DOI QR코드

DOI QR Code

Service ability design of vibrating chiral SWCNTs: Validation and parametric study

  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed R. Ali (Faculty of Engineering and Technology, Future University in Egypt New Cairo) ;
  • Abdelhakim Benslimane (Laboratoire de Mecanique Materiaux et Energetique (L2ME), Departement Genie Mecanique, Faculte de Technologie, Universite de Bejaia) ;
  • Humaira Sharif (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Muhammad Nawaz Naeem (Department of Mathematics, Govt. College University Faisalabad) ;
  • Imene Harbaoui (Department of Chemical Engineering, College of Engineering, King Khalid University) ;
  • Sofiene Helaili (Carthage University, Tunisia Polytechnic School, LASMAP (LR03ES06)) ;
  • Aqib Majeed (Department of Mathematics, The University of Faisalabad, Sargodha Road, University Town Faisalabad) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University)
  • 투고 : 2023.05.07
  • 심사 : 2023.06.12
  • 발행 : 2023.10.25

초록

This paper provides the free vibrations of chiral carbon nanotubes. The governing equations of Flügge theory is considered for vibration frequencies of chiral single walled carbon nanotubes. The solution of frequency equation is obtained from a novel model for better representation of stubby and short vibration characteristics of chiral tubes with clamped-clamped and clamped-simply supported end conditions. For the harmonic response of this tube, the model displacement function is adopted. The variational approach Rayleigh-Ritz method with kinetic and strain energies are used. The Lagragian function is differentiated with respect to unknown functions. The frequency equation is written in compact form to solve with MATLAB software. The frequencies of chiral SWCNTs for first ten aspect ratios as small level are investigated. The results shown as for decreasing the aspect rations, the frequencies are increases. The presented results of this model are verified with experimental and numerical results, which found as an excellent agreement.

키워드

과제정보

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P. 2/34/44.

참고문헌

  1. Ansari, R. and Arash, B. (2013), "Nonlocal Flugge shell model for vibrations of double-walled carbon nanotubes with different boundary conditions", J. Appl. Mech., 80(2), 021006. https://doi.org/10.1115/1.4007432.
  2. Ansari, R. and Rouhi, H. (2015), "Nonlocal Flugge shell model for the axial buckling of single-walled carbon nanotubes: An analytical approach", Int. J. Nano Dimens., 6(5), 453-462. https://doi.org/10.7508/ijnd.2015.05.002.
  3. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with nano-fiber reinforced polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.6.1053.
  4. Chalak, H.D., Zenkour, A.M. and Garg, A. (2021), "Free vibration and modal stress analysis of FG-CNTRC beams under hygrothermal conditions using zigzag theory", Mech. Based Des. Struct. Mach., 51(8), 4709-4730. https://doi.org/10.1080/15397734.2021.1977659.
  5. Del Rosario, R.C. and Smith, R.C. (1997), "Spline approximation of thin shell dynamics", Int. J. Numer. Method. Eng., 20, 2807-2840. https://ntrs.nasa.gov/citations/19960022271. https://doi.org/10.1002/(SICI)1097-0207(19970815)40:15<2807::AID-NME192>3.0.CO;2-H
  6. Ehyaei, J. and Daman, M. (2017), "Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection", Adv. Nano Res., 5(2), 179-192. https://doi.org/10.12989/anr.2017.5.2.179.
  7. Garg, A., Chalak, H.D., Belarbi, M.O., Zenkour, A.M. and Sahoo, R. (2021), "Estimation of carbon nanotubes and their applications as reinforcing composite materials-An engineering review", Compos. Struct., 272, 114234. https://doi.org/10.1016/j.compstruct.2021.114234.
  8. Garg, A., Chalak, H.D., Zenkour, A.M., Belarbi, M.O. and Sahoo, R. (2022a), "Bending and free vibration analysis of symmetric and unsymmetric functionally graded CNT reinforced sandwich beams containing softcore", Thin Wall. Struct., 170, 108626. https://doi.org/10.1016/j.tws.2021.108626.
  9. Garg, A., Mukhopadhyay, T., Chalak, H.D., Belarbi, M.O., Li, L. and Sahoo, R. (2022b), "Multiscale bending and free vibration analyses of functionally graded graphene platelet/fiber composite beams", Steel Compos. Struct., 44(5), 707-720. https://doi.org/10.12989/scs.2022.44.5.707.
  10. Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431.
  11. Gupta, S.S., Bosco, F.G. and Batra, R.C. (2010), "Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration", Comput. Mater. Sci., 47(4), 1049-1059. https://doi.org/10.1016/j.commatsci.2009.12.007.
  12. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0.
  13. Jena, S.K., Chakraverty, S., Malikan, M. and Tornabene, F. (2021), "Stability analysis of single-walled carbon nanotubes embedded in winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory", Mech. Based Des. Struct. Mach., 49(4), 581-595. https://doi.org/10.1080/15397734.2019.1698437.
  14. Jorio, A., Saito, R., Hafner, J.H., Lieber, C.M., Hunter, D.M., McClure, T. and Dresselhaus, M.S. (2001), "Structural (n, m) determination of isolated single-wall carbon nanotubes by resonant Raman scattering", Phys. Rev. Lett., 86(6), 1118. https://doi.org/10.1103/PhysRevLett.86.1118.
  15. Kiani, K. (2014), "Vibration and instability of a single-walled carbon nanotube in a three dimensional magnetic field", J. Phys. Chem. Solid., 75(1), 15-22. https://doi.org/10.1016/j.jpcs.2013.07.022.
  16. Kim, P., Shi, L., Majumdar, A. and McEuen, P.L. (2001), "Thermal transport measurements of individual multi-walled nanotubes", Phys. Rev. Lett., 87(21), 2155021-2155024. https://doi.org/10.1103/PhysRevLett.87.215502.
  17. Lal, A. and Markad, K. (2018), "Deflection and stress behaviour of multi-walled carbon nanotube reinforced laminated composite beams", Comput. Concrete, 22(6), 501-514. https://doi.org/10.12989/cac.2018.22.6.501.
  18. Lee, H.L. and Chang, W.J. (2009), "Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory", J. Phys.: Condens. Matt., 21(11), 115302. https://doi.org/10.1088/0953-8984/21/11/115302.
  19. Lei, X.W., Natsuki, T., Shi, J.X. and Ni, Q.Q. (2012), "Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model", Compos. Part B: Eng., 43(1), 64-69. https://doi.org/10.1016/j.compositesb.2011.04.032.
  20. Leissa, A.W. (1973), Vibration of Shells, Scientific and Technical Information Office, National Aeronautics and Space Administration, Washington D.C., USA.
  21. Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-2499. https://doi.org/10.1016/S0020-7683(03)00056-8.
  22. Loghman, A., Arani, A.G. and Barzoki, A.A.M. (2017), "Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates", Comput. Concrete, 19(6), 677-687. https://doi.org/10.12989/cac.2017.19.6.677.
  23. Lordi, V. and Yao. N. (1998), "Young's modulus of single-walled carbon nanotubes", J. Appl. Phys., 84, 1939-1943. https://doi.org/10.1063/1.368323.
  24. Mahdavi, M.H., Jiang, L.Y. and Sun, X. (2011), "Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix", Phys. E: Low Dimens. Syst. Nanostruct., 43(10), 1813-1819. https://doi.org/10.1016/j.physe.2011.06.017.
  25. Meirovitch, L. (2002), Fundamentals of Vibrations, McGraw-Hill, New York City, NY, USA.
  26. Mousavi, M., Mohammadimehr, M. and Rostami, R. (2019), "Analytical solution for buckling analysis of micro sandwich hollow circular plate", Comput. Concrete, 24(3), 185-192. https://doi.org/10.12989/cac.2019.24.3.185.
  27. Pantano, A., Parks, D.M. and Boyce, M.C. (2004), "Mechanics of deformation of single-and multi-wall carbon nanotubes", J. Mech. Phys. Solid., 52(4), 789-821. https://doi.org/10.1016/j.jmps.2003.08.004.
  28. Rouhi. H., Bazdid-Vahdati, M. and Ansari, R. (2015), "Rayleigh-Ritz vibrational analysis of multi-walled carbon nanotubes based on the nonlocal Flugge shell theory", J. Compos., 2015, 1-12. https://doi.org/10.1155/2015/750392.
  29. Sayin, E. and Calayir, Y. (2015), "Comparison of linear and non-linear earthquake response of masonry walls", Comput. Concrete, 16(1), 17-35. https://doi.org/10.12989/cac.2015.16.1.017.
  30. Simsek, M. (2010), "Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory", Physica E, 43, 182-191. https://doi.org/10.1016/j.physe.2010.07.003.
  31. 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.
  32. Treacy, M.J., Ebbesen, T.W. and Gibson, J.M. (1996), "Exceptionally high Young's modulus observed for individual carbon nanotubes", Nature, 381(6584), 678-680. https://doi.org/10.1038/381678a0.
  33. Wang, C.Y. and Zhang, L.C. (2007), "Modeling the free vibration of single-walled carbon nanotubes", 5 th Australasian Congress on Applied Mechanics, Brisbane, Australia, December.
  34. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2005), "Terahertz vibration of short carbon nanotubes modeled as Timoshenko beams", J. Appl. Mech., 72(1), 10-17. https://doi.org/10.1115/1.1795814.
  35. Zamani, A., Kolahchi, R. and Bidgoli, M.R. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concrete, 20(6), 671-682. https://doi.org/10.12989/cac.2017.20.6.671.
  36. Zhang, C.L. and Shen, H.S. (2008), "Predicting the elastic properties of double-walled carbon nanotubes by molecular dynamics simulation", J. Phys. D: Appl. Phys., 41(5), 055404. https://doi.org/10.1088/0022-3727/41/5/055404.
  37. Zhang, Y.Q., Liu, G.R. and Wang, J.S. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys. Rev. B, 70(20), 205430. https://doi.org/10.1016/j.physleta.2006.04.026.