Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of double-walled carbon nanotubes based on Timoshenko beam theory and wave propagation approach

  • Emad Ghandourah (Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Amien Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulazi University ) ;
  • Abdulsalam Alhawsawi (Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Essam Mohammed Banoqitah (Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed R. Ali (Faculty of Engineering and Technology, Future University in Egypt New Cairo )
  • Received : 2022.01.05
  • Accepted : 2023.01.10
  • Published : 2023.06.25
⟨ Previous Next ⟩

Abstract

This paper concerned with the vibration of double walled carbon nanotubes (CNTs) as continuum model based on Timoshenko-beam theory. The vibration solution obtained from Timoshenko-beam theory provides a better presentation of vibration structure of carbon nanotubes. The natural frequencies of double-walled CNTs against half axial wave mode are investigated. The frequency decreases on decreasing the half axial wave mode. The shape of frequency arcs is different for various lengths. It is observed that model has produced lowest results for C-F and highest for C-C. A large parametric study is performed to see the effect of half axial wave mode on frequencies of CNTs. This numerically vibration solution delivers a benchmark results for other techniques. The comparison of present model is exhibited with previous studies and good agreement is found.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects under grant no. ( IFPIP 1811-135-1443 ) Therefore, authors gratefully acknowledge the technical and financial support from the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

References

  1. Ansari, R. and Arash, B. (2013), "Nonlocal Flugge shell model for vibrations of double-walled carbon nanotubes with different boundary conditions", J. Appl. Mech., 80(2), 021006. https://doi.org/10.1115/1.4007432
  2. Ansari, R., Rouhi, H. and Sahmani, S. (2011), "Calibration of the analytical nonlocal shell model for vibrations of double-walled carbon nanotubes with arbitrary boundary conditions using molecular dynamics", Int. J. Mech. Sci., 53, 786-792. https://doi.org/10.1016/j.ijmecsci.2011.06.010
  3. 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.
  4. Benmansour, D.L., Kaci, A., Bousahla, A.A., Heireche, H., Tounsi, A., Alwabli, A.S., Alhebshi, A.M., Al-ghmady, K. and Mahmoud, S.R. (2019), "The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory", Adv. Nano Res., 7(6), 443. https://doi.org/10.12989/anr.2019.7.6.443
  5. Ebrahimi, F., Dabbagh, A., Rabczuk, T., and Tornabene, F. (2019). "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., 7(2), 135. https://doi.org/10.12989/anr.2019.7.2.135
  6. Elishakoff, I. and Pentaras, D. (2009), "Fundamental natural frequencies of double-walled carbon nanotubes", J. Sound Vib., 322(4-5), 652-664. https://doi.org/10.1016/j.jsv.2009.02.037
  7. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039
  8. Georgantzinos, S.K., Giannopoulos, G.I. and Anifantis, N.K. (2009), "An efficient numerical model for vibration analysis of single-walled carbon nanotubes", Comput. Mech., 43(6), 731-741. https://doi.org/10.1007/s00466-008-0341-8
  9. Hutchison, J.L., Kiselev, N.A., Krinichnaya, E.P., Krestinin, A.V., Loutfy, R.O., Morawsky, A.P., Muradyan, V.E., Obraztsova, E. D., Sloan, J., Terekhov, S.V. and Zakharov, D.N. (2001), "Double-walled carbon nanotubes fabricated by a hydrogen arc discharge method", Carbon, 39, 761. http://doi.org/10.1016/S0008-6223(00)00187-1
  10. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(7), 56-58. https://doi.org/10.1038/354056a0
  11. Kiani, K. (2014), "Vibration and instability of a single-walled carbon nanotube in a three dimensional magnetic field", J. Phys. Chem. Solids, 75(1), 15-22. https://doi.org/10.1016/j.jpcs.2013.07.022
  12. Kumar, B.R. (2018), "Investigation on mechanical vibration of double-walled carbon nanotubes with inter-tube Van der waals forces", Adv. Nano Res., 6(2), 135. https://doi.org/10.12989/anr.2018.6.2.135
  13. Kwon, Y.K. and Tomanek, D. (1998), "Electronic and structural properties of multiwall carbon nanotubes", Phys. Rev. B, 58, 16001-16004. https://doi.org/10.1103/PhysRevB.58.R16001
  14. Li, C. and Chou, T. W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid Struct., 40(10), 2487-2499. https://doi.org/10.1016/S0020-7683(03)00056-8
  15. Mahdavi, M.H., Jiang, L.Y. and Sun, X. (2011), "Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix", Physica E, 43(10), 1813-1819. https://doi.org/10.1016/j.physe.2011.06.017
  16. Natsuki, T., Leib, X.W., Ni, Q.Q. and Endo, M. (2010), "Vibrational analysis of double-walled carbon nanotubes with inner and outer nanotubes of different lengths", Phys. Lett. A. 374, 4684-4689. https://doi.org/0.1016/J.PHYSLETA.2010.08.080 1016/J.PHYSLETA.2010.08.080
  17. Ren, Z., Lan, Y. and Wang, Y. (2011), "Aligned carbon nanotubes: Physics, concepts, fabrication and devices", Carbon Nanostruct., Berlin, Springer. https://doi.org/10.1007/978-3-642-30490-3
  18. Rysaeva, L.K., Bachurin, D.V., Murzaev, R.T., Abdullina, D.U., Korznikova, E.A., Mulyukov, R.R. and Dmitriev, S.V. (2020), "Evolution of the carbon nanotube bundle structure under biaxial and shear strains", Facta Univ. Series: Mech. Eng., 18(4), 525-536. http://doi.org/10.22190/FUME201005043R
  19. Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv Nano Res, 7(4), 265-275. https://doi.org/10.12989/anr.2019.7.4.265
  20. Shahsavari, D., Karami, B., and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated composite plates", Adv. Nano Res., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337
  21. Subramanian, A., Oden, P.I., Kennel, S.J., Jacobson, K.B., Warmack, R.J., Thundat, T., and Doktycz, M.J. (2002), "Glucose biosensing using an enzyme-coated microcantilever", Appl. Phys. Lett., 81(2), 385-387. https://doi.org/10.1063/1.1492308
  22. Timoshenko, S. (1974), "Vibration Problems in Engineering", New York, Wiley; 1974.
  23. 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
  24. Wildoer J.W.G., Venema, L.C., Rinzler, A.G., Smalley, R.E. and Dekker, C. (1998), "Electronic structure of atomically resolved carbon nanotubes", Nature, 391, 59-62. https://doi.org/10.1038/34139
  25. 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.
  26. Yan, Y., He, X.Q., Zhang, L.X. and Wang, Q. (2007), "Flow-induced instability of double-walled carbon nanotubes based on an elastic shell model", J. Appl. Phys., 102(4), 044307. https://doi.org/10.1063/1.2763955
  27. Yoon, J., Ru, C. Q. and Mioduchowski, A. (2005), "Terahertz vibration of short carbon nanotubes modeled as Timoshenko beams", J. Appl. Mech., 72(1), 10-17. https://doi.org/10.1115/1.1795814
  28. Yoon, J., Ru, C.Q. and Mioduchowski, A. (2002), "Non- coaxial resonance of an isolated multiwall carbon nanotube", Phys Rev B, 66, 233402. https://doi.org/10.1103/PhysRevB.66.233402
  29. 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.