Computers and Concrete

  • 제30권4호
  • /
  • Pages.269-276
  • /
  • 2022
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effect of dimensionless nonlocal parameter: Vibration of double-walled CNTs

  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed Amine (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Ayed, Hamdi (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Alghamdi, Sami (Electrical and Computer Engineering Department, King Abdulaziz University) ;
  • Bhutto, Javed Khan (Electrical Engineering Department, College of Engineering, King Khalid University) ;
  • Mahmoud, S.R. (GRC Department, Faculty of Applied Studies, King Abdulaziz University) ;
  • Tounsi, Abdelouahed (FL (Yonsei Frontier Lab), Yonsei University)
  • 투고 : 2022.03.17
  • 심사 : 2022.08.25
  • 발행 : 2022.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, frequency vibrations of double-walled carbon nanotubes (CNTs) has been investigated based upon nonlocal elastic theory. The inference of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. An innovational nonlocal model to examine the scale effect on vibrational behavior of armchair, zigzag and chiral of double-walled CNTs. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of dimensionless nonlocal parameter has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

키워드

과제정보

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University (KKU) for funding this work through the Research Group Program Under the Grant Number: (R.G.P.2/91/43).

참고문헌

  1. Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. http://doi.org/10.12989/sem.2020.76.3.413.
  2. 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.
  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. Asrari, R., Ebrahimi, F. and Kheirikhah, M.M. (2020), "On scale-dependent stability analysis of functionally graded magneto-electro-thermo-elastic cylindrical nanoshells", Struct. Eng. Mech., 75(6), 659-674. http://doi.org/10.12989/sem.2020.75.6.659.
  5. 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.
  6. 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. http://doi.org/10.12989/cac.2016.18.5.1053.
  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/10.1007/s11665-018-3673-3.
  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. 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.
  11. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Science and Business Media, New York.
  12. 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.
  13. Farazin, A., Mohammadimehr, M. and Ghorbanpour-Arani, A. (2021), "Simulation of different carbon structures on significant mechanical and physical properties based on MDs method", Struct. Eng. Mech., 78(6), 691-702. http://doi.org/10.12989/sem.2021.78.6.691.
  14. Fattahi, A.M., Safaei, B., Qin, Z. and Chu, F. (2021), "Experimental studies on elastic properties of high density polyethylene-multi walled carbon nanotube nanocomposites", Steel Compos. Struct., 38(2), 177-187. http://doi.org/10.12989/scs.2021.38.2.177.
  15. 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.
  16. 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. http://doi.org/10.12989/cac.2018.21.4.431.
  17. 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.
  18. Hussain, M. and Naeem, M.N. (2019b), "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.
  19. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(1), 56-58. https://doi.org/10.1038/354056a0.
  20. 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. http://doi.org/10.12989/cac.2018.22.6.501.
  21. Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-249992. https://doi.org/10.1016/S0020-7683(03)00056-8.
  22. 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.
  23. 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. http://doi.org/10.12989/cac.2017.19.6.677.
  24. Love, A.E.H. (1888), "XVI, The small free vibrations and deformation of a thin elastic shell", Philos. Trans. Roy. Soc. London. (A.), 179, 491-546. https://doi.org/10.1098/rsta.1888.0016.
  25. Love, A.E.H. (2013), A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
  26. Markus, S. (1988), Mechanics of Vibrations of Cylindrical Shells, Vol. 17, Elsevier Science Limited.
  27. 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. http://doi.org/10.12989/cac.2019.24.3.185.
  28. Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and buckling of functionally graded carbon nanotubes/graphene platelets Timoshenko sandwich beam resting on variable elastic foundation", Adv. Nano Res., 10(6), 539-548. https://doi.org/10.12989/anr.2021.10.6.539.
  29. 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.
  30. 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.
  31. 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
  32. 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. http://doi.org/10.12989/acc.2020.9.1.043.
  33. 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.
  34. 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.
  35. Sosa, E.D., Darlington, TK., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., Article ID 705687, 12. http://doi.org/10.1155/2014/705687.
  36. Timesli, A. (2021), "A cylindrical shell model for nonlocal buckling behavior of CNTs embedded in an elastic foundation under the simultaneous effects of magnetic field, temperature change, and number of walls", Adv. Nano Res., 11(6), 581-593. https://doi.org/10.12989/anr.2021.11.6.581.
  37. 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.
  38. 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.
  39. 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.
  40. 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. http://doi.org/10.12989/sem.2020.75.1.109.
  41. 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.
  42. 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. Sci., 8(4), 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5.
  43. Yoon, J., Ru, C.Q. and Mioduchowski. A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sci. Tech., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.
  44. 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. http://doi.org/10.12989/cac.2017.20.6.671.
  45. Zeighampour, H. and Beni, Y. (2021), "Vibration analysis of boron nitride nanotubes by considering electric field and surface effect", Adv. Nano Res., 11(6), 607-620. https://doi.org/10.12989/anr.2021.11.6.607.
  46. 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.
  47. 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.
  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(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.