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Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment

  • Xu, Chen (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Jing-Lei, Zhao (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Gui-Lin, She (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Yan, Jing (College of Mechanical and vehicle Engineering, Chongqing University) ;
  • Hua-Yan, Pu (School of Mechatronics Engineering and Automation, Shanghai University) ;
  • Jun, Luo (College of Mechanical and vehicle Engineering, Chongqing University)
  • Received : 2022.05.18
  • Accepted : 2022.11.23
  • Published : 2022.12.10
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Abstract

Fluid-conveying tubes are widely used to transport oil and natural gas in industries. As an advanced composite material, functionally graded carbon nanotube-reinforced composites (FG-CNTRC) have great potential to empower the industry. However, nonlinear free vibration of the FG-CNTRC fluid-conveying pipe has not been attempted in thermal environment. In this paper, the nonlinear free vibration characteristic of functionally graded nanocomposite fluid-conveying pipe reinforced by single-walled carbon nanotubes (SWNTs) in thermal environment is investigated. The SWCNTs gradient distributed in the thickness direction of the pipe forms different reinforcement patterns. The material properties of the FG-CNTRC are estimated by rule of mixture. A higher-order shear deformation theory and Hamilton's variational principle are employed to derive the motion equations incorporating the thermal and fluid effects. A two-step perturbation method is implemented to obtain the closed-form asymptotic solutions for these nonlinear partial differential equations. The nonlinear frequencies under several reinforcement patterns are presented and discussed. We conduct a series of studies aimed at revealing the effects of the flow velocity, the environment temperature, the inner-outer diameter ratio, and the carbon nanotube volume fraction on the nature frequency.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No. 62103065, 61922053 and U2013202), "Shuguang Program" (18SG36) sponsored by Shanghai Education Development Foundation and Shanghai Municipal Education Commission, and China Postdoctoral Science Foundation (No. 2021M700593).

References

  1. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M. A. (2021), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct. Machines, 1-24. http://doi.org/10.1080/15397734.2021.1999263.
  2. Abdollahi, R., Dehghani Firouz-abadi, R. and Rahmanian, M. (2021), "On the stability of rotating pipes conveying fluid in annular liquid medium", J. Sound Vibr., 494. http://doi.org/10.1016/j.jsv.2020.115891.
  3. Abouelregal, A.E., Ersoy, H. and Civalek, O. (2021), "Solution of Moore-Gibson-Thompson Equation of an Unbounded Medium with a Cylindrical Hole", Mathematics, 9. http://doi.org/10.3390/math9131536.
  4. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224, 2185-2201. http://doi.org/10.1007/s00707-013-0883-5.
  5. Akgoz, B. and Civalek, O. (2015), "A novel microstructure-dependent shear deformable beam model", Int. J. Mech. Sci., 99, 10-20. http://doi.org/10.1016/j.ijmecsci.2015.05.003.
  6. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022a), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano Res., 12, 117-137. http://doi.org/10.12989/anr.2022.12.2.117.
  7. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40, 389-404. http://doi.org/10.12989/scs.2021.40.3.389.
  8. Alazwari, M.A., Esen, I., Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022b), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermomagnetic fields and moving load", Adv. Nano Res., 12, 231-251. http://doi.org/10.12989/anr.2022.12.3.231.
  9. Askarian, A.R., Permoon, M.R. and Shakouri, M. (2020), "Vibration analysis of pipes conveying fluid resting on a fractional Kelvin-Voigt viscoelastic foundation with general boundary conditions", Int. J. Mech. Sci., 179. http://doi.org/10.1016/j.ijmecsci.2020.105702.
  10. Babaei, H. (2021), "On frequency response of FG-CNT reinforced composite pipes in thermally pre/post buckled configurations", Compos. Struct., http://doi.org/10.1016/j.compstruct.2021.114467.
  11. Basha, M., Daikh, A.A., Melaibari, A., Wagih, A., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M. A. (2022), "Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates", Steel Compos. Struct., 43, 639-660. http://doi.org/10.12989/scs.2022.43.5.639.
  12. Chen, X., Zhao, J.-L., She, G.-L., Jing, Y., Luo, J. and Pu, H.-Y. (2022), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plu., 137. http://doi.org/10.1140/epjp/s13360-022-03234-0.
  13. Civalek, O., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Mathem. Meth. Appl. Sci., http://doi.org/10.1002/mma.7069.
  14. Civalek, O. and Jalaei, M.H. (2020), "Shear buckling analysis of functionally graded (FG) carbon nanotube reinforced skew plates with different boundary conditions", Aerosp. Sci. Technol., 99. http://doi.org/10.1016/j.ast.2020.105753.
  15. Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Eur. Phys. J. Plu., 135. http://doi.org/10.1140/epjp/s13360-020-00385-w.
  16. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36, 643-656. http://doi.org/10.12989/scs.2020.36.6.643.
  17. Dastjerdi, S., Akgoz, B. and Civalek, O. (2020), "On the effect of viscoelasticity on behavior of gyroscopes", Int. J. Eng. Sci., 149. http://doi.org/10.1016/j.ijengsci.2020.103236.
  18. Ding, H.-X. and She, G.-L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80, 63-72. http://doi.org/10.12989/sem.2021.80.1.063.
  19. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28, 2394-2401. http://doi.org/10.1016/j.matdes.2006.09.022.
  20. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2021), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., http://doi.org/10.1007/s00366-021-01389-5.
  21. Esen, I., Alazwari, M.A., Eltaher, M.A. and Abdelrahman, A.A. (2022), "Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load", Steel Compos. Struct., 42, 805-826. http://doi.org/10.12989/scs.2022.42.6.805.
  22. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39, 315-323. http://doi.org/10.1016/j.commatsci.2006.06.011.
  23. Heshmati, M. (2020), "Influence of an eccentricity imperfection on the stability and vibration behavior of fluid-conveying functionally graded pipes", Ocean Eng., 203. http://doi.org/10.1016/j.oceaneng.2020.107192.
  24. Iijima, S. (1991), "Helical microtubes of graphitic carbon", Nature, 354, 56-58. http://doi.org/10.1038/354056a0.
  25. Jalaei, M.H., Thai, H.T. and Civalek, O. (2022), "On viscoelastic transient response of magnetically imperfect functionally graded nanobeams", Int. J. Eng. Sci., 172. http://doi.org/10.1016/j.ijengsci.2022.103629.
  26. Kanagaraj, S., Varanda, F.R., Zhil'tsova, T.V., Oliveira, M.S.A. and Simoes, J.A.O. (2007), "Mechanical properties of high density polyethylene/carbon nanotube composites", Compos. Sci. Technol., 67, 3071-3077. http://doi.org/10.1016/j.compscitech.2007.04.024.
  27. Khodabakhsh, R., Saidi, A.R. and Bahaadini, R. (2020), "An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects", Appl. Ocean Res., 101. http://doi.org/10.1016/j.apor.2020.102277.
  28. Khosravi, F., Simyari, M., Hosseini, S.A. and Tounsi, A. (2020), "Size dependent axial free and forced vibration of carbon nanotube via different rod models", Adv. Nano Res., 9, 157-172. http://doi.org/10.12989/anr.2020.9.3.157.
  29. Liang, F., Gao, A., Li, X.-F. and Zhu, W.-D. (2021), "Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity", Appl. Math. Model. 95, 320-338. http://doi.org/10.1016/j.apm.2021.02.007.
  30. Liew, K. M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review", Compos. Struct., 120, 90-97. http://doi.org/10.1016/j.compstruct.2014.09.041.
  31. Lu, L., She, G.-L. and Guo, X. (2021a), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199. http://doi.org/10.1016/j.ijmecsci.2021.106428.
  32. Lu, L., Wang, S., Li, M. and Guo, X. (2021b), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272. http://doi.org/10.1016/j.compstruct.2021.114231.
  33. Lu, Z.-Q., Zhang, K.-K., Ding, H. and Chen, L.-Q. (2020), "Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials", Nonlinear Dyn., 100, 1091-1104. http://doi.org/10.1007/s11071-020-05577-8.
  34. Numanoglu, H.M., Ersoy, H., Akgoz, B. and Civalek, O. (2021), "A new eigenvalue problem solver for thermo-mechanical vibration of Timoshenko nanobeams by an innovative nonlocal finite element method", Mathem. Meth. Appl. Sci., 45, 2592-2614. http://doi.org/10.1002/mma.7942.
  35. Odom, T.W., Huang, J.L., Kim, P. and Lieber, C.M. (1998), "Atomic structure and electronic properties of single-walled carbon nanotubes", Nature, 391, 62-64. https://doi.org/10.1038/34145
  36. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2020), "Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method", Aerosp. Sci. Technol., 105. http://doi.org/10.1016/j.ast.2020.105998.
  37. Shahali, P., Haddadpour, H. and Kordkheili, S.A.H. (2020), "Nonlinear dynamics of viscoelastic pipes conveying fluid placed within a uniform external cross flow", Appl. Ocean Res., 94. http://doi.org/10.1016/j.apor.2019.101970.
  38. She, G.-L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Thermal Stresses, 44, 1289-1305. http://doi.org/10.1080/01495739.2021.1974323.
  39. She, G.-L., Liu, H.-B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin-Walled Struct., 160. http://doi.org/10.1016/j.tws.2020.107407.
  40. Shen, H.-S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91, 9-19. http://doi.org/10.1016/j.compstruct.2009.04.026.
  41. Shen, H.-S. and Zhang, C.-L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31, 3403-3411. http://doi.org/10.1016/j.matdes.2010.01.048.
  42. Shirvanimoghaddam, K., Polisetti, B., Dasari, A., Yang, J., Ramakrishna, S. and Naebe, M. (2018), "Thermomechanical performance of cheetah skin carbon nanotube embedded composite: Isothermal and non-isothermal investigation", Polymer, 145, 294-309. http://doi.org/10.1016/j.polymer.2018.04.079.
  43. Tan, X., Ding, H., Sun, J.-Q. and Chen, L.-Q. (2020), "Primary and super-harmonic resonances of Timoshenko pipes conveying high-speed fluid", Ocean Eng., 203. http://doi.org/10.1016/j.oceaneng.2020.107258.
  44. Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. http://doi.org/10.1016/j.commatsci.2013.01.028.
  45. Yang, J., Huang, X.-H. and Shen, H.-S. (2020), "Nonlinear Vibration of Temperature-Dependent FG-CNTRC Laminated Beams with Negative Poisson's Ratio", Int. J. Struct. Stab. Dyn. 20. http://doi.org/10.1142/s0219455420500431.
  46. Zhang, P. and Fu, Y. (2013), "A higher-order beam model for tubes", Eur. J. Mech. A-Solids, 38, 12-19. http://doi.org/10.1016/j.euromechsol.2012.09.009
  47. Zhang, Y. W. and She, G. L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42, 397-405. http://doi.org/10.12989/scs.2022.42.3.397
  48. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38, 293-304. http://doi.org/10.12989/scs.2021.38.3.293.
  49. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H. Y. and Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43, 797-808. http://doi.org/10.12989/scs.2022.43.6.797.
  50. Zhen, Y., Gong, Y. and Tang, Y. (2021), "Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature", Compos. Struct., 268. http://doi.org/10.1016/j.compstruct.2021.113980.
  51. Zhong, J., Fu, Y., Wan, D. and Li, Y. (2016), "Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model", Appl. Math. Model., 40, 7601-7614. http://doi.org/10.1016/j.apm.2016.03.031.
  52. Zhou, K., Ni, Q., Wang, L. and Dai, H.L. (2020), "Planar and non-planar vibrations of a fluid-conveying cantilevered pipe subjected to axial base excitation", Nonlinear Dyn., 99, 2527-2549. http://doi.org/10.1007/s11071-020-05474-0.
  53. Zhu, B., Xu, Q., Li, M. and Li, Y. (2020), "Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation", Compos. Struct., 252. http://doi.org/10.1016/j.compstruct.2020.112672.