Vibration analysis of carbon nanotubes based on cylindrical shell by inducting Winkler and Pasternak foundations

References

• M. R. Falvo et al., “Bending and buckling of carbon nanotubes under large strain”, Nature., vol. 389, pp. 582–584, 1997.
   PubMed Web of Science ®Google Scholar
• C. Y. Li and T. A. Chou, “A structural mechanics approach for the analysis of carbon nanotubes”, Int. J. Solids Struct., vol. 40, pp. 2487–2499, 2003.
   Web of Science ®Google Scholar
• B. I. Yakobson, C. J. Brabee, and J. Bernhole, “Vibrational analysis of single-walled carbon nanotubes using beam element”, Phys. Rev. Lett., vol. 76, pp. 2511–2514, 1996.
   PubMed Web of Science ®Google Scholar
• T. Vodenitcharova and L. C. Zhang, “Resonance frequency of chiral carbon nanotubes using Timoshenko beam theory”, Phys. Rev. B., vol. 68, pp. 165401, 2003.
   Web of Science ®Google Scholar
• J. C. Hsu, R. P. Chang, and W. J. Chang, “Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory”, Phys. Lett A., vol. 372, pp. 2757–2759, 2008.
   Web of Science ®Google Scholar
• J. Bocko and P. Lengvarsky, “Nonlocal elasticity theory for free vibration of single walled carbon nanotubes”, Amer. J. Mech. Eng., vol. 2, pp. 195–198, 2014.
   Google Scholar
• T. Chawis, C. Somchai, and T. Li, “Young's modulus of single-walled carbon nanotubes”, Adv. Mate. Res., vol. 747, pp. 257–260, 2013.
   Google Scholar
• J. Yang, L. L. Ke, and S. Kitipornchai, “Vibration of carbon nanotube by using non local theory”, Phys. E: low-dimensional Syst. Nano Struct., vol. 42, pp. 1727–1735, 2010.
   Web of Science ®Google Scholar
• C. M. Wang, Y. Q. Ma, Y. Y. Zhang, and K. K. Ang, “Electromechanical sensors based on carbon nanotubes”, J. Appl. Phys., vol. 99, pp. 114317, 2006.
   Google Scholar
• R. Ansari, H. Rouhi, and S. Sahmani, “Calibration of the analytical nonlocal shell modelled for vibration of double walled carbon nanotube using arbitrary boundary conditions using molecular dynamics”, Int. J. Mech. Sci., vol. 53, pp. 786–792, 2011.
   Web of Science ®Google Scholar
• S. H. Arshad, M. N. Naeem, N. Sultana, A. G. Shah, and Z. Iqbal, “Vibration analysis of bi-layered FGM cylindrical shells”, Arch. Appl. Mech., vol. 81, pp. 319–343, 2011.
   Web of Science ®Google Scholar
• He. Saito and H. Yamaguchi, “Vibration damping characteristics of a thin cylindrical shell stiffened with viscoelastic rings”, Arch. Appl. Mech., vol. 48.5, pp. 301–311, 1979.
   Google Scholar
• J. H. Kang, “Vibration analysis of a circular cylinder closed with a hemi-spheroidal cap having a hole”, Arch. Appl. Mech., vol. 87, pp. 183–199, 2017.
   Web of Science ®Google Scholar
• S. Sun, D. Cao, and S. Chu, “Free vibration analysis of thin rotating cylindrical shells using wave propagation approach”, Arch. Appl. Mech., pp. 1–11, 2013.
   Web of Science ®Google Scholar
• M. Hassan, A. Zeeshan, A. Majeed, and R. Ellahi, “Particle shape effects on ferrofuids flow and heat transfer under influence of low oscillating magnetic field”, J. Mag. Magn. Mater., vol. 443, pp. 36–44, 2017.
   Web of Science ®Google Scholar
• J. A. Esfahani, M. Akbarzadeh, S. Rashidi, M. A. Rosen, and R. Ellahi, “Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat”, Int. J. Heat and Mass Transfer., vol. 109, pp. 1162–1171, 2017.
   Web of Science ®Google Scholar
• S. Rashidi, S. Akar, M. Bovand, and R. Ellahi, “Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still”, Renew. Ener., vol. 115, pp. 400–410. 2018.
   Web of Science ®Google Scholar
• K. M. Shirvan, M. Mamourian, S. Mirzakhanlari, and R. Ellahi, “Numerical investigation of heat exchanger effectiveness in a double pipe heat exchanger filled with nanofluid: A sensitivity analysis by response surface methodology”, Powd. Tech., vol. 313, pp. 99–111, 2017.
   Web of Science ®Google Scholar
• A. E. H. Love, “The small free vibrations and deformation of a thin elastic shell”, Philo. Trans. Royal Soci. London A., vol. 179, pp. 491–546, 1888.
   Google Scholar
• P. B. Goncalves, F. Silva, and Z. J. del Prado, “Transient stability of empty and fluid-filled cylindrical shells”, J. Braz. Soc. Mech. Sci. Eng., vol. 28, pp. 331–338, 2006.
   Google Scholar
• S. S. Gupta, F. G. Bosco and R. C. Batra, “Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration”, Comput. Mater. Sci., vol. 47, pp. 1049–1059, 2010.
   Web of Science ®Google Scholar