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Prediction of small-scale vibration of zigzag DWCNTs: Numerical approach

  • Asghar, Sehar (Department of Mathematics, Govt. College University Faisalabad) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khadimallah, Mohamed Amine (Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department) ;
  • Naeem, Muhammad N. (Department of Mathematics, Govt. College University Faisalabad) ;
  • Ali, Zainab (Department of Mathematics, Govt. College University Faisalabad) ;
  • Khedher, Khaled Mohamed (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Taj, Muhammad (Department of Mathematics, University of Azad Jammu and Kashmir) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2011.02.24
  • Accepted : 2021.05.18
  • Published : 2021.06.25
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Abstract

In this article, free vibration attributes of zigzag double-walled carbon nanotubes (CNTs) based on nonlocal elastic shell model have been investigated. The impact of small scale is being perceived by establishing Flugge 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. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

Keywords

Acknowledgement

The Authors extend their thanks to the Deanship of Scientific Research at King Khalid University for funding this work through the large research groups under grant number RGP. 2/173/42.

References

  1. Adela, I. (2018), Computational Fluid Dynamics, Romania.
  2. Akbas S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dynam., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X.
  3. Akbas, S.D. (2016b), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., 59(3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579
  4. Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009.
  5. Akbas, S.D. (2018), "Forced vibration analysis of cracked nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(8), 1-11. https://doi.org/10.1007/s40430-018-1315-1.
  6. Akbas, S.D. (2018a), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. http://dx.doi.org/10.12989/anr.2018.6.1.039.
  7. Akbas, S.D. (2018b), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219-243. http://dx.doi.org/10.12989/anr.2018.6.3.219.
  8. Akbas, S.D. (2019), "Axially forced vibration analysis of cracked a nanorod", J. Comput. Appl. Mech., 50(1), 63-68. http://dx.doi.org/10.22059/JCAMECH.2019.281285.392.
  9. Akbas, S.D. (2020), "Modal analysis of viscoelastic nanorods under an axially harmonic load", Adv. Nano Res., 8(4), 277-282. https://doi.org/10.12989/anr.2020.8.4.277.
  10. 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.
  11. 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.
  12. Ansari, R., Hemmatnezhad, M. and Rezapour, J. (2011), "The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions", Current Appl. Phys., 11(3), 692-697. https://doi.org/10.1016/j.cap.2010.11.034.
  13. 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.
  14. 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.
  15. 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.
  16. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  17. Benguediab, S., Tounsi, A., Ziadour, 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. http://dx.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. Civalek, O. (2020), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", Int. J. Numer. Method. Eng., 121(5), 990-1019. https://doi.org/10.1002/nme.6254.
  21. Civalek, O. and Jalaei, M.H. (2020), "Buckling of carbon nanotube (CNT)-reinforced composite skew plates by the discrete singular convolution method", Acta Mechanica, 231(6), 2565-2587. https://doi.org/10.1007/s00707-020-02653-3.
  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. Duan, W.H., Wang, C.M. and Zhang, Y.Y. (2007), "Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics", J. Appl. Phys., 101(2), 024305. https://doi.org/10.1063/1.2423140.
  24. 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.
  25. Eringen, A.C. (2002), Nonlocal continuum field theories, Science and Business Media, New York.
  26. 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", Measurement, 73, 127-136. https://doi.org/10.1016/j.measurement.2015.05.009.
  27. Fazilati, J. (2018), "Stability of tow-steered curved panels with geometrical defects using higher order FSM", Steel Compos. Struct., 28(1), 25-37. https://doi.org/10.12989/scs.2018.28.1.025.
  28. Flugge, and Wilhelm, (1962), Statik und Dynamik der Scahlen, Springer, Berlin, Germany.
  29. 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.
  30. Gao, S., Peng, Z., Wang, X. and Liu, J. (2019), "Compressive behavior of circular hollow and concrete-filled steel tubular stub columns under atmospheric corrosion", Steel Compos. Struct., 33(4), 615-627. https://doi.org/10.12989/scs.2019.33.4.615
  31. 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/Solids, 29(1), 49-55. https://doi.org/10.1016/j.euromechsol.2009.05.008.
  32. 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.
  33. 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.
  34. 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.
  35. 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. Solids, 56, 3475-3485. https://doi.org/10.1016/j.jmps.2008.08.010.
  36. 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.
  37. 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.
  38. kbas, S.D. (2016a), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125.
  39. 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.
  40. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889.
  41. 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(3), 359-367. https://doi.org/10.12989/scs.2017.24.3.359.
  42. 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.
  43. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of Nonlocal Continuum Models to Nanotechnology", Int. J. Eng. Sci., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0.
  44. 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.
  45. 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.
  46. 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.
  47. Rouhi, H., BazdidVahdati, 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.
  48. 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.
  49. 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.
  50. 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.
  51. 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..
  52. Simsek, M. (2011), "Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory", Steel Compos. Struct., 11(1), 59-76. https://doi.org/10.12989/scs.2011.11.1.059.
  53. Soldano, C. (2015), "Hybrid metal-based carbon nanotubes", "Novel platform for multifunctional applications", Progress Mater. Sci., 69, 183-212. https://doi.org/10.1016/j.pmatsci.2014.11.001.
  54. Sosa, E.D., Darlington, TK., Hanos, B.A. and O'Rourke, M.J.E. (2014), "Multifunctional thermally remendable nanocomposites", J. Compos., 705687. http://dx.doi.org/10.1155/2014/705687.
  55. 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.
  56. Sun, C.T. and Zhang, H. (2002), "Size-dependent elastic moduli of plate like nanomaterials", J. Appl. Phys., 93, 212-1218. https://doi.org/10.1063/1.1530365.
  57. 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.
  58. Taiyari, F., Mazzolani, F.M. and Bagheri, S. (2019), "Seismic performance assessment of steel building frames equipped with a novel type of bending dissipative braces", Steel Compos. Struct., 33(4), 525-535. https://doi.org/10.12989/scs.2019.33.4.525.
  59. Usuki, T. and Yogo, K. (2009), "Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory", Proc. Roy. Soc. A., 465(2104). https://doi.org/10.1098/rspa.2008.0394.
  60. 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.
  61. Wang, C.Y. and Zhang, L.C. (2007), Proceedings of the 5th Australasian Congress on Applied Mechanics, ACAM, Brisbane, Australia.
  62. 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.
  63. Wang, Q., Zhou, G.Y. and Lin, K.C. (2006), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solids Struct., 43, 6071-6084. https://doi.org/10.1016/j.ijsolstr.2005.11.005.
  64. 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.
  65. 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.
  66. 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.
  67. 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.
  68. Yan, J. B., Dong, X. and Wang, T. (2020), "Flexural performance of double skin composite beams at the Arctic low temperature", Steel Compos. Struct., 37(4), 431-446. https://doi.org/10.12989/scs.2020.37.4.431.
  69. 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.
  70. 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
  71. 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.
  72. Zhang, Y.Y., Wang, C.M. and Tan, V.B.C. (2009), "Assessment of Timoshenko beam models for vibrational behavior of single-walled carbon nanotubes using molecular dynamics", Adv. Appl. Math. Mech., 1, 89-106.
  73. Zhou, C., Chen, Z., Li, J., Cai, L. and Huang, Z. (2020), "Structural performance of novel SCARC column under axial and eccentric loads", Steel Compos. Struct., 37(5), 503-516. https://doi.org/10.12989/scs.2020.37.5.503.