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Impacts of surface irregularity on vibration analysis of single-walled carbon nanotubes based on Donnell thin shell theory

  • Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Sciences and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Althobaiti, Saad (Department of Sciences and Technology, Ranyah University Collage, Taif University) ;
  • Yahia, I.S. (Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University) ;
  • Mohammed, Ibtisam M.O. (Department of Mathematics, Al_ukhwa College of science and Art, Al-Baha University) ;
  • Hussin, Amira M. (Department of Mathematics, Al-Aflaj College of Sciences and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Mohamed, Abdel-Baset A. (Department of Mathematics, Al-Aflaj College of Sciences and Humanities, Prince Sattam bin Abdulaziz University)
  • 투고 : 2020.06.30
  • 심사 : 2022.02.21
  • 발행 : 2022.05.25

초록

The present work is an attempt to study the vibration analysis of the single-walled carbon nanotubes (SWCNTs) under the effect of the surface irregularity using Donnell's model. The surface irregularity represented by the parabolic form. According to Donnell's model and three-dimensional elasticity theory, a novel governing equations and its solution are derived and matched with the case of no irregularity effects. To understand the reaction of the nanotube to the irregularity effects in terms of natural frequency, the numerical calculations are done. The results obtained could provide a better representation of the vibration behavior of an irregular single-walled carbon nanotube, where the aspect ratio (L/d) and surface irregularity all have a significant impact on the natural frequency of vibrating SWCNTs. Furthermore, the findings of surface irregularity effects on vibration SWCNT can be utilized to forecast and prevent the phenomena of resonance of single-walled carbon nanotubes.

키워드

과제정보

This research is supported by Taif University Researchers Supporting Project number (TURSP-2020/305), Taif University, Taif, Saudi Arabia. Also, the authors express their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a research group program under grant number R.G.P.2/112/41. The authors express their appreciation to the Deputyship for Research & Innovation, Ministry of Education, in Saudi Arabia, for funding this research work through the project number: (IFP-KKU-2020/10).

참고문헌

  1. Abuhimd, H., Uddin, G.M., Zeid, A., Jung, Y.J. and Kamarthi, S. (2013), "Chemical vapor deposition-grown vertically aligned single walled carbon nanotubes length assurance", Int. J. Adv. Manuf. Tech., 64(1-4), 545-553. https://doi.org/10.1007/s00170-012-4426-3.
  2. Ajri, M. and Fakhrabadi, M.M.S. (2018), "Nonlinear free vibration of viscoelastic nanoplates based on modified couple stress theory", J. Comput. Appl. Mech., 49(1), 44-53. https://doi.org/10.22059/JCAMECH.2018.228477.129.
  3. Arghavan, S. and Singh, A. (2011), "On the vibrations of single-walled carbon nanotubes", J. Sound Vib., 330(13), 3102-3122. https://doi.org/10.1016/j.jsv.2011.01.032.
  4. Avouris, P., Appenzeller, J., Martel, R. and Wind, S.J. (2003), "Carbon nanotube electronics", Proc. IEEE, 91(11), 1772-1784. https://doi.org/10.1109/JPROC.2003.818338.
  5. Baughman, R.H., Zakhidov, A.A. and de Heer, W.A. (2002), "Carbon nanotubes-the route toward applications", Science, 297(5582), 787-792. https://doi.org/10.1126/science.1060928/
  6. Belhadj, A., Boukhalfa, A. and Belalia, S.A. (2017), "Free vibration analysis of a rotating nanoshaft based SWCNT", Eur. Phys. J. Plus, 132, 513. https://doi.org/10.1140/epjp/i2017-11783-2.
  7. Choi, W.B., Bae, E., Kang, D., Chae, S., Cheong, B. and Ko, J. (2004), "Aligned carbon nanotubes for nanoelectronics", Nanotechnology, 15(10), S512-S516. https://doi.org/10.1088/0957-4484/15/10/003
  8. Chowdhury, R., Wang, C., Adhikari, S. (2010), "Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries", J. Phys. D Appl. Phys., 43, 085405. https://doi.org/10.1088/0022-3727/43/8/085405
  9. Chuen, J. (2017), "Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect", J. Nanomater., 11(5700),1-6. https://doi.org/10.1155/2017/6142927,1-6.
  10. Collins, P.G. and Avouris, P. (2000), "Nanotubes for electronics", Sci. Am., 283(6), 62-69. https://doi.org/10.1038/scientificamerican1200-62
  11. Dai, H.J. (2002), "Carbon nanotubes: Opportunities and challenges", Surface Sci., 500(1-3), 218-241. https://doi.org/10.1016/S0039-6028(01)01558-8.
  12. Ghavanloo, E. and Fazelzadeh, S.A. (2012), "Effects of the growth time and the thickness of the buffer layer on the quality of the carbon nanotubes", Appl. Math. Model., 36, 4988-5000. https://doi.org/10.1155/2017/6142927.
  13. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  14. Ebrahimi, F. and Farazmandnia, N. (2018), "Vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in thermal environment", Adv. Aircr. Spacecr. Sci., 5(1), 107-128. https://doi.org/10.12989/aas.2018.5.1.107.
  15. Foroutan K., Ahmadi H. and Carrera E. (2019), "Nonlinear vibration of imperfect FG-CNTRC cylindrical panels under external pressure in the thermal environment", Compos. Struct., 227, 111310. https://doi.org/10.1016/j.compstruct.2019.111310.
  16. Foroutan K., Carrera E. and Ahmadi H. (2021), "Nonlinear hygrothermal vibration and buckling analysis of imperfect FG-CNTRC cylindrical panels embedded in viscoelastic foundations", Eur. J. Mech. A Solids, 85, 104107. https://doi.org/10.1016/j.euromechsol.2020.104107.
  17. He, X.Q., Eisenberger, M. and Liew, K.M. (2006), "The effect of van der waals interaction modelling on the vibration characteristics of multiwalled carbon nanotubes", J. Appl. Phys., 100(12), 124317. https://doi.org/10.1063/1.2399331.
  18. Hussain, M., Naeem, M.N., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Adv., 7(4), 045114. https://doi.org/10.1063/1.4979112.
  19. Iijima S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0.
  20. Khan, R., Khan, M.I., Almesfer, M.K., Elkhaleefa A., Ali, I.H., Ullah, A., Rahman, N., Khan, M.S., Khan, A.A. and Khan, A. (2022), "The structural and dilute magnetic properties of (Co, Li) co-doped-ZnO semiconductor nanoparticles", MRS Commun., 1-6. https://doi.org/10.1557/s43579-022-00153-0.
  21. Liu, J., Fan, S.S. and Dai, H.J. (2004), "Recent advances in methods of forming carbon nanotubes", MRS Bull., 29(4), 244-250. https://doi.org/10.1557/mrs2004.75.
  22. Liu, R. and Wang, L. (2015), "Coupling between flexural modes in free vibration of single-walled carbon nanotubes", AIP Adv., 5(12), 127110. https://doi.org/10.1063/1.4937743.
  23. Preethi, K., Raghu, P., Rajagopal, A. and Reddy, J. (2018), "Nonlocal nonlinear bending and free vibration analysis of a rotating laminated nano cantilever beam", Mech. Adv. Mater. Struct., 25(5), 439-450. https://doi.org/10.1080/15376494.2016.1278062.
  24. Qian, D., Wagner, J.G., Liu, W.K., Yu, M.F. and Ruoff, R.S. (2002) "Mechanics of carbon nanotubes", Appl. Mech. Rev., 55(6), 495-533. https://doi.org/10.1115/1.1490129.
  25. Rajasekaran, S. and Khaniki, H.B. (2018), "Free vibration analysis of bi-directional functionally graded single/multi-cracked beams", Int. J. Mech. Sci., 144, 341-356. https://doi.org/10.1016/j.ijmecsci.2018.06.004.
  26. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., 4(1), 31-44. https://doi.org/10.12989/anr.2016.4.1.031.
  27. Selim, M.M. (2007), "Static deformation of an irregular initially stressed medium", Appl. Math. Comput., 188(2), 1274-1284. https://doi.org/10.1016/j.amc.2006.11.003.
  28. Selim, M.M. (2010), "Torsional vibration of carbon nanotubes under initial compression stress", Brazil. J. Phys., 40(3), 283-287. https://doi.org/10.1590/S0103-97332010000300004
  29. Selim, M.M. (2011), "Vibrational analysis of initially stressed carbon nanotubes", Acta Phys. Pol. A, 119(6), 778-782. https://doi.org/10.12693/APhysPolA.119.778
  30. Selim, M.M. (2020a), "Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes", Physica Scripta, 95(11), 115218. https://doi.org/10.1088/1402-4896/abc0c4
  31. Selim, M.M. (2020b), "Propagation of longitudinal waves in a single-walled carbon nanotube under thermoelastic damping", J. Micro Nano Lett., 15(11), 717-722. https://doi.org/10.1049/mnl.2019.0801
  32. Selim, M.M. (2021), "Torsional vibration of irregular single-walled carbon nanotube incorporating compressive initial stress effects", J. Mech., 37, 260-269. https://doi.org/10.1093/jom/ufab002.
  33. Selim, M.M and Ahmed, M.K. (2006), "Propagation and attenuation of seismic body waves in dissipative medium under initial and couple stresses", Appl. Math. Comput., 182(2), 1264-1274. https://doi.org/10.1016/j.amc.2006.05.005.
  34. Selim, M.M., Abe, S. and Harigaya, K. (2009), "Effects of initial compression stress on wave propagation in carbon nanotubes", Eur. Phys. J. B, 69(4), 523-528. https://doi.org/10.1140/epjb/e2009-00184-5.
  35. Selim M.M. and Nofal, T.A. (2021), "A mathematical model of torsional vibrations of SWCNTs incorporating surface irregularity effects", Physica Scripta, 96(5), 055709. https://doi.org/10.1088/1402-4896/abecfc
  36. Shaban, M. and Alibeigloo, A. (2014), "Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity", Lat. Am. J. Solid Struct., 11, 2122-2140. https://doi.org/10.1590/S1679-78252014001200002.
  37. Strozzi, M., Manevitch, L.I., Pellicano, F.,Smirnov, V.V. and Shepelev, D.S.(2014), "Low-frequency linear vibrations of single-walled carbon nanotubes: Analytical and numerical models", J. Sound Vib., 333(13), 2936-2957. https://doi.org/10.1016/j.jsv.2014.01.016
  38. Tsukagoshi, K., Yoneya, N., Uryu, S., Aoyagi, Y., Kanda, A. and Ootuka Y. (2002), "Carbon nanotube devices for electronics", Physica B, 323(1-4), 107-114. https://doi.org/10.1016/S0921-4526(02)00993-6.
  39. Thostenson, E.T. Ren, Z. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: A review", Compos. Sci. Technol., 61(13), 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X.
  40. Ullah, A., Alzahrani, E.O., Shah, Z., Ayaz, M. and Zhang, S.I. (2019a), "Nanofluids thin film flow of Reiner-Philippoff fluid over an unstable stretching surface with brownian motion and thermophoresis effects", Coatings, 9(1), 21. https://doi.org/10.3390/coatings9010021.
  41. Ullah, A., Shah, Z., Kumam, P., Ayaz, M., Islam, S. and Jameel, M. (2019b), "Viscoelastic MHD nanofluid thin film flow over an unsteady vertical stretching sheet with entropy generation", Processes, 7(5), 262. https://doi.org/10.3390/pr7050262.
  42. Ullah, A., Hafeez, A., Mashwani, W.K., Kumam, W., Kumam, P. and Ayaz, M. (2020), "Non-linear thermal radiations and mass transfer analysis on the processes of magnetite carreau fluid flowing past a permeable stretching/shrinking surface under cross diffusion and hall effect", Coatings, 10(6), 523. https://doi.org/10.3390/coatings10060523.
  43. Wang, X., Jiang, Q., Xu, W., Cai, W., Inoue, Y. and Zhu, Y. (2013), "Effect of carbon nanotube length on thermal, electrical and mechanical properties of CNT/ bismaleimide composites", Carbon, 53, 145-152. https://doi.org/10.1016/j.carbon.2012.10.041.
  44. Xu, K.Y., Aifantis, E.C. and Yan, Y.H. (2008), "Vibrations of double-walled carbon nanotubes with different boundary conditions between inner and outer tubes", J. Appl. Phys., 75(2), 021013. https://doi.org/10.1115/1.2793133.
  45. Yi, X., Li, B. and Wang, Z. (2019), "Vibration analysis of fluid conveying carbon nanotubes based on nonlocal timoshenko beam theory by spectral element method", Nanomaterials, 9(12), 1780. https://doi.org/10.3390/nano9121780.
  46. Zargaripoor, A. and Bahrami, A. (2018), "Free vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach", J. Comput. Appl. Mech., 49(1), 102-124. https://doi.org/10.22059/JCAMECH.2018.249468.227.
  47. Zhang, Y.Y., Wang, C.M. and Tan, V.B.C. (2009), "Assessment of Timoshenko beam models for vibration behavior of single-walled carbon nanotubes using molecular dynamics", Adv. Appl. Math. Mech., 1(1), 1-18.