Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube Van der waals forces

  • Kumar, B. Ravi (School of Mechanical Engineering, SASTRA Deemed University)
  • Received : 2018.04.26
  • Accepted : 2018.06.03
  • Published : 2018.06.25
⟨ Previous Next ⟩

Abstract

This work represents the study of the vibration response of the double walled carbon nanotubes (DWCNT) for various boundary conditions. The inner and outer carbon nanotubes are modeled as two individual Euler-Bernoulli's elastic beams interacting each other by Van der waals force. Differential transform method (DTM) is used as a numerical method to solve the governing differential equations and associated boundary conditions. The influence of Winkler elastic medium on vibration frequency is also examined and results are interpreted. MATLAB is used as a tool for solving the governing differential equations. The fundamental natural frequencies are validating with those available in literature and observed a good agreement between them.

Keywords

References

  1. Affoune, A.M., Prasad, B.L.V., Sato, H., Enoki, T., Kaburagi, Y. and Hishiyama, Y. (2001), "Experimental Evidence of a Single Nano-Graphene", Chem. Phys. Lett., 348(1-2), 17-20. DOI: 10.1016/S0009-2614(01)01066-1
  2. Akgoz, B. and Civalek, O. (2016), "Bending Analysis of Embedded Carbon Nanotubes Resting on an Elastic Foundation Using Strain Gradient Theory", Acta Astronautica, 119, 1-12. DOI: 10.1016/J.ACTAASTRO.2015.10.021
  3. 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. DOI: 10.1016/j.physleta.2010.10.028
  4. Askari, H. and Esmailzadeh, E. (2017), "Forced vibration of fluid conveying carbon nanotubes considering thermal effect and nonlinear foundations", Compos. Part B: Eng., 113, 31-43. DOI: 10.1016/J.COMPOSITESB.2016.12.046
  5. Ball, P. (2001), "Roll up for the revolution", Nature, 414(6860), 142-144. DOI: 10.1038/35102721
  6. Baughman, R.H., Zakhidov, A.A. and De Heer, W.A. (2002), "Carbon nanotubes--the route toward applications", Science, 297(5582), 787-792. DOI: 10.1126/science.1060928
  7. Bikramsingh, R.K. and Sankara Subramanian, H. (2017), "Investigation on vibration characteristics of fluid conveying single walled carbon nanotube via DTM", Austral. J. Mech. Eng. DOI: 10.1080/14484846.2017.1354448
  8. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. DOI: 10.12989/scs.2016.20.2.227
  9. Chen, C.O.K. and Ho, S.H. (1999), "Solving partial differential equations by two-dimensional differential transform method", Appl. Math. Comput., 106(2-3), 171-179. DOI: 10.1016/S0096-3003(98)10115-7
  10. Elishakoff, I. and Pentaras, D. (2009), "Fundamental natural frequencies of double-walled carbon nanotubes", J. Sound Vib., 322(4-5), 652-664. DOI: 10.1016/j.jsv.2009.02.037
  11. Fang, B., Zhen, Y.X., Zhang, C.P. and Tang, Y. (2013), "Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory", Appl. Math. Model., 37(3), 1096-1107. DOI: 10.1016/J.APM.2012.03.032
  12. Fernandes, R., El-Borgi, S., Mousavi, S.M., Reddy, J.N. and Mechmoum, A. (2017), "Nonlinear sizedependent longitudinal vibration of carbon nanotubes embedded in an elastic medium", Physica E: Low-Dimens. Syst. Nanostruct., 88, 18-25. DOI: 10.1016/J.PHYSE.2016.11.007
  13. Frank, I.W., Tanenbaum, D.M., van der Zande, A.M. and McEuen, P.L. (2007), "Mechanical properties of suspended graphene sheets", J. Vacuum Sci. Technol. B: Microelectro. Nanometer Struct., 25(6), 2558. DOI: 10.1116/1.2789446
  14. Gul, U. and Aydogdu, M. (2018), "Noncoaxial vibration and buckling analysis of embedded double-walled carbon nanotubes by using doublet mechanics", Compos. Part B: Eng., 137, 60-73. DOI: 10.1016/J.COMPOSITESB.2017.11.005
  15. He, X.Q., Eisenberger, M. and Liew, K.M. (2006), "The effect of van der Waals interaction modeling on the vibration characteristics of multiwalled carbon nanotubes", J. Appl. Phys., 100(12), 124317. DOI: 10.1063/1.2399331
  16. Hosseini, M., Sadeghi-Goughari, M., Atashipour, S.A. and Eftekhari, M. (2014), "Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model", Arch. Mech., 66(4), 217-244.
  17. Iijima, S. (1991), "Helical Microtubules of Graphitic Carbon", Nature, 354(6348), 56-58. DOI: 10.1038/354056a0
  18. Jiang, J., Wang, L. and Zhang, Y. (2017), "Vibration of single-walled carbon nanotubes with elastic boundary conditions", Int. J. Mech. Sci., 122, 156-166. DOI: 10.1016/J.IJMECSCI.2017.01.012
  19. Karlicic, D., Cajic, M., Murmu, T. and Adhikari, S. (2015), "Nonlocal longitudinal vibration of viscoelastic coupled double-nanorod systems", Eur. J. Mech. - A/Solids, 49, 183-196. DOI: 10.1016/J.EUROMECHSOL.2014.07.005
  20. Kumar, R. and Deol, S. (2016), "Nonlocal Buckling Analysis of Single-Walled Carbon Nanotube Using Differential Transform Method (DTM)", Int. J. Sci. Res. (IJSR), 5(3), 1768-1773. URL: www.ijsr.net
  21. Kumar, B.R. and Reddy, K.P. (2017), "Investigation on Mechanical Vibration of Double-Walled Carbon Nanotubes on Winkler Foundation with Length Effects via DTM", Rasayan J. Chem., 10(2), 481-487. DOI: 10.7324/RJC.2017.1021711
  22. Li, C. and Chou, T.W. (2004), "Vibrational behaviors of multiwalled-carbon-nanotube-based nanomechanical resonators", Appl. Phys. Lett., 84(1), 121-123. DOI: 10.1063/1.1638623
  23. Mandal, U. and Pradhan, S.C. (2014), "Transverse vibration analysis of single-layered graphene sheet under magneto-thermal environment based on nonlocal plate theory", J. Appl. Phys., 116(16), 164303. DOI: 10.1063/1.4898759
  24. Manevitch, L.I., Smirnov, V.V., Strozzi, M. and Pellicano, F. (2017), "Nonlinear optical vibrations of single-walled carbon nanotubes", Procedia Eng., 199, 705-710. DOI: 10.1016/J.PROENG.2017.09.011
  25. Murmu, T. and Pradhan, S.C. (2009a), "Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory", J. Appl. Phys., 105(6), 64319. DOI: 10.1063/1.3091292
  26. Murmu, T. and Pradhan, S.C. (2009b), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Computat. Mater. Sci., 46(4), 854-859. DOI: 10.1016/J.COMMATSCI.2009.04.019
  27. Pei, Q.X., Zhang, Y.W. and Shenoy, V.B. (2010), "A molecular dynamics study of the mechanical properties of hydrogen functionalized graphene", Carbon, 48(3), 898-904. DOI: 10.1016/j.carbon.2009.11.014
  28. Pop, E., Mann, D., Wang, Q., Goodson, K. and Dai, H. (2005), "Thermal conductance of an individual single-wall carbon nanotube above room temperature", Am. Chem. Soc., 6(1), 96-100. DOI: 10.1021/NL052145F
  29. Pop, E., Mann, D.A., Goodson, K.E. and Dai, H. (2007), "Electrical and thermal transport in metallic singlewall carbon nanotubes on insulating substrates", J. Appl. Phys., 101(9), 93710. DOI: 10.1063/1.2717855
  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. DOI: 10.1115/1.1490129
  31. Rafiee, R. and Moghadam, R.M. (2014), "On the modeling of carbon nanotubes: a critical review", Compos. Part B: Eng., 56, 435-449. DOI: 10.1016/j.compositesb.2013.08.037
  32. Ravi Kumar, B. (2017a), "Mechanical Buckling Analysis of Single-Walled Carbon Nanotube with Nonlocal Effects", J. Nano Res., 48, 85-94. DOI: 10.4028/www.scientific.net/JNanoR.48.85
  33. Ravi Kumar, B. (2017b), "Nonlocal Vibration Analysis of Fluid Conveying Single-Walled Carbon Nanotube With Magnetic Effects", Rasayan J. Chem., 10(2), 643-651. DOI: 10.7324/RJC.2017.1021669
  34. Ravi Kumar, B., Mano, S. and Subramanian, H.S. (2017), "Vibration Analysis and Design Modification of Automobile Muffler", J. Adv. Res. Dyn. Control Syst., Special Issue 11, 120-127.
  35. Roth, S. (Siegmar) and David, L. (David Loren) Carroll (2015), One-Dimensional Metals : Conjugated Polymers, Organic Crystals, Carbon Nanotubes, Weinheim, Wiley-VCH.
  36. Saito, R., Matsuo, R., Kimura, T., Dresselhaus, G. and Dresselhaus, M.S. (2001), "Anomalous potential barrier of double-wall carbon nanotube", Chemical Physics Letters, 348(3-4), 187-193. DOI: 10.1016/S0009-2614(01)01127-7
  37. Stallard, J.C., Tan, W., Smail, F.R., Gspann, T.S., Boies, A.M. and Fleck, N.A. (2018), "The mechanical and electrical properties of direct-spun carbon nanotube mats", Extreme Mechanics Letters, 21, 65-75. DOI: 10.1016/J.EML.2018.03.003
  38. Thamaraikannan, S. and Pradhan, S.C. (2016), "Atomistic Study of Carbon Nanotubes: Effect of Cut-Off Distance", TMS 2016 145th Annual Meeting & Exhibition, pp. 293-300. DOI: 10.1007/978-3-319-48254-5_36
  39. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. DOI: 10.12989/anr.2013.1.1.001
  40. Treacy, M.J., Ebbesen, T.W. and Gibson, J.M. (1996), "Exceptionally high Young's modulus observed for individual carbon nanotubes", Nature, 381(6584), 678-680. DOI: 10.1038/381678a0
  41. Wang, Q. and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15(2), 659-666. DOI:10.1088/0964-1726/15/2/050
  42. Xu, K.Y., Guo, X.N. and Ru, C.Q. (2006), "Vibration of a double-walled carbon nanotube aroused by nonlinear intertube van der Waals forces", J. Appl. Phys., 99(6), 64303. DOI: 10.1063/1.2179970
  43. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2002), "Noncoaxial resonance of an isolated multiwall carbon nanotube", Phys. Rev. B, 66(23), 233402. DOI: 10.1103/PhysRevB.66.233402
  44. Zhao, Y., Ma, C.C., Chen, G. and Jiang, Q. (2003), "Energy dissipation mechanisms in carbon nanotube oscillators", Phys. Rev. Lett., 91(17), 175504. DOI: 10.1103/PhysRevLett.91.175504

Cited by

  1. Effectiveness of piezoelectric fiber reinforced composite laminate in active damping for smart structures vol.31, pp.4, 2018, https://doi.org/10.12989/scs.2019.31.4.387
  2. Frequency and thermal buckling information of laminated composite doubly curved open nanoshell vol.10, pp.1, 2018, https://doi.org/10.12989/anr.2021.10.1.001
  3. Molecular dynamics investigation of pull-in instability in graphene sheet under electrostatic and van der Waals forces vol.11, pp.2, 2018, https://doi.org/10.12989/anr.2021.11.2.173
  4. Computer modeling for frequency performance of viscoelastic magneto-electro-elastic annular micro/nanosystem via adaptive tuned deep learning neural network optimization vol.11, pp.2, 2018, https://doi.org/10.12989/anr.2021.11.2.203