Structural Engineering and Mechanics

  • 제84권1호
  • /
  • Pages.77-83
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  • 2022
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Direct strength measurement of Timoshenko-beam model: Vibration analysis of double walled carbon nanotubes

  • Ghandourah, Emad (Nuclear Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Thobiani, Faisal Al (Marine Engineering Department, Faculty of Maritime Studies, King Abdulaziz University) ;
  • Hefni, Mohammed (Mining Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Alghamdi, Sami (Electrical and Computer Engineering Department, King Abdulaziz University)
  • 투고 : 2021.06.26
  • 심사 : 2022.08.27
  • 발행 : 2022.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

In the last ten years, many researchers have studied the vibrations of carbon nanotubes using different beam theories. The nano- and micro-scale systems have wavy shape and there is a demand for a powerful tool to mathematically model waviness of those systems. In accordance with the above mentioned lack for the modeling of the waviness of the curved tiny structure, a novel approach is employed by implementing the Timoshenko-beam model. Owing to the small size of the micro beam, these structures are very appropriate for designing small instruments. The vibrations of double walled carbon nanotubes (DWCNTs) are developed using the Timoshenko-beam model in conjunction with the wave propagation approach under support conditions to calculate the fundamental frequencies of DWCNTs. The frequency influence is observed with different parameters. Vibrations of the double walled carbon nanotubes are investigated in order to find their vibrational modes with frequencies. The aspect ratios and half axial wave mode with small length are investigated. It is calculated that these frequencies and ratios are dependent upon the length scale and aspect ratio.

키워드

과제정보

"The authors extend their appreciation to the Deputyship for Research and Innovation, Ministry of Education in Saudi Arabia for funding this research work through the project number IFPIP-839-135-1442" at King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

참고문헌

  1. 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.
  2. 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.
  3. Ansari, R., Hemmatnezhad, M. and Rezapour, J. (2011), "The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions", Curr. Appl. Phys., 11(3), 692-697. https://doi.org/10.1016/j.cap.2010.11.034.
  4. Basirjafari, S., Esmaeilzadeh Khadem, S. and Malekfar, R. (2013), "Validation of shell theory for modeling the radial breathing mode of a single-walled carbon nanotube", Int. J. Eng. Trans. A, 26(4), 447-454.
  5. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., ... & Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., 7(6), 443. https://doi.org/10.12989/anr.2019.7.6.443.
  6. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.
  7. Budiansky, B. (1963), "On the'best'first-order linear shell theory", The Prager Anniversary Volume-Progress in Applied Mechanics.
  8. Chwal, M. (2018), "Nonlocal analysis of natural vibrations of carbon nanotubes", J. Mater. Eng. Perform., 27(11), 6087-6096. https://doi.org/10.1016/j.cma.2004.07.048.
  9. Cirak, F., Ortiz, M. and Pandolfi, A. (2005), "A cohesive approach to thin-shell fracture and fragmentation", Comput. Meth. Appl. Mech. Eng., 194(21-24), 2604-2618. https://doi.org/10.1016/j.cma.2004.07.048
  10. 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.
  11. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene, F. (2019), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., 7(2), 135. https://doi.org/10.12989/anr.2019.7.2.135.
  12. Elishakoff, I. and Pentaras, D. (2009), "Fundamental natural frequencies of double-walled carbon nanotubes", J. Sound Vib., 322(4-5), 652-664. https://doi.org/10.1016/j.jsv.2009.02.037.
  13. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039.
  14. 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.
  15. Eringen, A.C. (2002), "Nonlocal continuum field theories", Science and Business Media, New York.
  16. Fakhrabadi, M.M.S., Rastgoo, A. and Ahmadian, M.T. (2015), "Application of electrostatically actuated carbon nanotubes in nanofluidic and bio-nanofluidic sensors and actuators", Measure., 73, 127-136. https://doi.org/10.1016/j.measurement.2015.05.009.
  17. Fu, Y.M., Hong, J.W. and Wang, X.Q. (2006), "Analysis of nonlinear vibration for embedded carbon nanotubes", J. Sound Vib., 296(4-5), 746-756. https://doi.org/10.1016/j.jsv.2006.02.024.
  18. Hernandez, E., Goze, C., Bemier, P. and Rubio, A. (1998), "Elastic properties of C and BxCyNz composite nanotubes", Phys. Rev. Lett, 80, 4502-505. https://doi.org/10.1103/PhysRevLett.80.4502.
  19. Hussain, M. and Naeem, M.N. (2017), "Vibration analysis of single-walled carbon nanotubes using wave propagation approach", Mech. Sci., 8(1), 155-164. https://doi.org/10.5194/ms-8-155-2017.
  20. Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B: Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  21. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(1), 56-58. https://doi.org/10.1038/354056a0.
  22. Kagimoto, H., Yasuda, Y. and Kawamura, M. (2015), "Mechanisms of ASR surface cracking in a massive concrete cylinder", Adv. Concrete Constr., 3(1), 039. http://doi.org/10.12989/acc.2015.3.1.039.
  23. Kumar, B.R. (2018), "Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube Van der waals forces", Adv. Nano Res., 6(2), 135. https://doi.org/10.12989/anr.2018.6.2.135.
  24. Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-249992. https://doi.org/10.1016/S0020-7683(03)00056-8.
  25. Liew, K.M. and Wang, Q. (2007), "Analysis of wave propagation in carbon nanotubes via elastic shell theories", Int. J. Eng. Sci., 45(2-8), 227-241. https://doi.org/10.1016/j.ijengsci.2007.04.001.
  26. Love, A.E.H. (1888), "The small free vibrations and deformation of a thin elastic shell", Proc. Roy Soc. London Ser. I, 179, 491-546. https://doi.org/10.1098/rsta.1888.0016.
  27. Love, A.E.H. (2013), A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
  28. Markus, S. (1988), "Mechanics of vibrations of cylindrical shells", Amsterdam. https://www.amazon.com/Mechanics-Vibrations-Cylindrical-Studies-Applied/dp/0444989102.
  29. 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.
  30. Qian, D., Wagner, G.J., 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.
  31. Rabczuk, T., Areias, P.M.A. and Belytschko, T. (2007), "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Meth. Eng., 72(5), 524-548. https://doi.org/10.1002/nme.2013.
  32. Rayleigh, L. (1882), "On the equilibrium of liquid conducting masses charged with electricity", London Edinburgh Dublin Philos. Mag. J. Sci., 14(87), 184-186. https://doi.org/10.1080/14786448208628425.
  33. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv. Nano Res., 7, 265-275. https://doi.org/10.12989/anr.2019.7.4.265.
  34. 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.
  35. Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P. (1999), "Ab-initio structural, elastic, and vibrational properties of carbon nanotubes", Phys. Rev. B, 59, 12678-2688. http://doi.org/10.1103/PhysRevB.59.12678.
  36. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated composite plates", Adv. Nano Res., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337.
  37. Soldano, C. (2015), "Hybrid metal-based carbon nanotubes: Novel platform for multifunctional applications", Prog. Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001.
  38. Sosa, E.D., Darlington, TK., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., 2014, Article ID 705687. http://doi.org/10.1155/2014/705687.
  39. Torkaman-Asadi, M.A., Rahmanian, M. and Firouz-Abadi, R.D. (2015), "Free vibrations and stability of high-speed rotating carbon nanotubes partially resting on Winkler foundations", Compos. Struct., 126, 52-61. https://doi.org/10.1016/j.compstruct.2015.02.037.
  40. Vodenitcharova, T. and Zhang, L.C. (2003), "Effective wall thickness of single walled carbon nanotubes", Phy. Rev. B., 68, 165401. https://doi.org/10.1103/PhysRevB.68.165401.
  41. Wang, Q. Varadan, V.K. and Quek, S.T. (2006), "Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models", Phys. Lett. A, 357(2), 130-135. https://doi.org/10.1016/j.physleta.2006.04.026.
  42. Yakobson, B.I., Brabec, C.J. and Bernholc, J. (1996), "Nano-mechanics of carbon tubes: Instabilities beyond linear response", Phy. Rev. Lett., 76, 2511-2514. https://doi.org/10.1103/PhysRevLett.76.2511.
  43. Yakobson, B.I., Campbell, M.P., Brabec, C.J. and Bemholc J. (1997), "High strain rate fracture and C-chain unravelling in carbon nanotubes", Comput. Mater. Sei., 8(4), 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5.
  44. Yoon, J., Ru, C.Q. and Mioduchowski. A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Technol., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.
  45. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. http://doi.org/10.12989/sem.2015.54.4.693.
  46. Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Vibration analysis of thin cylindrical shells using wave propagation approach", J. Sound Vib., 239(3), 397-403. https://doi.org/10.1006/jsvi.2000.3139.