Advances in nano research

  • 제8권3호
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  • Pages.229-244
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  • 2020
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis

  • Hussain, Muzamal (Department of Mathematics, Government College University Faisalabad) ;
  • Naeem, Muhammad N. (Department of Mathematics, Government College University Faisalabad) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department)
  • 투고 : 2019.10.05
  • 심사 : 2020.02.24
  • 발행 : 2020.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, modified Kelvin's model has been used to analyze the orthotropic vibration frequencies of single walled carbon nanotubes with clamped-clamped and clamped-free boundary conditions. For this system the governing equation is developed with wave propagation approach. Armchair, zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different modes, in-plane rigidity and mass density per unit lateral area. Throughout the computations, on decreasing the length-to-diameter ratios, the frequencies of said structure increases. In addition, by increasing three different value of in-plane rigidity resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. The results generated using computer software MATLAB to furnish the evidence regarding applicability of present model and also verified by available published literature.

키워드

과제정보

The author(s) received no financial support for the research, authorship, and/or publication of this article.

참고문헌

  1. Akgoz, B. and Civalek, O. (2012), "Investigation of size effects on static response of single-walled carbon nanotubes based on strain gradient elasticity", Int. J. Computat. Methods, 9(2), 1240032. https://doi.org/10.1142/S0219876212400324
  2. Ansari, R. and Rouhi, H. (2013), "Nonlocal Flugge shell model for vibrations of double-walled carbon nanotubes with different boundary conditions", Int. J. Appl. Mech., 80, 021006-1. https://doi.org/10.1142/S179329201250018X
  3. Asghar, S., Hussain, M. and Naeem, M. (2019), "Non-local effect on the vibration analysis of double walled carbon nanotubes based on Donnell shell theory", Physica E: Low-dimens. Syst. Nanostruct., 116, 113726. https://doi.org/10.1016/j.physe.2019.113726
  4. Asghar, S., Naeem, M.N., Hussain, M., Taj, M. and Tounsi, A. (2020), "Prediction and assessment of nolocal natural frequencies DWCNTs: Vibration analysis", Comput. Concrete, Int. J., 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133
  5. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., Int. J., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871
  6. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  7. Azrar, A., Azrar, L. and Aljinaidi, A.A. (2011), "Length scale effect analysis on vibration behavior of single-walled Carbon Nanotubes with arbitrary boundary conditions", Revue de Mecanique Applique et Theorique, 2, 475-485.
  8. Chavan, S.G. and Lal, A. (2017), "Bending behavior of SWCNT reinforced composite plates", Steel Compos. Struct., Int. J., 24(5), 537-548. https://doi.org/10.12989/scs.2017.24.5.537
  9. Civalek, O., Ersoy, H., Numanoglu, H.M. and Akgoz, B. (2018), "Small size and rotary inertia effects on the natural frequencies of carbon nanotubes", Curved Layer. Struct., 5(1), 273-279. https://doi.org/10.1515/cls-2018-0020
  10. 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 dynamic", J. Appl. Phys., 101(2), 024305. https://doi.org/10.1063/1.2423140
  11. Ebrahimi, F. and Habibi, S. (2017), "Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment", Adv. Nano Res., Int. J., 5(2), 69-97. https://doi.org/10.12989/anr.2017.5.2.069
  12. Elishakoff, I. and Pentaras, D. (2009), "Fundamental natural frequencies of double-walled carbon nanotubes", J. Sound Vib., 322, 652-664. https://doi.org/10.1016/j.jsv.2009.02.037
  13. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109-123. https://doi.org/10.12989/anr.2019.7.2.109
  14. Fatahi-Vajari, A., Azimzadeh, Z. and Hussain, M. (2019), "Nonlinear coupled axial-torsional vibration of single-walled carbon nanotubes using Galerkin and Homotopy perturbation method", Micro Nano Lett., 14(14), 1366-1371. https://doi.org/10.1049/mnl.2019.0203
  15. Fazelzadeh, S.A. and Ghavanloo, E. (2012a), "Nonlocal anisotropic elastic shell model for vibrations of single-walled carbon nanotubes with arbitrary chirality", Compos. Struct., 94(3), 1016-1022. https://doi.org/10.1016/j.compstruct.2011.10.014
  16. Fereidoon, A., Rafiee, R. and Moghadam, R.M. (2013), "A modal analysis of carbon-nanotube-reinforced polymer by using a multiscale finite-element method", Mech. Compos. Mater., 49(3), 325-332. https://doi.org/10.1007/s11029-013-9350-6
  17. Flugge, S. (1973), Stresses in Shells, 2nd Edition, Springer, Berlin, Germany.
  18. Gao, Y. and An, L. (2010), "A nonlocal elastic anisotropic shell model for microtubule buckling behaviors in cytoplasm", Physica E: Low-dimens. Syst. Nanostruct., 42(9), 2406-2415. https://doi.org/10.1016/j.bbrc.2009.07.042
  19. Ghavanloo, E. and Fazelzadeh, S.A. (2012b), "Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect", Appl. Mathe. Model., 36(10), 4988-5000. https://doi.org/10.1016/j.apm.2011.12.036
  20. Gibson, R.F., Ayorinde, E.O. and Wen, Y.F. (2007), "Vibrations of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 67(1), 1-28. https://doi.org/10.1016/j.compscitech.2006.03.031
  21. Han, J., Globus, A., Jaffe, R. and Deardorff, G. (1997), "Molecular dynamics simulations of carbon nanotube-based gears", Nanotechnology, 8(3), 95. https://doi.org/10.1088/0957-4484/8/3/001
  22. 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. http://doi.org/10.1016/j.compstruct.2014.06.023
  23. 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
  24. Hussain, M. and Naeem, M. (2018a), "Vibration of single-walled carbon nanotubes based on Donnell shell theory using wave propagation approach", Chapter, Intechopen, Novel Nanomaterials - Synthesis and Applications. ISBN 978-953-51-5896-7 https://doi.org/10.5772/intechopen.73503
  25. Hussain, M. and Naeem, M.N. (2018b), "Effect of various edge conditions on free vibration characteristics of rectangular plates", Chapter, Intechopen, Advance Testing and Engineering. ISBN 978-953-51-6706-8
  26. Hussain, M. and Naeem, M. (2019a), "Vibration characteristics of single-walled carbon nanotubes based on non-local elasticity theory using wave propagation approach (WPA) including chirality", In: Perspective of Carbon Nanotubes.
  27. 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
  28. Hussain, M. and Naeem, M. (2019c), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathe. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  29. Hussain, M. and Naeem, M.N. (2020a), "Mass density effect on vibration of zigzag and chiral SWCNTs", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636220906257
  30. Hussain, M. and Naeem, M.N. (2020b), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluidfilled Fluid-filled cylindrical shell", J. Adv. Concrete Constr., 1099636220906257. https://doi.org/10.1177/1099636220906257
  31. Hussain, M., Naeem, M.N., Shahzad, A. and He, M. (2017), "Vibrational behavior of single-walled carbon nanotubes based on cylindrical shell model using wave propagation approach", AIP Advances, 7(4), 045114. https://doi.org/10.1063/1.4979112
  32. Hussain, M., Naeem, M., Shahzad, A. and He, M. (2018a), "Vibration characteristics of fluid-filled functionally graded cylindrical material with ring supports", Chapter, Intechopen, Computational Fluid Dynamics. ISBN 978-953-51-5706-9 https://doi.org/10.5772 /intechopen.72172
  33. Hussain, M., Naeem, M.N., Shahzad, A., He, M.G. and Habib, S. (2018b), "Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach", IMechE Part C: J. Mech. Eng. Sci., 232(23), 4342-4356. https://doi.org/10.1177/0954406218802320
  34. Hussain, M., Naeem, M.N. and Isvandzibaei, M. (2018c), "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 232(24), 4564-4577. https://doi.org/10.1177/0954406217753459
  35. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019a), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., Int. J., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431
  36. Hussain, M., Naeem, M.N. and Taj, M. (2019b), "Effect of length and thickness variations on the vibration of SWCNTs based on Flugge's shell model", Micro Nano Lett., 15(1), 1-6. https://doi.org/10.1049/mnl.2019.0309
  37. Hussain, M., Naeem, M.N. and Taj, M. (2019c), "Vibration characteristics of zigzag and chiral FGM rotating carbon nanotubes sandwich with ring supports", J. Mech. Eng. Sci., Part C, 233(16), 5763-5780. https://doi.org/10.5772/intechopen.85948
  38. Hussain, M., Naeem, M.N. and Tounsi, A. (2020a), "Simulating vibration of single-walled carbon nanotube based on Relagh-Ritz Method", Adv. Nano Res., Int. J., 8(3), 221-234. https://doi.org/10.12989/anr.2020.8.3.221
  39. Hussain, M., Naeem, M.N. and Tounsi, A. (2020b), "Numerical study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model", Adv. Concrete Constr., Int. J., 9(3), 301-312. https://doi.org/10.12989/acc.2020.9.3.301
  40. Jorio, A., Saito, R., Hafner, J.H., Lieber, C.M., Hunter, M., McClure, T., Dresselhaus, G. and Dresselhaus, M.S. (2001), "Structural (n,m) Determination of Isolated Single-Wall Carbon Nanotubes by Resonant Raman Scattering", Phys. Rev. Lett., 86(6), 1118-1121. https://doi.org/10.1103/PhysRevLett.86.1118
  41. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361
  42. Kotakoski, J., Krasheninnikov, A.V. and Nordlund, K. (2006), "Energetics, structure, and long-range interaction of vacancytype defects in carbon nanotubes: Atomistic simulations", Phys. Rev. B, 74, 245420/1-5. https://doi.org/10.12989/scs.2018.28.1.099
  43. Kulathunga, D.D.T.K., Ang, K.K. and Reddy, J.N. (2009), "Accurate modeling of buckling of single-and double-walled carbon nanotubes based on shell theories", J. Phys.: Condensed Matter, 21(43), 435301. https://doi.org/10.1088/0953-8984/21/43/435301
  44. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  45. Mehar, K. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038
  46. Mehar, K. and Panda, S.K. (2016b), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", Proceedings of IOP Conference Series: Materials Science and Engineering, 115(1), 012014. https://doi.org/10.1088/1757-899X/115/1/012014
  47. Mehar, K. and Panda, S.K. (2018a), "Dynamic response of functionally graded carbon nanotube reinforced sandwich plate", Proceedings of IOP Conference Series: Materials Science and Engineering, 338(1), p. 012017. https://doi.org/10.1088/1757-899X/338/1/012017
  48. Mehar, K. and Panda, S.K. (2018b), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266
  49. Mehar, K. and Panda, S.K. (2018c), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polym. Technol., 37(6), 1643-1657. https://doi.org/10.1002/adv.21821
  50. Mehar, K. and Panda, S.K. (2018d), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircr. Eng. Aerosp. Technol., 90(1), 11-23. https://doi.org/10.1108/AEAT-11-2015-0237
  51. Mehar, K. and Panda, S.K. (2018e), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565
  52. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., Int. J., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181
  53. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324
  54. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005
  55. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Thermal Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689
  56. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017c), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057
  57. Mehar, K., Panda, S.K. and Patle, B.K. (2017d), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466
  58. Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018a), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519
  59. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018b), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica, 25(5), 2722-2737.
  60. Mehar, K., Panda, S.K. and Patle, B.K. (2018c), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809. https://doi.org/10.1002/pc.24409
  61. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018d), "Nonlinear frequency responses of functionally graded carbon nanotubereinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X
  62. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002
  63. Moghadam, R.M., Hosseini, S.A. and Salehi, M. (2014), "The influence of Stone-Thrower-Wales defect on vibrational characteristics of single-walled carbon nanotubes incorporating Timoshenko beam element", Physica E: Low-dimens. Syst. Nanostruct.res, 62, 80-89. https://doi.org/10.1016/j.physe.2014.04.008
  64. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., Int. J., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431
  65. Natsuki, T., Endo, M. and Tsuda, 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
  66. Paliwal, D.N., Kanagasabapathy, H. and Gupta, K.M. (1995), "The large deflection of an orthotropic cylindrical shell on a Pasternak foundation", Compos. Struct., 31(1), 31-37. https://doi.org/10.1016/0263-8223(94)00068-9
  67. Rafiee, R. and Moghadam, R.M. (2012), "Simulation of impact and post-impact behavior of carbon nanotube reinforced polymer using multi-scale finite element modeling", Computat. Mater. Sci., 63, 261-268. https://doi.org/10.1016/j.commatsci.2012.06.010
  68. Rouhi, H., Ansari, R. and Arash, B. (2013), "Vibrational analysis of double-walled carbon nanotubes based on the nonlocal Donnell shell theory via a new numerical approach", Iran J. Sci Technol. Transact. B-Eng., 37, 91-105.
  69. Selim, M.M. (2010), "Torsional vibration of carbon nanotubes under initial compression stress", Brazil. J. Phys., 40(3), 283-287. http://dx.doi.org/10.1590/S0103-97332010000300004
  70. Semmah, A., Heireche, H., Bousahla, A.A. and Toumsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by nonlocal FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  71. Sharma, P., Singh, R. and Hussain, M. (2019), "On modal analysis of axially functionally graded material beam under hygrothermal effect", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 234(5), 1085-1101. https://doi.org/10.1177/0954406219888234
  72. Sofiyev, A.H. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the Pasternak foundation", Engineering, 2(4), 228-236. https://doi.org/10.4236/eng.2010.24033
  73. Swaddiwudhipong, S., Tian, J. and Wang, C.M. (1995), "Vibrations of cylindrical shells with intermediate supports", J. Sound Vib., 187, 69-93. https://doi.org/10.1006/jsvi.1995.0503
  74. Taj, M., Safeer, M., Hussain, M., Naeem, M.N., Ahmad, M., Abbas, K., Khan, A.Q. and Tounsi, A. (2020), "Effect of external force on buckling of cytoskeleton intermediate filaments within viscoelastic media", Comput. Concrete, Int. J., 25(3), 205-214. https://doi.org/10.12989/cac.2020.25.3.205
  75. Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., Int. J., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527
  76. Usuki, T. and Yogo, K. (2009), "Beam equations for multi-walled carbon nanotubes derived from Flugge shell theory", Proceedings of Royal Society A, 465(2104). https://doi.org/10.1098/rspa.2008.0394
  77. Wang, J. and Gao, Y. (2016), "Nonlocal orthotropic shell model applied on wave propagation in microtubules", Appl. Mathe. Model., 40(11-12), 5731-5744. https://doi.org/10.1016/j.apm.2016.01.013
  78. Wang, V. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro-and nanostructures", Phys. Lett. A, 363, 236-242. http://dx.doi.org/10.1016/j.physleta.2006.10.093
  79. 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, 89-106.
  80. Zou, R.D. and Foster, C.G. (1995), "Simple solution for buckling of orthotropic circular cylindrical shells", Thin-Wall. Struct., 22(3), 143-158. https://doi.org/10.1016/0263-8231(94)00026-V