Advances in concrete construction

  • 제13권6호
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  • Pages.451-459
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  • 2022
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  • 2287-5301(pISSN)
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  • 2287-531X(eISSN)
테크노프레스 (Techno-Press)
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Size dependent dynamic bending nonlocal response of armchair and chiral SWCNTs based on Flügge model

  • Hussain, Muzamal (Department of Mathematics, Government College University Faisalabad)
  • 투고 : 2021.11.25
  • 심사 : 2022.05.24
  • 발행 : 2022.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In present study, the nonlocal Flügge shell model based is utilized to investigate the vibration characteristics of armchair and chiral single-walled carbon nanotubes with impact of small-scale effect subjected to two boundary supports. The wave propagation approach is employed to determine eigen frequencies for armchair and chiral tubes. The fundamental frequencies scrutinized with assorted aspect ratios by varying the bending rigidity. The raised in value of nonlocal parameter reduces the corresponding fundamental frequency. It is investigated with higher aspect ratio, the boundary conditions have a momentous influence on vibration of CNT. It is concluded that frequencies would increase by increasing of the bending rigidity. Solutions of the frequency equation have determined by writing in MATLAB coding.

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참고문헌

  1. Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dyn., 17(03), 1750033. https://doi.org/10.1142/S021945541750033X.
  2. Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(07), 1750100. https://doi.org/10.1142/S1758825117501009.
  3. Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39. https://doi.org/10.12989/anr.2018.6.1.039.
  4. Akbas, S.D. (2018b), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219. https://doi.org/10.12989/anr.2018.6.3.219.
  5. Alibeigloo, A. and Shaban, M. (2013), "Free vibration analysis of carbon nanotubes by using three-dimensional theory of elasticity", Acta Mechanica, 224(7), 1415-1427. https://doi.org/10.1007/s00707-013-0817-2.
  6. Alijani, M. and Bidgoli, M.R. (2018), "Agglomerated SiO2 nanoparticles reinforced-concrete foundations based on higher order shear deformation theory: Vibration analysis", Adv. Concrete Constr., 6(6), 585. https://doi.org/10.12989/acc.2018.6.6.585.
  7. 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.
  8. 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.
  9. 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.
  10. Ansari, R., Sahmani, S. and Rouhi, H. (2011), "Rayleigh-Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions", Phys. Lett. A, 375, 1255-1263. https://doi.org/10.1016/j.physleta.2011.01.046.
  11. Bocko, J. and Lengvarsky, P. (2014), "Vibration of single-walled carbon nanotubes by using nonlocal theory", Am. J. Mech. Eng., 2, 195-198. https://doi.org/10.12691/ajme-2-7-5.
  12. Civalek, O., Demir, C. and Akgoz, B. (2009), "Static analysis of single-walled carbon nanotubes (SWCNT) based on Eringen's nonlocal elasticity theory", Int. J. Eng. Appl. Sci. (IJEAS), 2, 47-56.
  13. Das, S.L., Mandal, T. and Gupta, S.S. (2013), "Inextensional vibration of zig-zag single-walled carbon nanotubes using nonlocal elasticity theories", Int. J. Solid. Struct., 50(18), 2792-2797. https://doi.org/10.1016/j.ijsolstr.2013.04.019.
  14. Demir, A. D., and Livaoglu, R. (2019), "The role of slenderness on the seismic behavior of ground-supported cylindrical silos", Adv. Concrete Constr., 7(2), 65. https://doi.org/10.12989/acc.2019.7.2.065.
  15. Demir, C. and Civalek, O. (2016), "Nonlocal finite element formulation for vibration", Int. J. Eng. Appl. Sci. (IJEAS), 8, 109-117. https://doi.org/10.24107/ijeas.252149.
  16. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface-waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  17. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer-Verlag.
  18. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  19. Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solid., 41(12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N.
  20. 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.
  21. Hu, Y.G., Liew, K.M. and Wang, Q. (2012), "Modeling of vibrations of carbon nanotubes", Procedia Eng., 31, 343-347. https://doi.org/10.1016/j.proeng.2012.01.1034.
  22. Jorio, A., Saito, R., Hafner, J.H., Lieber, C.M., Hunter, D.M., McClure, T., ... & Dresselhaus, M.S. (2001). "Structural (n,m) Determination of Isolated Single-Wall Carbon Nanotubes by Resonant RamanScattering", Phys. Rev. Lett., 86(6), 1118-1121. https://doi.org/10.1103/PhysRevLett.86.1118.
  23. Kagimoto, H., Yasuda, Y. and Kawamura, M. (2015), "Mechanisms of ASR surface cracking in a massive concrete cylinder", Adv. Concrete Constr., 3(1), 39. https://doi.org/10.12989/acc.2015.3.1.039.
  24. Karami, B. and Janghorban, M. (2019), "A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams", Thin Wall. Struct., 143, 106227. https://doi.org/10.1016/j.tws.2019.106227.
  25. Karami, B. and Janghorban, M. (2020), "On the mechanics of functionally graded nanoshells", Int. J. Eng. Sci., 153, 103309. https://doi.org/10.1016/j.ijengsci.2020.103309.
  26. Karami, B. and Shahsavari, D. (2019), "Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers", Smart Struct. Syst., 23(3), 215-225. https://doi.org/10.12989/sss.2019.23.3.215.
  27. Karami, B., Shahsavari, D., Janghorban, M., Dimitri, R. and Tornabene, F. (2019), "Wave propagation of porous nanoshells", Nanomater., 9, 22. https://doi.org/10.3390/nano9010022
  28. Mesbah, H. A., and Benzaid, R. (2017)", Damage-based stress-strain model of RC cylinders wrapped with CFRP composites", Adv. Concrete Constr., 5(5), 539. https://doi.org/10.12989/acc.2017.5.5.539.
  29. Mindlin, R.D. and Tiersten, H. (1962). Effects of Couple-Stresses in Linear Elasticity, Columbia Univ New York.
  30. Murmu, T. and Pradhan, S.C. (2009), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Physica E, 41, 1232-1239. https://doi.org/10.1016/j.physe.2009.02.004.
  31. Narendar, S. and Gopalakrishnan, S. (2011), "Nonlocal wave propagation in rotating nanotube", Result. Phys., 1, 17-25. https://doi.org/10.1016/j.rinp.2011.06.002.
  32. 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. http://doi.org/10.12989/anr.2016.4.1.031.
  33. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004.
  34. Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103(2), 023511. https://doi.org/10.1063/1.2833431.
  35. Samadvand, H. and Dehestani, M. (2020), "A stress-function variational approach toward CFRP-concrete interfacial stresses in bonded joints", Adv. Concrete Constr., 9(1), 43-54. https://doi.org/10.12989/acc.2020.9.1.043.
  36. Soltani, P., Kassaei, A., Taherian, M.M. and Farshidianfar, A, (2012), "Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models", Int. J. Adv. Struct. Eng., 4(1), 3. https://doi.org/10.1186/2008-6695-4-3.
  37. Soltani, P., Saberian, J. and Bahramian, R. (2016), "Nonlinear vibration analysis of single-walled carbon nanotube with shell model based on the nonlocal elasticity theory", J. Comput. Nonlin. Dyn., 11(1), 011002. https://doi.org/10.1115/1.4030753.
  38. Swain, A., Roy, T. and Nanda, B.K. (2013), "Vibration behavior of single-walled carbon nanotube using finite element", Int. J. Theor. Appl. Res. Mech, Eng., 2, 129-133A.
  39. Tahouneh, V., Naei, M.H. and Mashhadi, M.M. (2020), "Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches", Steel Compos. Struct., 34(2), 261-277. https://doi.org/10.12989/scs.2020.34.2.261.
  40. Toupin, R.A. (1964), "Theory of elasticity with couple stresses", Arch. Ration. Mech. Anal., 17, 85-112. https://doi.org/10.1007/BF00253050.
  41. Tserpes, K.I. and Papanikos, P. (2005), "Finite element modeling of single-walled carbon nanotubes", Compos. Part B: Eng., 36, 468-477. https://doi.org/10.1016/j.compositesb.2004.10.003.
  42. Wang, C.Y. and Zhang, L.C. (2007), "Modeling the free vibration of single-walled carbon nanotubes", 5th Australasian Congress on Applied Mechanics, ACAM, Brisbane, Australia.
  43. Wu, C.P. and Lin, C.C. (2020), "Static analysis of multiple graphene sheet systems in cylindrical bending and resting on an elastic medium", Struct. Eng. Mech., 75(1), 109-122. https://doi.org/10.12989/sem.2020.75.1.109.
  44. Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Physica E: Low Dimens. Syst. Nanostruct., 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035.
  45. Yayli, M.O. (2013), "Torsion of nonlocal bars with equilateral triangle cross sections", J. Comput. Theor. Nanosci., 10, 376-379. https://doi.org/10.1166/jctn.2013.2707.
  46. Zhang, Y.Y., Wang, C.M. and Tan, V.B.C. (2009), "Assessment of Timoshenko beam models for vibrational behavior of singlewalled carbon nanotubes using molecular dynamics", Adv. Appl. Math. Mech., 1(1), 89-106.