Advances in concrete construction

  • 제9권6호
  • /
  • Pages.577-588
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  • 2020
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  • 2287-5301(pISSN)
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  • 2287-531X(eISSN)
테크노프레스 (Techno-Press)
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DOI QR Code

Effect of chiral structure for free vibration of DWCNTs: Modal analysis

  • Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad) ;
  • Naeem, Muhammad N. (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed Amine (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Iqbal, Zafar (Department of Mathematics, University of Sargodha) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2020.04.07
  • 심사 : 2020.05.29
  • 발행 : 2020.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, vibration attributes of chiral double-walled carbon nanotubes (CNTs) based on nonlocal elastic shell model have been investigated. The impact of small scale is being perceived by establishing Flügge shell model. The wave propagation is engaged to frame the ruling equations as eigen value system. The influence of nonlocal parameter subjected to different end supports has been overtly examined. A suitable choice of material properties and nonlocal parameter been focused to analyze the vibration characteristics. The new set of inner and outer tubes radii investigated in detail against aspect ratio and length. The dominance of boundary conditions via nonlocal parameter is shown graphically. Whereas for lower aspect ratio the frequencies coincide but as it continues to expand the difference between all respective boundary conditions slightly tend to increase. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

키워드

참고문헌

  1. Adela, I. (2018), Computational Fluid Dynamics, Romania.
  2. Amara, K., Tounsi, A., Mechab, I. and Adda-Bedia, E.A. (2010), "Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field", Appl. Math. Model., 34(12), 3933-3942. https://doi.org/10.1016/j.apm.2010.03.029.
  3. Ansari, R. and Rouhi, H. (2012), "Nonlocal analytical Flugge shell model for the axial buckling of double-walled carbon nanotubes with different end conditions", Int. J. Nano, 7, 1250081. https://doi.org/10.1142/S179329201250018X.
  4. Ansari, R. and Rouhi, H. (2013), "Nonlocal analytical Flugge shell model for the vibrations of double-walled carbon nanotubes with different end conditions", Int. J. Appl. Mech., 80, 021006-1. https://doi.org/10.1142/S179329201250018X.
  5. 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.
  6. Ansari, R., Sahmani, S. and Arash, B. (2010), "Nonlocal plate model for free vibrations of single-layered graphene sheets", Phys. Lett. A., 375(1), 53-62. https://doi.org/10.1016/j.physleta.2010.10.028.
  7. Arefi, M. and Zenkour, A.M. (2018), "Size-dependent thermoelastic analysis of a functionally graded nanoshell", Mod. Phys. Lett. B, 32(3), 1850033. https://doi.org/10.1142/S0217984918500331.
  8. Arefi, M., Bidgoli, E.M.R. and Rabczuk, T. (2019), "Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST", Eur. J. Mech.-A/Solid., 77, 103802. https://doi.org/10.1016/j.euromechsol.2019.103802.
  9. Arefi, M., Bidgoli, E.M.R. and Rabczuk, T. (2019), "Thermo-mechanical buckling behavior of FG GNP reinforced micro plate based on MSGT", Thin Wall. Struct., 142, 444-459. https://doi.org/10.1016/j.tws.2019.04.054.
  10. Arefi, M., Bidgoli, E.M.R., Dimitri, R. and Tornabene, F. (2018), "Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Aerosp. Sci. Technol., 81, 108-117. https://doi.org/10.1016/j.ast.2018.07.036.
  11. Arefi, M., Bidgoli, E.M.R., Dimitri, R., Bacciocchi, M. and Tornabene, F. (2019), "Nonlocal bending analysis of curved nanobeams reinforced by graphene nanoplatelets", Compos. Part B: Eng., 166, 1-12. https://doi.org/10.1016/j.compositesb.2018.11.092.
  12. Arefi, M., Karroubi, R. and Irani-Rahaghi, M. (2016), "Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer", Appl. Math. Mech., 37(7), 821-834. https://doi.org/10.1007/s10483-016-2098-9.
  13. Arefi, M., Mohammadi, M., Tabatabaeian, A., Dimitri, R. and Tornabene, F. (2018), "Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels", Steel Compos. Struct., 27(4), 525-536. https://doi.org/10.12989/scs.2018.27.4.525.
  14. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  15. Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699. https://doi.org/10.12989/scs.2019.33.5.699.
  16. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Des., 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
  17. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical and buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020.
  18. 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.
  19. Brischotto, S. (2015), "A continuum shell model including van der Waals interaction for free vibrations of double-walled carbon nanotubes", CMES, 104, 305-327.
  20. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2020), "Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect", Defence Technology. https://doi.org/10.1016/j.dt.2020.01.001.
  21. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2020), "Three dimensional free vibration analysis of functionally graded nano cylindrical shell considering thickness stretching effect", Steel Compos. Struct., 34(5), 657-670. https://doi.org/10.12989/scs.2020.34.5.657.
  22. Do, Q.C., Pham, D.N., Vu, D.Q., Vu, T.T.A. and Nguyen, D.D. (2019), "Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load", Steel Compos. Struct., 31(3), 243-259. https://doi.org/10.12989/scs.2019.31.3.243.
  23. 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.
  24. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Science and Business Media, New York.
  25. 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.
  26. Flugge, W. (1962), Statik und Dynamik der Scahlen, Springer, Berlin, Germany.
  27. 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.
  28. Hao, M.J., Guo, X.M. and Wang, Q. (2010), "Small-scale effect on torsional buckling of multi-walled carbon nanotubes", Eur. J. Mech. A/Solid., 29(1), 49-55. https://doi.org/10.1016/j.euromechsol.2009.05.008.
  29. 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.
  30. Heydarpour, Y., Aghdam, M.M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023.
  31. Hsu, J.C., Chang, R.P. and Chang, W.J. (2008), "Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory", Phys. Lett. A, 372(16), 2757-2759. https://doi.org/10.1016/j.physleta.2008.01.007.
  32. Hu, Y.G., Liew, K.M., Wang, Q., He, X.Q. and Yakobson, B.I. (2008), "Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes", J. Mech Phys. Solid., 56, 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010.
  33. Hussain, M. and Naeem, M.N. (2019a), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes". Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039.
  34. 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.
  35. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(1), 56-58. https://doi.org/10.1038/354056a0.
  36. Iijima, S., Brabec, C., Maiti, A. and Bemholc, J. (1996), "Structural flexibility of carbon nanotubes", J. Chem. Phys., 104(5), 2089-2092. https://doi.org/10.1063/1.470966.
  37. Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FG-CNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.
  38. Ke, L.L., Xiang, Y., Yang, J. and Kitipornchai, S. (2009), "Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory", Comput. Mater. Sci., 47(2), 409-417. https://doi.org/10.1016/j.commatsci.2009.09.002.
  39. Khosrazadeh, A. and Hajabasi, M.A. (2012), "Free vibrations of embedded doube-walled carbon nanotubes considering nonlinear interlayer van der Waals forces", J. AMP, 36, 997-1007. https://doi.org/10.1016/j.apm.2011.07.063.
  40. Lei, Z. and Zhang, Y. (2018), "Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers", Steel Compos. Struct., 28(4), 495-508. https://doi.org/10.12989/scs.2018.28.4.495.
  41. Li, C. and Chou, T.W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid. Struct., 40(10), 2487-2492. https://doi.org/10.1016/S0020-7683(03)00056-8.
  42. Loy, C.T. Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41, 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X.
  43. Moradi-Dastjerdi, R. and Payganeh, G. (2017), "Transient heat transfer analysis of functionally graded CNT reinforced cylinders with various boundary conditions", Steel Compos. Struct., 24, 359-367. https://doi.org/10.12989/scs.2017.24.3.359.
  44. Narwariya, M., Choudhury, A. and Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Comput. Des., 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113.
  45. Natsuki, T., Morinobu, E. andTsuda, H. (2006), "Vibration analysis of embedded carbon nanotubes using wave propagation approach", J. Appl. Phys., 99(3), 034311. https://doi.org/10.1063/1.2170418.
  46. Natsuki, T., Qing, Q.N. and Morinobu, E. (2007), "Wave propagation in single-walled and double-walled carbon nanotubes filled with fluids", J. Appl. Phys., 101(3), 034319-034319-5. https://doi.org/10.1063/1.2432025.
  47. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sei., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0.
  48. Pradhan, S.C. and Phadikar, J.K. (2009), "Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models", Phys. Lett. A., 373(11), 1062-9. https://doi.org/10.1016/j.physleta.2009.01.030.
  49. 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.
  50. Rouhi, H., Ansari, R. and Arash, B. (2013), "Vibration analysis of double-walled carbon nanotubes based on the non-local donnell shell via a new numerical approach", Int J. Mech. Sei., 37, 91-105.
  51. Rouhi, H., Bazdid Vahdati, M. and Ansari, R. (2015), "Rayleigh-Rits vibrational analysis of multi-walled carbon nanotubes based on the non-local Flugge shell theory", J. Compos., 750392. https://doi.org/10.1155/2015/750392.
  52. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 33(6), 805. https://doi.org/10.12989/scs.2019.33.6.805.
  53. 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://dx.doi.org/10.1103/PhysRevB.59.12678.
  54. Sedighi, H.M. and Yaghootian, A. (2016), "Dynamic instability of vibrating carbon nanotubes near small layers of graphite sheets based on nonlocal continuum elasticity", J. Appl. Mech. Techn. Phys., 57(1), 90-100. https://doi.org/10.1134/S0021894416010107.
  55. Sedighi, H.M., Reza, A. and Zare, J. (2011)", Study on the frequency-amplitude relation of beam vibration", Int. J. Phys. Sci., 6(36), 8051-8056. https://doi.org/10.5897/IJPS11.1556.
  56. Shafiei, H. and Setoodeh, A.R. (2017), "Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation", Steel Compos. Struct., 24(1), 65-77. https://doi.org/10.12989/scs.2017.24.1.065.
  57. She, G.L., Ren, Y.R. and Yuan, F.G. (2019), "Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems", Steel Compos. Struct., 31(6), 641-653. https://doi.org/10.12989/scs.2019.31.6.641.
  58. Shen, H.S. and Zhang, C.L. (2010), "Torsional buckling and post buckling of double-walled carbon nanotubes by nonlocal shear deformable shell model", Compos. Struct., 92(5), 1073-1084. https://doi.org/10.1016/j.compstruct.2009.10.002.
  59. 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.
  60. 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://dx.doi.org/10.1155/2014/705687.
  61. Sudak, L.J. (2003), "Column buckling of multi-walled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94, 7281-7287. https://doi.org/10.1063/1.1625437.
  62. Tahouneh, V. (2017), "Effects of CNTs waviness and aspect ratio on vibrational response of FG-sector plate", Steel Compos. Struct., 25(6), 649-661. https://doi.org/10.12989/scs.2017.25.6.649.
  63. Usuki, T. and Yogo, K. (2009), "Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory", Proc. Royal Soc. A., 465(2104), 1199-1226. https://doi.org/10.1098/rspa.2008.0394.
  64. Vodenitcharova, T. and Zhang, L.C. (2003), "Effective wall thickness of single walled carbon nanotubes", Phys. Rev. B, 68, 165401. https://doi.org/10.1103/PhysRevB.68.165401.
  65. Wang, C.Y. and Zhang, L.C. (2007), "Modelling the free vibration of single-walled carbon nanotubes", Proceedings of the 5th Australasian Congress on Applied Mechanics, Engineers Australia.
  66. 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.
  67. Wang, Q., Zhou, G.Y. and Lin, K.C. (2006), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solid. Struct., 43, 6071-6084. https://doi.org/10.1016/j.ijsolstr.2005.11.005.
  68. Xiaobin, L., Shuangxi, X., Weiguo, W. and Jun, L. (2014), "An exact dynamic stiffness matrix for axially loaded double-beam systems", Sadhana, 39(3), 607-623. https://doi.org/10.1007/s12046-013-0214-5.
  69. Xu, K.U., 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. Mech., 75(2), 021013-1. https://doi.org/10.1115/1.2793133.
  70. Yakobson, B.I., Brabec, C.J. and Bernholc, J. (1996), "Nanomechanics of carbon tubes: instabilities beyond linear response", Phys. Rev. Lett., 76, 2511-2514. https://doi.org/10.1103/PhysRevLett.76.2511.
  71. 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.
  72. Yazdani, R. and Mohammadimehr, M. (2019), "Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution", Comput. Concrete, 24(6), 499-511. https://doi.org/10.12989/cac.2019.24.6.499.
  73. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2003), "Vibration of an embedded multiwall carbon nanotube", Compos. Sei. Tech., 63(11), 1533-1542. https://doi.org/10.1016/S0266-3538(03)00058-7.
  74. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065.
  75. 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://dx.doi.org/10.12989/sem.2015.54.4.693.
  76. Zhang, Y., Li, G. and Liew, K.M. (2018), "Thermomechanical buckling characteristic of ultrathin films based on nonlocal elasticity theory", Compos. Part B: Eng., 153, 184-193. https://doi.org/10.1016/j.compositesb.2018.07.046.

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