Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Correlation between frequency and Poisson's ratio: Study of durability of armchair SWCNTs

  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad) ;
  • Mohamed A. Khadimallah (Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University)
  • Received : 2023.03.27
  • Accepted : 2023.05.17
  • Published : 2023.09.25
⟨ Previous Next ⟩

Abstract

An analysis of the Poisson's ratios influence of single walled carbon nanotubes (SWCNTs) based on Sander's shell theory is carried out. The effect of Poisson's ratio, boundary conditions and different armchairs SWCNTs is discussed and studied. The Galerkin's method is applied to get the eigen values in matrix form. The obtained results shows that, the decrease in ratios of Poisson, the frequency increases. Poisson's ratio directly measures the deformation in the material. A high Poisson's ratio denotes that the material exhibits large elastic deformation. Due to these deformation frequencies of carbon nanotubes increases. The frequency value increases with the increase of indices of single walled carbon nanotubes. The prescribe boundary conditions used are simply supported and clamped simply supported. The Timoshenko beam model is used to compare the results. The present method should serve as bench mark results for agreeing the results of other models, with slightly different value of the natural frequencies.

Keywords

Acknowledgement

This study is supported via funding from Prince Satam bin Abdulaziz University project number (PSAU/2023/R/1444).

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. and Rouhi, H. (2015), "Nonlocal Flugge shell model for the axial buckling of single-walled Carbon nanotubes: An analytical approach", Int. J. Nano Dimens., 6(5), 453-462. https://doi.org/10.1142/S179329201250018X. 
  3. Banerjee, J. and Williams, F. (1996), "Exact dynamic stiffness matrix for composite Timoshenko beams with applications", J. Sound Vib., 194(4), 573-585. https://doi.org/10.1006/jsvi.1996.0378. 
  4. Chawis, T., Somchai, C. and Li, T. (2013), "Nonlocal theory for free vibration of single-walled carbon nanotubes", Adv. Mater. Res., 747, 257-260. https://doi.org/10.1093/jom/ufab028. 
  5. De Heer, W.A., Chatelain, A. and Ugarte, D. (1995), "A carbon nanotube field-emission electron source", Sci., 270(5239), 1179-1180. https://doi.org/10.1126/science.270.5239.1179. 
  6. Demir, C ., Civalek, O . and Akgoz, B. (2010), "Free vibration analysis of carbon nanotubes based on shear deformable beam theory by discrete singular convolution technique", Math. Comput. Appl., 15(1), 57-65. https://doi.org/10.3390/mca15010057. 
  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), 39-49. https://doi.org/10.12989/anr.2019.7.1.039. 
  8. 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. https://doi.org/10.1016/j.apm.2012.03.032. 
  9. Flugge, W. (1960), Stresses in Shells, Springer, Berlin, Germany.
  10. Faroughi, S. and Shaat, M. (2018), "Poisson's ratio effects on the mechanics of auxetic nanobeams", Eur. J. Mech. A/Solids, 70, 8-14. https://doi.org/10.1016/j.euromechsol.2018.01.011. 
  11. Fauzi, M.A., Arshad1a, M.F., Nor, N.M. and Ghazali, E. (2022), "Sustainable controlled low-strength material: Plastic properties and strength optimization", Comput. Concrete, 30(6), 393-407. https://doi.org/10.12989/cac.2022.30.6.393. 
  12. Ghavanloo, E. and Fazelzadeh, S.A. (2012), "Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect", Appl. Math. Model., 36(10), 4988-5000. https://doi.org/10.1016/j.apm.2011.12.036. 
  13. He, X.Q., Eisenberger, M. and Liew, K.M. (2006), "The effect of van der Waals interaction modeling on the vibration characteristics of multi-walled carbon nanotubes", J. Appl. Phys., 100(12), 124317. https://doi.org/10.1063/1.2399331. 
  14. Hu, Z.L., Guo, X.M. and Ru, C.Q. (2008), "Enhanced critical pressure for buckling of carbon nanotubes due to an inserted linear carbon chain", Nanotechnol., 19(30), 305703. https://doi.org/10.1088/0957-4484/19/30/305703. 
  15. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(7), 56-58. https://doi.org/10.1038/354056a0. 
  16. Kepenek, E., Korkmaz K.A. and Gencel, Z. (2023), "Comparative study on rapid seismic risk prioritization for reinforced concrete buildings in Antalya, Turkiye", Comput. Concrete, 31(3), 185-195. https://doi.org/10.12989/cac.2023.31.3.185. 
  17. Kuzuo, R., Terauchi, M.T.M. and Tanaka, M.T.M. (1992), "Electron energy-loss spectra of carbon nanotubes", Japan. J. Appl. Phys., 31(10B), L1484. https://doi.org/10.1143/JJAP.31.L1484. 
  18. Kwon, Y.K. and Tomanek, D. (1998), "Electronic and structural properties of multiwall carbon nanotubes" Phys. Rev. B, 58, 16001-16004. https://doi.org/10.1021/jp993592k. 
  19. Lal, A. and Markad, K. (2018), "Deflection and stress behaviour of multi-walled carbon nanotube reinforced laminated composite beams", Comput. Concrete, 22(6), 501-514. https://doi.org/10.12989/cac.2018.22.6.501. 
  20. Leissa, A.W. (1993), Vibration of Shells, Acoustical Society of America, Columbus, OH, USA. 
  21. Leung, A.Y.T. and Kuang, J.L. (2005), "Nanomechanics of a multi-walled carbon nanotube via Flugge's theory of a composite cylindrical lattice shell", Phys. Rev. B, 71(16), 165415. https://doi.org/10.1103/PhysRevB.71.165415. 
  22. Liang, X., Hu, S. and Shen, S. (2014), "A new Bernoulli-Euler beam model based on a simplified strain gradient elasticity theory and its applications", Compos. Struct., 111, 317-323. https://doi.org/10.1016/j.compstruct.2014.01.019. 
  23. Liew, K.M. and Wang, Q. (2007), "Analysis of wave propagation in carbon nanotubes via elastic shell theories", Int. J. Eng. Sci., 45(2-8), 227-241. https://doi.org/10.1016/j.ijengsci.2007.04.001. 
  24. Majeed, S.S., Haido, J.H., Atrushi, D.S., Al-Kamaki, Y., Dinkha, Y.Z., Saadullah, S.T. and Tayeh, B.A. (2021), "Properties of self-compacted concrete incorporating basalt fibers: Experimental study and gene expression programming (GEP) analysis", Comput. Concrete, 28(5), 451-463. https://doi.org/10.12989/cac.2021.28.5.451. 
  25. Mousavi, M., Mohammadimehr, M. and Rostami, R. (2019), "Analytical solution for buckling analysis of micro sandwich hollow circular plate", Comput. Concrete, 24(3), 185-192. https://doi.org/10.12989/cac.2019.24.3.185. 
  26. 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/10.1016/j.physleta.2010.08.080. 
  27. Rabczuk, T., Areias, P.M.A. and Belytschko, T. (2007), "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Method. Eng., 72(5), 524-548. https://doi.org/10.1002/nme.2013. 
  28. Rao, A.M., Richter, E., Bandow, S., Chase, B., Eklund, P.C., Williams, K.A. and Dresselhaus, M.S. (1997), "Diameter-selective Raman scattering from vibrational modes in carbon nanotubes", Sci., 275(5297), 187-191. https://doi.org/10.1126/science.275.5297.187. 
  29. Selim, M.M., Althobaiti, S., Yahia, I.S., Mohammed, I.M., Hussin, A.M. and Mohamed, A.B.A. (2022), "Impacts of surface irregularity on vibration analysis of single-walled carbon nanotubes based on Donnell thin shell theory", Adv. Nano Res., 12(5), 483-488. https://doi.org/10.12989/anr.2022.12.5.483. 
  30. Stephan, O., Ajayan, P.M., Colliex, C., Redlich, P., Lambert, J.M., Bernier, P. and Lefin, P. (1994), "Doping graphitic and carbon nanotube structures with boron and nitrogen", Sci., 266(5191), 1683-1685. https://doi.org/10.1126/science.266.5191.1683. 
  31. Su, Y.C. and Cho, T.Y. (2021), "Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model", J. Mech., 37, 616-635. https://doi.org/10.1093/jom/ufab028. 
  32. Sun, C.Q. and Liu, K.X. (2009), "Vibration of multi-walled carbon nanotubes with initial axial force and radial pressure", J. Phys. D: Appl. Phys., 42(17), 175412. https://doi.org/10.1088/0022-3727/42/17/175412. 
  33. Torkaman-Asadi, M.A., Rahmanian, M. and Firouz-Abadi, R.D. (2015), "Free vibrations and stability of high-speed rotating carbon nanotubes partially resting on Winkler foundations", Compos. Struct., 126, 52-61. https://doi.org/10.1016/j.compstruct.2015.02.037. 
  34. Tsang, S.C., Harris, P.J.F. and Green, M.L.H. (1993), "Thinning and opening of carbon nanotubes by oxidation using carbon dioxide", Nature, 362(6420), 520-522. https://doi.org/10.1038/362520a0. 
  35. Vieira, A.A., Melo, G.S.S. and Miranda, A.C. (2020), "RC deep beams with unconventional geometries: Experimental and numerical analyses", Comput. Concrete, 26(4), 351-365. https://doi.org/10.12989/cac.2020.26.4.351. 
  36. Yang, J., Ke, L.L. and Kitipornchai, S. (2010), "Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", Phys. E: Low-Dimens. Syst. Nanostruct., 42(5), 1727-1735. https://doi.org/10.1016/j.physe.2010.01.035. 
  37. Zamani, A., Kolahchi, R. and Bidgoli, M.R. (2017), "Seismic response of smart nanocomposite cylindrical shell conveying fluid flow using HDQ-Newmark methods", Comput. Concrete, 20(6), 671-682. https://doi.org/10.12989/cac.2017.20.6.671. 
  38. Strozzi, M., Smirnov, V.V., Pellicano, F. and Kovaleva, M. (2022), "Nonlocal anisotropic elastic shell model for vibrations of double-walled carbon nanotubes under nonlinear van der Waals interaction forces", Int. J. Non-Linear Mech., 146, 104172. https://doi.org/10.1016/j.ijnonlinmec.2022.104172. 
  39. Strozzi, M., Elishakoff, I.E., Bochicchio, M., Cocconcelli, M., Rubini, R. and Radi, E. (2023), "A comparison of shell theories for vibration analysis of single-walled carbon nanotubes based on an anisotropic elastic shell model", Nanomater., 13(8), 1390. https://doi.org/10.3390/nano13081390.