analysis of silica nanoparticles-reinforced beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333.
  48. Simsek, M. (2010), "Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load", Compos. Struct., 92, 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008.
  49. Su, Y., Li, J., Wu, C and Li, Z.X. (2016), "Influences of nano-particles on dynamic strength of ultra-high performance", Compos. Part B-Eng., 91, 595-609. https://doi.org/10.1016/j.compositesb.2016.01.044.
  50. Thinh, T.I. and Nguyen, M.C. (2016), "Dynamic stiffness method for free vibration of composite cylindrical shells containing fluid", Appl. Math. Model., 40, 9286-9301. https://doi.org/10.1016/j.apm.2016.06.015.
  51. Yoon, H.I. and Son, I. (2007), "Dynamic response of rotating flexible cantilever fluid with tip mass", Int. J. Mech. Sci., 49, 878-887. https://doi.org/10.1016/j.ijmecsci.2006.11.006.
  52. ZamaniNouri, A. (2017), "Mathematical modeling of pipes reinforced with CNTs conveying fluid for vibration and stability analyses", Comput. Concrete, 19(3), 325-331. https://doi.org/10.12989/cac.2017.19.3.325.
  53. Zhai, H., Wu, Z., Liu, Y. and Yue, Z. (2011), "Dynamic response of pipeline conveying fluid to random excitation", Nucl. Eng. Des., 241, 2744-2749. https://doi.org/10.1016/j.nucengdes.2011.06.024.
  54. Zhou, X.Q., YU, D.Y., Shao, X.Y., Zhang, C.Y. and Wang, S. (2017), "Dynamics characteristic of steady fluid conveying in the periodical partially viscoelastic composite pipeline", Compos. Part B-Eng., 111, 387-408. https://doi.org/10.1016/j.compositesb.2016.11.059.